ohlson

Prévia do material em texto

Earnings, Book Values, and Dividends in Equity 
Valuation: An Empirical Perspective*
JAMES A. OHLSON, New York University
Abstract
This paper revisits Ohlson 1995 to make a number of points not generally appreciated in the
literature. First, the residual income valuation (RIV) model does not serve as a crucial cen-
terpiece in the analysis. Instead, RIV plays the role of condensing and streamlining the anal-
ysis, but without any effect on the substantive empirical conclusions. Second, the concept of
“other information” in the model can be given concrete empirical content if one presumes that
next-period expected earnings are observable.
Keywords Accounting data; Equity valuation; Expected earnings; Residual income valuation
Condensé
Dans une récente publication, Dechow, Hutton et Sloan (1998) (DHS ci-après) analysent
une évaluation empirique du modèle de la valeur et des données comptables, proposé par
Ohlson en 1995 (« Earnings, Book Values, and Dividends in Equity Valuation », EBD ci-
après). L’étude de DHS fournit, selon ses auteurs, « une évaluation empirique du modèle
d’évaluation du résultat résiduel (ou anormal) proposé par Ohlson [1995] ». Comparative-
ment aux autres études empiriques se rapportant aux analyses de Ohlson et de Feltham et
Ohlson (1995), celle de DHS a pour but de lier de manière beaucoup plus étroite les évalua-
tions empiriques aux attributs du modèle EBD. Les équations liées au modèle EBD n’ont pas
pour seul résultat de légitimer sommairement l’étude de DHS : elles portent sur le comporte-
ment autorégressif du résultat net résiduel et permettent d’estimer le paramètre connexe de
« régularité » (ou sa dépendance sériale, dénotée ω). DHS évaluent ensuite la mesure dans
laquelle les estimations du paramètre de régularité contribuent à expliquer les valeurs à la
cote et les rendements. Cette méthode semble logique, du fait que le résultat résiduel et le
résultat résiduel imprévu, en conjonction avec le paramètre de régularité, se rattachent
directement à la valeur et aux rendements dans le modèle EBD. DHS comparent également
les résultats empiriques basés sur le modèle EBD à certains éléments de référence populaires
comme les modèles d’évaluation basés sur les prévisions de bénéfices des analystes.
Répliquant à l’étude de DHS, l’auteur s’intéresse à deux questions étroitement liées :
Premièrement, pourquoi le modèle EBD est-il axé sur le résultat net résiduel ? Deuxièmement,
quelles hypothèses empiriques peut-on inférer à partir du modèle EBD ? La première question
nécessite une analyse du rôle du modèle d’évaluation du résultat net résiduel (residual
income valuation model ou RIV-model). Maints auteurs ont traité de ce modèle d’évaluation
Contemporary Accounting Research Vol. 18 No. 1 (Spring 2001) pp. 107–20 © CAAA
* Accepted by Jerry Feltham. This paper was presented at the 1999 Contemporary Accounting
Research Conference, generously supported by the CGA-Canada Research Foundation, CMA
Canada, the Canadian Institute of Chartered Accountants, Certified General Accountants of
British Columbia, and the Institute of Chartered Accountants of British Columbia. The
author thanks P. Easton, S. Penman, and X. J. Zhang for valuable discussions.
 
108 Contemporary Accounting Research
 
(notamment Preinreich, 1938, et Peasnell, 1981, 1982). Comme Bernard (1995) et d’autres,
DHS attachent une importance considérable à l’évaluation du résultat net résiduel dans le
contexte du modèle EBD. Pour ce qui est de la seconde question, DHS devaient aborder le
sujet de ce qu’EBD appellent l’« autre information ». EBD conceptualisent cette informa-
tion au moyen d’une variable scalaire, mais sans en concrétiser le contenu empirique. La
variable n’étant pas spécifiée, DHS considèrent cet aspect du modèle EBD comme une
limite très importante du point de vue empirique. Ils choisissent de supprimer la variable du
modèle. Le procédé de DHS paraît radical et nous amène à nous demander si le modèle
EBD, dans sa forme générale, offre un contenu empirique tant soit peu substantiel.
1. Introduction
A recent paper by Dechow, Hutton, and Sloan (1998) (DHS henceforth) considers
an empirical evaluation of Ohlson’s 1995 model of value and accounting data
(“Earnings, book values, and dividends in equity valuation”; EBD henceforth).
DHS view their work as providing “an empirical assessment of the residual income
valuation model proposed in Ohlson [1995]” (abstract, first sentence). Compared
with other empirical studies referring to Ohlson’s, and Feltham and Ohlson’s 1995,
analyses, the DHS paper tries to link empirical evaluations much closer to the EBD
model’s attributes.1 Equations related to the EBD model do more than broadly jus-
tify the DHS study: they focus on the auto-regressive behavior of residual income
and estimate the related “persistence” parameter (or its serial dependence, denoted
by ω). DHS then evaluate the extent to which estimates of the persistence parameter
help to explain market values and returns. This approach seemingly makes sense in
that residual income and unexpected residual income, in combination with the per-
sistence parameter, relate directly to value and returns in the EBD model. DHS
also contrast the empirical results predicated on the EBD model to some popular
benchmarks, such as valuation models based on analysts’ forecasts of earnings.
Motivated by the DHS study, this paper addresses two closely related ques-
tions. First, why does the EBD model focus on residual income? Second, what
empirical hypotheses can one infer from the EBD model? The first question
necessitates an analysis of the role of the residual income valuation model (RIV-
model). Numerous authors have discussed this valuation formula (in particular,
Preinreich 1938; and Peasnell 1981, 1982). Like Bernard 1995 and others, DHS
affix considerable significance to RIV within the EBD-model context.2 Concerning
the second question, the DHS study must deal with what EBD refers to as “other
information”. EBD conceptualizes such information by a scalar variable, but without
making its empirical content concrete. Because the variable is unspecified, DHS
view this aspect of the EBD model as a major limitation from an empirical perspec-
tive.3 They proceed by eliminating the variable from the model. DHS’s scheme
seems drastic, and it challenges whether the EBD model in its general form has any
meaningful empirical content.
2. The RIV model and the EBD model
Some notation will be necessary; we use the same as in DHS (which differs only
marginally from EBD).
CAR Vol. 18 No. 1 (Spring 2001)
 
Earnings, Book Values, and Dividends in Equity Valuation 109
 
Pt = Market value (or price) of equity at date t.
dt = Net dividends at date t.
r = R − 1 discount factor.
Et [.] = The expectation operator conditional on the date t information.
bt = Book value at date t.
xt = Earnings (net income) for the period (t − 1, t).
To introduce the RIV model, assume the following:
PRESENT VALUE OF EXPECTED DIVIDENDS ASSUMPTION (PVED).
Pt = Et
CLEAN SURPLUS RELATION ASSUMPTION (CSR).
bt − 1 = bt + dt − xt
As is well-known, PVED and CSR imply the RIV model:
Pt = bt + Et ,
where ≡ xt − rbt − 1 defines residual (or abnormal) income (earnings). In fact,
one can make the slightly stronger statement that, given the clean surplus relation
CSR, PVED implies RIV, and conversely. This equivalence has been much noted
in recent literature, including DHS.
Having established RIV, it appears reasonable that one next imposes a time-series
stochastic process related to residual income in lieu of dividends. The particularly sim-
ple first-order auto-regressive (AR(1)) process suggests itself. Suppose that
= + (1),
in which case
Pt = bt + (2).
The derivation that yields (2), given RIV and (1), is of course elementary.
R τ–
τ 1=
∞
∑ d̃ t τ+( )
R τ–
τ 1=
∞
∑ x̃ t τ+
a( )
x ta
x̃ t 1+
a ωx t
a ε̃ t 1+
ω
R ω–
------------- x t
a
CAR Vol. 18 No. 1 (Spring 2001)
 
110 Contemporary Accounting Research
 
The EBD model adds no significant analytical complications. It extends the
simple AR(1) dynamic by introducing information other than current residual
income. Such information influences forecasts of subsequent residual incomes. A
scalar variable ν t represents “other information”, and two stochastic dynamic
equations specify the evolution of ( , ν t):
ASSUMPTION 1.
= + νt + 
 = γνt + [A1],
where the disturbance terms are zero-mean unpredictable but otherwise unre-
stricted.4 The dynamic equations have two parameters, ω and γ (known by the
market, but unknown to researchers). Combining Assumption 1 with RIV results in
Pt = bt + + (3),
where
α1 = ω/(R − ω), and
α 2 = R/[(R − ω)(R − γ)].
The model PVED, CSR, and Assumption 1 also explains returns:
/Pt − 1 = R + (1 + α1) /Pt − 1 + /Pt − 1 (4).
The above developments appeal because the ingredients/steps are few and
straightforward. In spite of this simplicity, the model leads to expressions relating
value and returns to accounting data. The accounting data focus on book values
and residual incomes. But one can also express Pt as a function of (xt, bt, dt )
instead of ( , bt ) by invoking the CSR (note that [ = xt − r (bt + dt − xt )]).
More important here, the presence of “other information” makes conceptual sense
since it reduces the model’s rigidity. To suggest that current residual income can
substantially explain goodwill — as is implied by (1) and (2) — seems far too strong.
Appealing as the assumptions/derivations might be, thinking about the model
requires care. Close examination of the model will reveal a number of subtleties.
Of particular concern is the apparent prominence of the RIV model and residual
income. To what extent are these two features central?
As a first point, one needs to keep in mind that RIV concerns future residual
incomes, whereas Assumption 1 assigns a concrete role for current residual income
as relevant information when the future is visualized. A priori, there is no apparent
reason why one of these aspects of residual income should require the other.
x t
a
x̃ t 1+
a ωx t
a ε̃ 1t 1+
ṽ t 1+ ε̃ 2t 1+
α1x
t
a α 2νt
P̃t( d̃t )+ ε̃ 1t α 2ε̃ 2t
x t
a x t
a
CAR Vol. 18 No. 1 (Spring 2001)
Earnings, Book Values, and Dividends in Equity Valuation 111
As a second point, RIV enters the analysis primarily because it condenses and
streamlines the mathematics. While this aspect of RIV is obviously useful, it also
means that RIV should not be thought of as the formula necessary to derive con-
clusions bearing on values and returns. After all, a model’s implications are inher-
ent in the underlying assumptions, and thus the absence of RIV in the analysis will
not change the EBD model’s empirical content. As outlined below, one can derive
(3) (and (4)) without relying on RIV.
One can even argue that the use of RIV in the analysis has an unfortunate side
effect of obscuring interesting implications of PVED, CSR, and Assumption 1. To
develop this argument, suppose that we had no knowledge of the RIV model but
nevertheless wanted to derive Pt as a function of accounting data and “other informa-
tion”. The absence of RIV would naturally take us back to a direct PVED evaluation,
which in turn demands forecasting the sequence of expected dividends. A third
stochastic equation handles this problem.
Consider the linear equation
= β1xt + β 2bt + β3dt + β4νt + ,
where β1, β 2, β3, and β4 are fixed constants reflecting a dividend policy.5 Combin-
ing this equation with CSR and Assumption 1 allows for a derivation of the elements
in the sequence Et , Et , … as functions of the current values of xt, bt,
dt , and νt . One can then move one step further and evaluate PVED explicitly.
Though a tedious exercise, such analysis will show that the valuation solution (3)
does indeed hold regardless of the “policy” parameters (β1, β 2, β3, β4). Dividend
policy irrelevancy therefore applies, a feature of the model that is less than appar-
ent if one combines RIV with the dynamic equation Assumption 1.6 In sum, it is
worthwhile to keep in mind that although RIV usefully integrates with PVED,
CSR, and Assumption 1, key implications of the model do not substantially depend
on the RIV framework.
As a third point, the tight flow of ideas — PVED, CSR yielding RIV, then add-
ing Assumption 1 yielding (3) and (4) — misses an important issue altogether.
Mathematical simplicity aside, how can one make sense of Assumption 1? To
introduce Assumption 1 subsequent to RIV conveys the distinct impression that
Assumption 1 has been “picked” because it blends conveniently with RIV. In other
words, the RIV model originates residual income, and the related dynamic retains
the variable to ensure a straightforward, closed form, valuation solution. (As noted,
in mathematical terms it is a minor matter to replace the auto-regressive equation 1
with Assumption 1.) One can argue that this way of thinking about accounting data
and value is too mechanistic. Some conceptual justification for the assumed
dynamic would seem necessary before one proceeds to assess empirically equa-
tions like (3) and (4).
EBD addresses the question of making sense of Assumption 1. Rather than
assuming Assumption 1 outright, one can deduce Assumption 1 from properties
associated with accounting measurements. These go beyond CSR, yet they seem
d̃ t 1+ ε̃ 3t 1+
d̃ t 1+( ) d̃ t 2+( )
CAR Vol. 18 No. 1 (Spring 2001)
112 Contemporary Accounting Research
no less reasonable (see below). Thus one motivates Assumption 1 on the basis of
accounting concepts rather than analytical advantage.
Consider the following general dynamic equation:
 = θ1xt + θ2bt + θ3dt + νt + (5).
This equation is isomorphic to Assumption 1 if and only if one restricts θ1, θ2, and
θ3, to satisfy θ1 = ωR, θ2 = (1 − ω)r, and θ3 = −ωr. What accounting concepts
suggest that these restrictions should be met? EBD shows that if we (i) expand on
CSR to include ∂xt /∂dt = 0, ∂bt /∂dt = −1 and assume (ii) ∂Et /
∂dt = −(R2 − 1), and (iii) ∂νt /∂dt = 0, then (5) reduces to the special case Assump-
tion 1.7 The three conditions make accounting sense: (i) requires that “dividends
reduce current book value but not current earnings”, (ii) requires that current dividends
reduce future expected earnings with a marginal effect of R2 − 1 for two periods,
and (iii) requires the evolution of “other information” to be dividend-independent.8
This result is viewed as fundamental in EBD because, in a subtle and consis-
tent fashion, it integrates owners’ equity accounting with dividend policy irrelevancy
concepts to yield insights about how expected next-period earnings can reasonably
depend on current accounting data and other information. Residual income and the
dynamic Assumption 1 are thereby cast in a different light. With Assumption 1 in
place, due to restrictions on the accounting combined with dividend policy irrele-
vancy, RIV serves a limited, albeit useful, role in facilitating the evaluation of
PVED. But one cannot say that RIV is central. Instead, the focus is on the valuation
implication of Assumption 1 combined with PVED and CSR; these have economic
appeal that goes beyond simplicity in derivations via the RIV model.
3. “Other information” and its empirical implications
We now turn our attention to the model’s empirical implications. To discern these
requires one to identify a role for the perhaps somewhat mysterious scalar variable
νt. Equating νt to zero may be of analytical interest, but it severely reduces the
model’s empirical content. How can one think of νt without reducing the dynamic
Assumption 1 to the simple AR(1) model?
The dynamic Assumption 1 is no more than a statistical model of residual
income. It tells us nothing about the “raw input” that ν t would reflect, and the vari-
able cannot be observed directly. In this regard ν t differs from residualincome,
since the latter poses no observability problems given r. However, although ν t is
not directly observable, one can infer ν t from its influence on expectations.9 This
unobtrusive concept, combined with the simplicity of Assumption 1, will be devel-
oped in detail next.10
Before proceeding, one “fact” must be agreed on: expected earnings are no
less observable than are realizations of accounting data. In a strict sense this claim
is, of course, questionable, since (real world) individuals almost always have
diverse opinions about the future. Nevertheless, to assess the EBD model empir-
ically, analysts’ consensus forecasts of next-year earnings would seem to be a
x̃ t 1+ ε̃ 1t 1+
x̃[ t 2+ x̃ t 1+ rd̃t 1+ ]+ +
CAR Vol. 18 No. 1 (Spring 2001)
Earnings, Book Values, and Dividends in Equity Valuation 113
reasonable measure of expected earnings. The approach maintains the model’s
“objective expectations” spirit.
To distinguish between the observability date and the accounting period’s end
date, we use the notation
≡ Et
for expected earnings. The subscript therefore indicates the observability date, just
like realized earnings, x t. The superscript indicates the accounting period’s end
date; the lack of a superscript means it is the same as the subscript — that is,
xt ≡ . Similarly, write
≡ Et = − rbt
for expected residual income. Given that is date t observable, so is .
For purposes of the current discussion, assume that ω and γ are known. One
can now identify νt as a date t observable variable:
νt = − (6).
In words, νt equals next period’s expected residual income adjusted for . In
this context one can think of as the first-cut estimate of next period’s expected
residual income; thus νt captures “other information” relevant to forecasting the
future.
Substituting (6) into (3) and simplifying, one obtains Pt as a linear function of
the three date t observable accounting variables (bt, , ):
Pt = bt + (α1 − ωα2) + α 2 (7).
As before, α1 = ω/(R − ω) and α 2 = R/(R − ω)(R − γ).
The model restricts the Pt function since there are three variables on the right-
hand side, but the only parameters that can vary are ω and γ.
Simple manipulations will express Pt as a function of bt , xt , dt , and . The
“content” of this equation is, of course, the same as (7) given CSR. We will focus
on (7) because it is slightly easier to deal with. Apendix 1 provides the alternative
version of (7).
Initial empirical implications of (7) can be assessed by examining the two
coefficients associated with and . With respect to the latter coefficient,
α 2 is always positive. The former coefficient, however, equals α1 − ωα2 = −ωγ/
(R − ω )(R − γ ), so the sign of the coefficient is the opposite of the sign of ωγ.
Hence, the effect of current residual income on value, given current book value and
x t
t 1+
x̃ t 1+( )
x t
t
x t
at 1+
x̃ t 1+
a( ) x t
t 1+
x t
t 1+
x t
at 1+
x t
at 1+ ωx t
a
ωx t
a
ωx t
a
x t
a x t
at 1+
x t
a x t
at 1+
x t
t 1+
x t
a x t
at 1+
CAR Vol. 18 No. 1 (Spring 2001)
114 Contemporary Accounting Research
expected residual income, is always nonpositive if one imposes the a priori plausi-
ble condition (ω, γ ) ≥ 0. A strictly negative coefficient is conceptually sensible:
given bt and , value increases to the extent that residual income is also
expected to improve for period t + 1 as compared with t.
Empirical implications of the parameters (ω, γ ) are put into sharper light if one
considers the no expected change condition = . In this case
Pt = bt + = k[(R/r)xt − dt] + (1 − k)bt,
where λ = (R − ωγ)/(R − ω)(R − γ) and k = λ r. The last expression shows value as
a weighted average of capitalized earnings (adjusted for dividends) and book
value. One can further demonstrate that
1 − k = (1 + ωγ − ω − γ)R/(R − ω)(R − γ).
If one hypothesizes that book value is a relevant, albeit limited, positive indicator
of a firm’s value when there is no expected short-term change in residual income,
then 1 − k should be a relatively small positive number (say 0.1). Thus, 1 + ωγ
should be somewhat larger than ω + γ. This requirement suggests that ω + γ should
approximate 1, with either ω or γ being (relatively) close to zero so that ωγ is also
close to zero (but not necessarily empirically immaterial).
Consider next the instructive boundary cases (ω, γ ) = (1, 0) or (0, 1). Without
restricting how relates to , one obtains
Pt = /r,
since bt + /r = /r. Put simply, capitalized expected earnings alone
determine value. The condition (ω, γ ) = (0, 1) or (1, 0) is necessary as well as suffi-
cient for this result.
One sees that the EBD model subsumes one of the most basic hypotheses in
equity valuation. With this perspective, the issue arises whether the models (ω, γ ) =
(1, 0) or (0, 1) can be rejected empirically when compared with (i) a model of
value that satisfies (7) but with the looser restriction ω + γ = 1; (ii) a model of value
that satisfies (7) but does not restrict (ω, γ ) at all; and (iii) a model of value that
depends on bt, , , but deviates from the EBD model by having (three)
unrestricted coefficients.11
The inquisitive reader may have noted that (7) can be rejected empirically a
priori since it prescribes a perfect R2. This objection seems overly harsh, since no
nonvacuous model of value and accounting data combined with consensus expec-
tations can ever provide a perfect fit. More importantly, one can in fact extend
Assumption 1 so that (7) generalizes to permit an error term that does not correlate
with the included accounting variables. Appendix 2 develops this model and dis-
cusses some related issues.
x t
at 1+
x t
a x t
at 1+
λx t
a
x t
a x t
at 1+
x t
t 1+
x t
at 1+ x t
t 1+
x t
a x t
at 1+
CAR Vol. 18 No. 1 (Spring 2001)
Earnings, Book Values, and Dividends in Equity Valuation 115
As a complement (or alternative) to fitting data in a value framework (7), one
can consider implications of a return model — that is, (4). Realizations of ε1t and
ε 2t explain the market return, and both of these “independent” variables are
observable.12 For the return period (t − 1, t),
ε1t = − = xt − .
Hence, one identifies ε1t as the traditional “unexpected earnings” variable. Con-
cerning ε 2t , note that ε 2t = νt − γνt − 1 and, since νt = − , one obtains13
ε1t = − ( + − ).
In this expression the key variable is , which represents the expected resid-
ual income for the period subsequent to the current market return interval with end
date t. Realizations of convey “good” or “bad” news depending on, (i)
what is already inherent in contemporaneously realized residual income, and (ii)
the start-of-period variables, and .
To get a better feel for the model, consider again what happens if (ω, γ ) = (1, 0)
or (0, 1). The case (ω, γ ) = (1, 0) implies ε 2t = − , whereas (ω, γ ) = (0, 1)
implies ε 2t = − . Both of these constructs would seem to provide rea-
sonable reference points for “good” and “bad” news when analysts produce forecasts
beyond the current return period.14 The less restrictive condition ω + γ = 1 entails a
convexification plus an adjustment for an interactive term as specified by .
So far the discussion has presumed the parameters ω and γ to be known.
Empirical research with a close focus on the EBD model must, of course, try to
estimate/evaluate these two parameters. It is beyond the scope of this paper to con-
sider how this can or ought to be done. Here we only point out that the modeling
and previous expressions supply a number of reasonable starting points. For exam-
ple, one can concentrate on values (expression (7)) or, alternatively, on returns
(expression (4)) as dependent variables. But there is no requirement to introduce
market-value data to get an initial sense of (ω, γ ). Specifically, given any ω one can
estimate a related γ, since − satisfies a simple auto-regressive process
with parameter γ. In yet another approach, one can try to evaluate how 
relates empirically to , , and and thereby estimate ω and γ.
We conjecturethat empirical data will support the approximation ω + γ = 1,
and with a marginally significant interactive effect ωγ > 0. Be this as it may, one
can thereafter proceed to investigate whether other models of valuation and returns
do a better job of explaining the data than the EBD framework.
4. Concluding remarks
Regardless of the EBD model’s conceptual and empirical merits (or lack thereof),
we reemphasize that it centers on the residual income dynamic. “Does the dynamic
Assumption 1 make sense from an accounting perspective?” is more than an inciden-
x t
a x t 1–
at x t 1–
t
x t
at 1+ ωx t
a
x t
at 1+ ωx t
a γx t 1–
at ωγx t 1–
a
x t
at 1+
x t
at 1+
x t 1–
at x t 1–
a
x t
at 1+ x t
a
x t
at 1+ x t 1–
at
ωγx t 1–
a
x t
at 1+ ωx t
a
x t
at 1+
x t
a x t 1–
at 1+ x t 1–
a
CAR Vol. 18 No. 1 (Spring 2001)
116 Contemporary Accounting Research
tal question. Having answered the question in the affirmative, it then so happens that
the dynamic permits an easy-to-derive valuation solution via the beneficial observa-
tion that PVED and RIV must yield the same solution. Although RIV comes in
handy, to view it as the model’s centerpiece misleads.
Given the valuation solution, one can proceed to explicate how earnings, book
value, dividends, and next-period expected (residual) income explain returns as
well as value. The EBD model thus yields specific empirical hypotheses. There are
two degrees of freedom, which allow for versatility, but the model does indeed
restrict how the world can work. Further, the model becomes patently simplistic
without “other information”. But no apparent reasons suggest that one must elimi-
nate “other information” from the model, as long as one grants the observability of
expected earnings.15
Empirical research that focuses on (intrinsic) value can exploit RIV without
the use of a formal information dynamic. In such case, analysts’ expectations or
statistical extrapolation models provide estimates of anticipated earnings for a few
years. See, for example, Frankel and Lee 1998. This approach leads to the “termi-
nal value” problem, which raises a large number of possibilities. Penman (1997)
discusses these in some detail. He also shows that terminal value models for RIV
generally reconcile with terminal value models in the traditional PVED framework.
Though the details concerning such reconciliations may occasionally surprise, the
fact that PVED and RIV yield identical answers even when there are terminal val-
ues must be expected, since the two formulas are conceptually and structurally
equivalent. (To presume that there is a real “choice” between RIV as opposed to
PVED in research or practice therefore requires careful motivation.)
One can also exploit RIV without any formal information dynamic in research
that focuses on returns rather than values. Liu and Thomas (2000) consider this
possibility. With an infinite horizon it follows that
Pt + 1 + dt + 1 − RPt = [Et + 1 − Et ],
and with a finite horizon one must deal with the usual terminal value issues. Liu
and Thomas assess/estimate the change in expected residual incomes for a number
of years beyond the return year by use of analysts’ expected earnings and analysts’
expectations of growth in earnings. They also model changes in expected terminal
values. Hence Liu and Thomas avoid parameterization of the expected residual
earnings dynamic, in sharp contrast to the EBD model.
It appears that the reintroduction of the RIV model into the accounting litera-
ture has been associated with some confusion. On the one hand, the RIV formula
allures since it suggests that earnings and book values can jointly take on prominent
roles in valuation analysis. RIV has therefore led many researchers to underscore that
it can be used to articulate accounting-based equity valuation, with the appealing fea-
ture that it elegantly distinguishes the creation of wealth from the distribution of
R
τ–
τ 0=
∞
∑ x̃ t 1 τ+ +
a( ) x̃ t 1 τ+ +
a( )
CAR Vol. 18 No. 1 (Spring 2001)
Earnings, Book Values, and Dividends in Equity Valuation 117
wealth inherent in PVED. On the other hand, the equivalence of the RIV and
PVED formulas is mathematically trite, and one can reasonably argue that trite
analyses generally lead to trite insights. Both perspectives make some sense, I
believe. Only taste can resolve the rather philosophical question whether analytical
simplicity rules out interesting insights. However, the matter does not end with this
observation. This paper has tried to articulate a more subtle point: if one introduces
assumptions on the accounting in addition to CSR, then RIV can streamline the
analysis and in the process enhance our economic intuition as to how value relates
to accounting data. This role for RIV ought not to be neglected; it reminds us that
any theory of value and accounting data must be conceptualized as a totality rather
than as being pried from a confined subset of its parts.
Appendix 1
Value (Pt ) as a function of xt, bt , dt , and , and some of its special cases
Replacing with − rbt, and with xt − r (bt + dt − xt), one can restate
(7) as
Pt = β1bt + β2(ζ xt − dt) + β3 ( /r),
where ζ ≡ R/r. Further, define ∆ ≡ (R − ω)(R − γ ) and
β1 = R(1 − ω)(1 − γ )/∆,
β2 = −rωγ/∆, and
β3 = Rr/∆.
Note that β1 + β2 + β3 = 1. This makes economic sense: given ∂xt /∂dt = 0, ∂ bt /∂dt
= −1, and Assumption 1, one infers that /∂dt = −r; hence ∂Pt /∂dt = −1 if and
only if the betas sum to 1. The condition ∂Pt /∂dt = −1 reflects the dividend policy
irrelevancy property that a dollar of dividends displaces a dollar of market value.
Special cases of the model are
β1 = 0 iff ω = 1 or γ = 1, and
β2 = 0 iff ω = 0 or γ = 0.
Hence, as noted, β1 = β2 = 0 iff ωγ = 0 and ω + γ = 1.
The coefficient β3 is always positive.
The case ω = γ = 0 reduces to
Pt = R−1 Et [ + ] = R−1( + bt).
x t
t 1+
x t
at 1+ x t
t 1+ x t
a
x t
t 1+
∂xt 1+
t
b̃t 1+ d̃t 1+ x t
t 1+
CAR Vol. 18 No. 1 (Spring 2001)
118 Contemporary Accounting Research
The case ω = γ = 1 reduces to
Pt = dt/r + ( − xt)/r.
Appendix 2
Equation (7) with a disturbance term
One can generalize the EBD model so that (7) includes a disturbance term that
does not correlate with the accounting variables. Replace Assumption 1 with
= + ν t + 
= γ νt + ut + 
= ,
where Covt( , ) = 0, i = 1, 2, all τ ≥ 1. With this assumption it follows
that
Pt = bt + (α1 − ωα2) + α 2 + α 3ε3t,
where α 3 = 1/(R − ω)(R − γ ) and α1 and α 2 are the same as in Assumption 1.
Hence, this model now allows for a disturbance term that does not correlate with
any of the observable variables on the right-hand side.
What happens if ε3t correlates with the included accounting variables? In that
case one has to try to measure ε3t, or the estimates of the valuation coefficients will
be biased. Measuring ε3t poses no problem if is observable (in addition to
). The algebra to show this is tedious but straightforward.
Endnotes
1. It should be noted that subsequent to a draft of the current paper, DHS revised their 
1998 working paper in light of comments made: see DHS 1999.
2. The discussants of the Ohlson 1995 and Feltham and Ohlson 1995 papers — 
Lundholm 1995 and Bernard 1995, respectively — both emphasize the importance of 
RIV. Some writers, like Beaver 1997, almost equate Feltham and Ohlson 1995 to RIV. 
(Feltham and I believe that such a characterization of our work is unfortunate. 
Origination of RIV cannot be attributed to Feltham or Ohlson. The acronym “EBO” 
often used in lieu of RIV therefore seems inappropriate, at least with respect to the 
“O”.)
3. See DHS 1998, page 9.
4. The parameters must satisfy |ω|, |γ|5. It is not necessary that the right-hand side of the equation depend on prior date 
variables. One can replace the date t variables with t + 1 variables (i.e., dt + 1 = δ1 xt + 1 
+ … + δ4 ν t + 1 + ), yet conclusions will remain the same.
6. As discussed in EBD, page 679, this dividend irrelevancy result requires mild 
regularity conditions on the parameters β.
7. The precise statement and proof of the above result is found in EBD, page 678.
8. Another way of looking at the same problem runs as follows. If we want to forecast 
earnings, then we might as well forecast residual income. But why should Et[ ] 
depend only on ( , νt), and not at all on xt, bt, dt given ( , νt)? The three conditions 
on the accounting provide the answer to the question.
9. The concepts developed in this paper to show how one identifies νt in terms of 
observables are completely general. These can therefore also be applied to the Feltham 
and Ohlson 1995 model. Liu and Ohlson (2000) provide all the details to extract 
empirical implications associated with the Feltham and Ohlson 1995 model.
10. Numerous empirical studies have referred to (3) either neglecting νt entirely or 
attempting to explicate information potentially relevant for νt. For example, see 
Collins, Maydew, and Weiss 1997; Guenther and Trombley 1994; and Sougiannis 
1994.
11. In estimating ω and γ from (7), one must keep in mind that only the sum, ω + γ, and the 
product, ωγ, are unique. Pt is symmetric in ω and γ ; if, say = 0.8 and = 0.15 are 
“good” estimates, then so are = 0.15 and = 0.8.
12. Equation (4) allows the two variables on the right-hand side to correlate.
13. There is no requirement that one uses measures of ε1t and ε 2t as independent variables 
in the regression setting (4). Any invertible linear transformation of (1, ε1t , ε 2t) works 
just as well. Keeping this observation in mind, one can show that ε 2t = νt = 0, all t, and 
ω = 0 or 1 implies that (Pt + dt)/Pt − 1 and xt /Pt − 1 correlate perfectly. Easton and Harris 
(1991) motivate their study using this fact. See also Ohlson and Shroff (1992).
14. Ou (1990) is the only empirical study I know of that tries to conceptualize/measure ε 2t 
(in addition to ε1t) in a return model context. Ou does not, however, use analysts’ 
forecasts as input. Instead, she develops measures that work like leading indicators for 
earnings (changes) expected subsequent to the return interval. The measures derive 
from financial ratios.
15. We do not wish to imply that the absence of analysts’ forecasts would require that one 
equate νt to zero. For example, the EBD model restricts how relates (linearly) to 
xt, bt, dt, and Pt . This class of earnings forecasting specifications can be tested and 
evaluated empirically.
References
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NJ: Prentice-Hall.
Bernard, V. 1995. The Feltham-Ohlson framework: Implications for empiricists. 
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Collins, D. W., E. L. Maydew, and I. S. Weiss. 1997. Changes in the value-relevance of 
earnings and book values over the past forty years. Journal of Accounting and 
Economics 24 (1): 39–67.
ε̃3t 1+
x̃ t 1+
a
xt
a xt
a
ω̂ γ̂
ω̂ γ̂
x̃ t 1+
CAR Vol. 18 No. 1 (Spring 2001)
120 Contemporary Accounting Research
Dechow, P., A. P. Hutton, and R. G. Sloan. 1998. An empirical assessment of the residual 
income valuation model. Unpublished paper. [A revised version appears in Journal of 
Accounting and Economics (see reference below).]
———. 1999. An empirical assessment of the residual income valuation model. Journal of 
Accounting and Economics 26 (1–3): 1–34.
Easton, P., and T. Harris. 1991. Earnings as an explanatory variable for returns. Journal of 
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Feltham, G., and J. A. Ohlson. 1995. Valuation and clean surplus accounting for operating 
and financial activities. Contemporary Accounting Research 11 (2): 689–731.
Frankel, R., and C. M. C. Lee. 1998. Accounting valuation, market expectation, and cross-
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Guenther, D. A., and M. A. Trombley. 1994. The “LIFO” reserve and the value of the firm: 
Theory and empirical evidence. Contemporary Accounting Research 10 (2): 433–52.
Liu, J., and J. A. Ohlson. 2000. The Feltham-Ohlson (1995) model: Empirical implications. 
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Liu, J., and J. Thomas. 2000. Stock returns and accounting earnings. Journal of Accounting 
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frequently asked questions. Contemporary Accounting Research 11 (2): 749–61.
Ohlson, J. A. 1995. Earnings, book values, and dividends in equity valuation. Contemporary 
Accounting Research 11 (2): 661–87.
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Ou, J. 1990. The information content of nonearnings accounting numbers as earnings 
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Peasnell, K. V. 1981. On capital budgeting and income measurement. Abacus 17 (1): 52–67.
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CAR Vol. 18 No. 1 (Spring 2001)
	Earnings, Book Values, and Dividends in Equity Valuation: An Empirical Perspective*
	1.� Introduction
	2.� The RIV model and the EBD model
	3.� “Other information” and its empirical implications
	4.� Concluding remarks
	Appendix 1
	Value (Pt) as a function of xt�, bt�, dt�, and, and some of its special cases
	Appendix 2
	Equation (7) with a disturbance term
	Endnotes
	References