equity valuation employing the ideal versus ad hoc terminal value … · 2018. 9. 27. · equity...

Equity Valuation Employing the Ideal versus Ad Hoc Terminal Value Expressions*

LUCIE COURTEAU, Université Laval

JENNIFER L. KAO, University of Alberta

GORDON D. RICHARDSON, University of Waterloo

AbstractRecently, Penman and Sougiannis (1998) and Francis, Olsson, and Oswald (2000) comparedthe bias and accuracy of the discounted cash flow model (DCF) and Edwards-Bell-Ohlsonresidual income model (RIM) in explaining the relation between value estimates andobserved stock prices. Both studies report that, with non–price-based terminal values, RIMoutperforms DCF.

Our first research objective is to explore the question whether, over a five-year valua-tion horizon, DCF and RIM are empirically equivalent when Penman’s (1997) theoretically“ideal” terminal value expressions are employed in each model. Using Value Line terminalstock price forecasts at the horizon to proxy for such values, we find empirical support forthe prediction of equivalence between these valuation models. Thus, the apparent superior-ity of RIM does not hold in a level playing field comparison.

Our second research objective is to demonstrate that, within each class of the DCF andRIM valuation models, the model that employs Value Line forecasted price in the terminalvalue expression generates the lowest prediction errors, compared with models that employnon–price-based terminal values under arbitrary growth assumptions. The results indicate

Contemporary Accounting Research Vol. 18 No. 4 (Winter 2001) pp. 625–61 © CAAA

* Accepted by Jerry Feltham. This paper was presented at the 2000 Contemporary AccountingResearch Conference, generously supported by the CGA-Canada Research Foundation, theCanadian Institute of Chartered Accountants, the Society of Management Accountants ofCanada, the Certified General Accountants of British Columbia, the Certified ManagementAccountants Society of British Columbia, and the Institute of Chartered Accountants ofBritish Columbia. We would like to thank workshop participants at the 2000 American Account-ing Association meetings; 2000 Canadian Academic Accounting Association Conference; 2000Contemporary Accounting Research Conference; 2000 European Accounting Association Confer-ence; HEC, Laval; University of Queensland, University of Technology–Sydney; and Universityof Waterloo for their comments.

Special thanks are extended to Sati Bandyopadhyay, Joy Begley, Brian Bushee, Peter Clark-son, Steve Fortin, Kin Lo, Russell Lundholm (the discussant), Pat O’Brien, Terry O’Keefe, StevePenman, Ranjini Sivakumar, Theodore Sougiannis, Ken Vetzal, and especially Jerry Feltham (theeditor) for their helpful comments and suggestions on earlier versions of the paper; KendrickFiorito and Mort Siegel at Value Line for their advice on the project; Nick Favron for program-ming assistance; and Daniel Roy and Nicole Sirois for their excellent research assistance.

The research is supported by the Social Sciences and Humanities Research Council of Canadaand the Canadian Academic Accounting Association. Jennifer Kao also receives financial supportfrom Canadian Utilities Fellowship for this project. All remaining errors are the authors’ soleresponsibility.

626 Contemporary Accounting Research

that, for both DCF and RIM, price-based valuation models outperform the correspondingnon–price-based models by a wide margin. These results imply that researchers shouldexercise care in interpreting findings from models using ad hoc terminal value expressions.

Keywords Financial information; Residual income model; Terminal values; Valuation

CondenséPenman et Sougiannis (1998, ci-après P&S) comparaient récemment la distorsion et laprécision du modèle d’actualisation des flux de trésorerie (DCF) et du modèle des bénéficesrésiduels d’Edwards, Bell et Ohlson (RIM) dans l’explication de la relation entre lesestimations de valeur et le cours observé des actions. Utilisant les bénéfices futurs réelscomme mesure des bénéfices attendus, P&S (1998) constatent que les erreurs d’évaluationdu modèle DCF sur un horizon de 10 ans excèdent largement celles du modèle RIM. Ilsattribuent ce résultat au fait que des montants comptabilisés conformément aux PCGR dansle modèle RIM permettent une prise en compte plus rapide de flux de trésorerie futurs, desorte que leur pertinence à l’égard de la valeur est plus grande que celle des flux de tréso-rerie ou des dividendes. Francis, Olsson et Oswald (2000) jettent un nouveau regard sur ceparallèle, en recourant à une méthode ex ante et aux prévisions de Value Line (VL), pourconclure à leur tour que, lorsque les valeurs finales ne sont pas fondées sur les prévisions ducours des actions, l’efficacité du RIM est supérieure à celle du DCF.

Le premier objectif des auteurs est de vérifier si, sur un horizon prévisionnel de cinqans, le DCF et le RIM sont empiriquement équivalents, lorsqu’on utilise les expressions devaleur finale théoriquement « idéales » de Penman (1997), dans l’application de chacun desmodèles. Ces expressions de valeur nécessitent le cours du marché prévu (P) au terme del’horizon prévisionnel et l’excédent de ce cours sur la valeur comptable, pour un systèmecomptable donné. L’équivalence des modèles DCF et RIM pour des horizons finis et dansdes conditions idéales, malgré qu’elle soit bien établie en théorie, n’a pas été démontréedans les études empiriques. Au premier abord, les arguments semblent circulaires : si desprévisions fiables de cours sont disponibles, le modèle d’actualisation des dividendes(DDM) devrait suffire, et il n’est pas nécessaire de recourir au DCF ou au RIM. La chosen’est cependant pas évidente, du fait que les prévisions de cours formulées par le marchéne sont pas observables ; les auteurs utilisent donc les prévisions de cours final de VL commesubstitut. Bien que ces prévisions soient loin d’être idéales et qu’elles puissent contenir deserreurs de distorsion ou de mesure (voir Abarbanell et Bernard, 2000), les auteurs fontl’hypothèse que toute erreur de distorsion ou de mesure serait un facteur constant dans lescomparaisons entre DCF et RIM. Ils supposent également, comme P&S (1998) et Francis etal. (2000), que le marché est efficient.

Le deuxième objectif des auteurs consiste à démontrer que les valeurs intrinsèquescalculées à l’aide des prévisions de cours final de VL donnent lieu à des erreurs d’évaluationplus modestes que les valeurs intrinsèques déterminées en fonction des expressions devaleur finale improvisées. Les expressions simples de perpétuité, qui supposent que lesbénéfices anormaux postérieurs à l’horizon prévisionnel croîtront soit au taux de 0 pour cent,soit au taux nominal d’inflation, ont été amplement utilisées dans les recherches empiriques(par Francis et al., 2000, et par Frankel et Lee, 1998, entre autres). Gebhardt, Lee et Swami-nathan (2001) utilisent un procédé de taux de décroissance qui est aussi problématique que

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Equity Valuation Employing Terminal Value Expressions 627

les expressions basées sur la perpétuité, étant donné qu’il suppose que le rendement anormaldu capital investi postérieur à l’horizon prévisionnel convergera vers la moyenne du secteurd’activité, sur une période de sept ans. Les auteurs constatent que les valeurs finales sont enmoyenne sensiblement sous-évaluées lorsque des estimations improvisées de l’achalandageau terme de l’horizon prévisionnel sont utilisées, ce qui suppose que les estimations de lavaleur intrinsèque (Frankel et Lee, 1998) ou du coût du capital ex ante (Gebhardt et al.,2001) sont sous-évaluées lorsque de telles expressions de valeur finale sont employées. Cesinférences peuvent être importantes, selon le but visé par la recherche, et elles demeurentvalides même dans les dernières années de la période étudiée, une fois que s’est atténuél’optimisme de VL dans les prévisions de cours.

L’échantillon des auteurs compte 422 sociétés (ou 2 110 exercices-société), à l’égarddesquelles ils disposent de données prévisionnelles et historiques complètes pour toute ladurée de la période couverte. Le fait que l’échantillon soit constant et que les mesures serépètent au fil d’une période donnée pour les mêmes sociétés retient l’attention des auteursqui empruntent la méthodologie de l’échantillon constant (voir Kmenta, 1986) exploitant lesautocorrélations dans les données pour réaliser certains tests statistiques. Le coût des capi-taux propres est calculé à l’aide du modèle d’évaluation des actifs financiers. Le taux sansrisque est mesuré comme étant le taux constant à l’échéance des bons du trésor de cinq ans,au début du mois de prévision, provenant de la base de données de la Chicago FederalReserve Bank, et la prime de risque est mesurée comme étant le produit du bêta de l’entreprisefourni par VL et de la prime de marché historique approximative de 6 pour cent. Les auteursutilisent les premières prévisions complètes de VL, habituellement publiées au troisièmetrimestre de l’exercice de l’entreprise. À l’instar de Francis et al. (2000), les auteursactualisent les prévisions de VL pour les attributs d’évaluation du ne exercice en utilisant unfacteur de (n − 1 + f ), où f représente la portion d’exercice se situant entre la date où sontfaites les prévisions et la clôture du premier exercice. Étant donné que tous les modèlesd’évaluation exigent des valeurs comptables à la date de la prévision, ce que VL ne fournitpas directement, il faut intrapoler les valeurs comptables (les actifs financiers nets) à cettedate pour le RIM (le DCF), à partir de leur valeur au début de l’exercice de prévision et desprévisions de VL relatives aux variables de l’exercice courant. VL publie des prévisionspour trois horizons : l’exercice en cours (soit l’exercice 1), l’exercice suivant (soit l’exercice2) et le long terme (soit l’exercice 5). Étant donné que les prévisions annuelles des attributsd’évaluation pour les exercices 3 et 4 ne sont pas publiées dans le Value Line InvestmentSurvey, à la suggestion des analystes de VL, les auteurs intrapolent de façon linéaire lesdonnées relatives à ces deux exercices, en fonction de la croissance prévue entre l’exercice 2et l’exercice 5. Le cours le plus récent rapporté par VL est utilisé dans cette étude commevariable dépendante. Dans le cas du RIM comme dans celui du DCF, le chercheur doit parfoisfaire face à la situation où les valeurs finales sont négatives. Le cas peut se produire si l’unou l’autre des excédents prévus du cours sur la valeur comptable, compte tenu des pré-visions de cours final ou des attributs de l’évaluation au terme de l’horizon prévisionnel, estnégatif. Les auteurs choisissent de ne pas plafonner les valeurs finales négatives à zéro parceque tout attribut négatif au terme de l’horizon prévisionnel devrait être intégré dans le coursdu marché en vigueur.

Les tests statistiques révèlent que, pour l’ensemble de l’échantillon, les erreursprévisionnelles absolues médianes sont de 13,71 pour cent et de 14,18 pour cent respectivement



pour le DCF et le RIM. Ainsi, en mettant l’accent sur la précision, on ne constate pas desupériorité du RIM sur le DCF lorsque les valeurs finales idéales sont employées. Toute« mise à l’épreuve » du RIM et du DCF risque de placer ce dernier en situation défavorableen raison des limites inhérentes à l’estimation de la version de Copeland et al. (1995) dumodèle financier des flux de trésorerie disponibles, une méthode employée par Francis et al.(2000) qui fait appel aux données de VL. Pour résoudre ce problème, les auteurs estiment laversion du DCF proposée par Penman (1997). Cette spécification particulière convientmieux aux données de VL parce que l’attribut d’évaluation — les flux de trésorerie dis-ponibles aux actionnaires ordinaires — peut être tiré directement des données VL et qu’iln’est pas nécessaire d’estimer le coût moyen pondéré du capital. Les auteurs formulentnéanmoins une mise en garde : l’application de la version du DCF proposée par Penman,qui fait un usage empirique des données de VL, peut encore contenir des erreurs de mesureétant donné que VL ne fournit pas de prévisions relatives aux impôts sur le revenu reportés ouaux sommes immobilisées dans le fonds de roulement. Compte tenu de ces limitationspratiques de l’estimation du DCF, il est assez remarquable d’avoir pu établir une équivalenceapproximative entre le DCF et le RIM.

Mettant en opposition les valeurs intrinsèques des modèles qui utilisent les prévisionsde cours final et les valeurs intrinsèques des modèles qui ne le font pas, les auteurs constatentque, tant pour le DCF que pour le RIM, l’efficacité des modèles d’évaluation basés sur lesprévisions de cours surpasse de beaucoup celle des modèles correspondants qui nes’appuient pas sur les cours. Bien sûr, l’utilisation des prévisions de cours VL comme pointde repère n’est pas valide si ces prévisions sont optimistes. Toutefois, même pour les deuxdernières années incluses dans l’étude (1995–1996), au moment où l’optimisme des pré-visions de cours de VL se trouve ramené à un niveau négligeable, l’erreur prévisionnellemédiane continue d’indiquer une importante distorsion à la baisse lorsque les expressionsimprovisées de valeur finale sont utilisées. Ces résultats donnent à penser que les chercheursqui étudient le coût du capital ex ante ou les stratégies d’investissement faisant appel auxexpressions simplifiées de valeur finale pour le RIM devraient interpréter leurs résultatsavec une certaine prudence.

En remplaçant les prévisions de cours final de VL par des expressions traditionnellesde valeur finale à l’aide d’estimations de croissance simples, semblables à celles qu’emploientP&S (1998) et Francis et al. (2000), les auteurs sont en mesure de reproduire les constatationsprécédentes selon lesquelles le RIM surpasse le DCF en efficacité. Ainsi, dans la régressiondes cours en vigueur en fonction des valeurs intrinsèques, la valeur de R2 est supérieure dansle cas du RIM comparativement au DCF (par exemple, 79,65 pour cent contre 67,95 pourcent, et 77,02 pour cent contre 60,46 pour cent, lorsque les hypothèses de croissance sontrespectivement de 0 et de 2 pour cent). La supériorité du RIM sur le DCF lorsque la valeurfinale idéale n’est pas disponible est expliquée par P&S (1998) dans les termes suivants : lavaleur comptable actuelle des capitaux propres inclut déjà une partie des flux de trésoreriefuturs et laisse relativement peu de valeur à encaisser au terme de l’horizon prévisionnel. Parexemple, selon l’hypothèse de croissance de 0 pour cent (2 pour cent), 20,77 pour cent (25,53pour cent) de la valeur intrinsèque dans le cas du RIM est dérivée de la valeur finale actualisée,le chiffre correspondant dans le cas du DCF étant de 91,81 pour cent (93,19 pour cent).

Lundholm et O’Keefe (2001, ci-après L&O) relèvent des erreurs dans l’application desmodèles du RIM et du DCF qui se soldent par des estimations incohérentes de la valeur



intrinsèque. Bien que leurs travaux mettent surtout en relief l’importance d’éviter cesécueils, L&O affirment que l’équivalence du RIM et du DCF est « assurée ». L’équivalencedu RIM et du DCF lorsqu’on emploie les expressions de valeur finale idéale, ne peut se con-firmer que si 1) la même prévision des cours de VL est utilisée dans les deux modèles et si2) le chercheur évite les écueils évoqués par L&O. L’un des écueils qu’évoquent L&O, sansproposer de solution pratique, est celui de la difficulté de l’estimation du coût moyen pondérédu capital pour le modèle DCF. La version Penman du modèle DCF utilisée par les auteursminimise le risque d’erreurs dans l’application du modèle DCF et n’exige pas l’estimationdu coût moyen pondéré du capital. Fait d’égale importance, elle ne fait pas intervenirl’hypothèse traditionnelle des versions empiriques précédentes du modèle des flux detrésorerie disponibles selon laquelle les actifs financiers nets sont comptabilisés à la valeurdu marché. S’ils ne le sont pas, le chercheur doit enrichir le modèle traditionnel des flux detrésorerie disponibles en y ajoutant un terme qui représente la différence entre la juste valeuret la valeur comptable des actifs financiers nets. Sans ce terme, l’équivalence entre le DCFet le RIM ne peut être démontrée. Un autre des apports de cette étude est qu’elle indique auxchercheurs comment réduire au minimum les incohérences dans l’estimation des valeursintrinsèques grâce à l’utilisation des données de VL dans l’application du modèle DCF.

Les questions de recherche de cette étude ont une pertinence pratique. L’équivalencedu DCF et du RIM est tenue pour acquise par ceux et celles qui étudient l’analyse des étatsfinanciers, et la démonstration empirique de cette équivalence est utile. Bien sûr, dans le casd’un horizon fini, l’équivalence n’est possible qu’avec des prévisions de cours final, faute dequoi il convient de déterminer avec soin la longueur de l’horizon prévisionnel et la formede l’expression de la valeur finale axée sur les cours, ainsi que l’ont démontré les travauxantérieurs.

1. Introduction

Recently, Penman and Sougiannis (1998; hereafter P&S) compared the bias andaccuracy of the discounted cash flow model (DCF) and Edwards-Bell-Ohlsonresidual income model (RIM) in explaining the relation between value estimatesand observed stock prices. Using a perfect foresight approach, P&S find that valu-ation errors for DCF over a 10-year horizon exceed those of RIM by a substantialmargin. They attribute this result to generally accepted accounting principles(GAAP)-based accounting accruals under RIM, which bring future cash flows for-ward and hence are more value-relevant than either cash flows or dividends. Fran-cis, Olsson, and Oswald (2000) take a second look at that comparison using an exante approach and Value Line (VL) forecasts and also conclude that with non–price-based terminal values RIM outperforms DCF.

Our first research objective is to explore whether, over a five-year valuationhorizon, DCF and RIM are empirically equivalent using Penman’s (1997) theoreti-cally “ideal” terminal value expressions in each model. These expressions requirethe market’s expected stock price (P) at the horizon and the premium of that priceover book value for a particular accounting system. The equivalence of DCF andRIM for finite horizons under ideal conditions, though well established theoreti-cally, has not been demonstrated in the empirical literature. At first glance, thearguments seem circular: if one has reliable price forecasts, the dividend discount



model (DDM) should suffice and one does not need DCF or RIM. However, thepoint is not obvious because the market’s stock price expectations are not observ-able, and we use VL’s terminal stock price forecasts as a surrogate. Although VLterminal price forecasts are far from ideal and may contain bias/measurement error(see Abarbanell and Bernard 2000), we invoke the assumption that any bias/measurement error will be a constant factor in comparisons across DCF and RIM.Market efficiency is a maintained assumption in our study, as it is in P&S 1998 andFrancis et al. 2000.

Our second research objective is to demonstrate that intrinsic values calcu-lated using VL terminal stock price forecasts produce smaller valuation errors thanintrinsic values employing ad hoc terminal value expressions. Simple perpetuityexpressions that assume that post-horizon abnormal earnings will grow at either arate of 0 percent or the rate of nominal inflation have been widely employed byempirical researchers (e.g., Francis et al. 2000 and Frankel and Lee 1998). Gebhardt,Lee, and Swaminathan (2001) use a fade rate procedure that is also ad hoc in that itassumes that post-horizon abnormal return on equity will converge to the industryaverage over a seven-year period beyond the forecast horizon. We find that terminalvalues are on average substantially understated using ad hoc estimates of horizongoodwill, implying that estimates of intrinsic value (Frankel and Lee) or the exante cost of capital (Gebhardt et al.) are understated when ad hoc terminal valueexpressions are used. These inferences can be important depending on the intendedresearch purpose, and hold even in the latter years of our sample when the opti-mism in VL stock price forecasts has abated.

Lundholm and O’Keefe (2001, hereafter L&O) identify errors in applicationof the RIM and DCF models that lead to inconsistent estimates of intrinsic value.While much of their paper emphasizes the importance of avoiding these pitfalls,L&O assert that the equivalence of RIM and DCF is “guaranteed” to hold. Theequivalence of RIM and DCF employing ideal terminal value expressions will onlyhold if (1) the same VL price forecast is used in RIM and DCF; and (2) theresearcher avoids the pitfalls discussed in L&O. One pitfall that L&O refer to, butoffer no practical suggestion for, is the conundrum of estimating the weightedaverage cost of capital for the DCF model. We introduce into the empirical litera-ture a version of DCF derived by Penman 1997 that minimizes the potential forerrors in applying the DCF model. Specifically, our version of DCF does notrequire estimates of the weighted average cost of capital (i.e., WACC) and, just asimportant, it does not invoke the assumption typical of prior empirical versions ofthe free cash flow model that net financial assets are marked to market. If financialassets are not marked to market, then the researcher must augment the traditionalfree cash flow model by incorporating a term representing the fair value incrementon current net financial assets. If this term is missing, the equivalence across DCFand RIM cannot be demonstrated. Thus, another contribution of our study is to showresearchers how to minimize inconsistent estimates of intrinsic values using VL datato estimate the DCF model.

Our research questions have practical importance. The equivalence of DCFand RIM is something students of financial statements analysis take “on faith” and



the empirical demonstration of this equivalence is useful. Of course, for a finitehorizon, the equivalence is possible only with terminal stock price forecasts. With-out such forecasts, careful attention must be paid to the length of the forecast horizonand the form of the non–price-based terminal value expression, as prior literaturehas shown.

We inherit the focus on pricing errors and the maintained assumption of marketefficiency from the “horse race” conducted by P&S 1998 and Francis et al. 2000.Our aim is to revisit the setting of these studies and set the record straight on theapparent superiority of RIM over DCF, employing a level playing field where bothmodels use an approximation of ideal terminal values. The pricing error approachseemingly conflicts with the rationale for VL and fundamental analysis — that is,to spot mispriced securities. In section 6, we provide suggestions for furtherresearch focusing on future excess returns.

The remainder of this study is organized as follows. A literature review is pro-vided in section 2. Section 3 lays out the research methodology and hypotheses.The sample selection and measurement issues are discussed in section 4, and theempirical results are presented in section 5. Finally, our summary and conclusionsappear in section 6.

2. Literature review

The DDM and DCF models are well-known approaches to valuation in the financeliterature (see Cornell 1993; Copeland, Koller, and Murrin 1995). RIM is discussedextensively by Ohlson 1995, who shows that theoretically GAAP book values andearnings are valid valuation attributes. Feltham and Ohlson (1995) establish thetheoretical equivalence of DDM, DCF, and RIM for infinite valuation horizons. Allthree models follow from the familiar present value of expected dividends (PVED)expression for value, and the last two models substitute out dividends in PVED forrelevant valuation attributes.1

Penman (1997) establishes the theoretical equivalence of DDM, DCF, andRIM for finite valuation horizons, provided one that has access to data necessary toestimate the following “ideal” terminal values at the end of forecast horizon T:Et(Pt + T) for DDM; Et(P − B) t + T for RIM; and Et(P − FA) t + T for DCF. In theabove, Et (·) denotes market expectations at time t; Pt + T and Bt + T denote fore-casted stock price and book value of owner’s equity at the horizon T periods hence;and FAt + T denotes forecasted net financial assets at the horizon. In his paper, Pen-man does not anticipate that the researcher would have access to forecasts of stockprice at the horizon, and hence much of his paper discusses possible estimates ofterminal values for each of the DDM, DCF, and RIM models when forecastedstock price is unavailable. One of the objectives of our research is to establish Pen-man’s hypothesized equivalence over a five-year forecast horizon using VL proxiesfor the above “ideal” terminal values. A potential limitation of this approach is thatmarket expectations can be measured with error using VL forecasts of future stockprice and other valuation attributes. An extensive literature exists that suggests thatVL earnings forecasts are biased and/or inefficient (see Abarbanell 1991; Abarba-nell and Bernard 1992; and Debondt and Thaler 1990). In a similar vein, Botosan



(1997) observes that the optimism in VL’s terminal price forecasts yields implausi-bly high estimates of the equity cost of capital. On the other hand, other research-ers have shown that the accuracy of VL forecasts and their association with stockprice changes are comparable to those of other analysts, such as I/B/E/S and Zacks(see Abarbanell 1991; Bandyopadhyay, Brown, and Richardson 1995; Philbrickand Ricks 1991; and Stickel 1992). The advantages of VL forecasts over I/B/E/Sare that VL’s long-run “target price range” yields forecasts of stock price at thehorizon five years hence, and no similar price forecasts exist in I/B/E/S. Moreover,VL forecasts dividends, earnings, book values, and future cash flows separately;whereas only forecasts of earnings are available in I/B/E/S.2 Forecasts of dividendsand book values are required by RIM, and forecasts of future free cash flows arerequired by DCF.

Although VL provides estimates of long-run target price range, neither pointnor range estimates of short-run stock price are made. However, in the Value LineInvestment Survey, VL publishes a timeliness rank, which is based on a mechanicalmodel (see Foster 1986, 430–2, for details) and represents expected price apprecia-tion over the next 12 months. Many studies have shown that, using VL’s timelinessmeasure, investors can earn abnormal returns around a three-day publication period(e.g., Copeland and Mayers 1982; Huberman and Kandel 1987). Similarly, Peter-son (1995) finds that publication of “stock highlights” by VL elicits positive abnormalreturns. Since VL’s long-run target price ranges come from the same underlying dataset that generates timeliness ranks and stock highlights, they can be taken seriouslyeven though their usefulness has not been established in the prior literature. In sec-tion 4, we elaborate on how VL constructs these long-run target price ranges.

In the empirical domain, P&S (1998) and Francis et al. (2000) are the directantecedents of our work. P&S use a perfect foresight approach and find that valua-tion errors for DCF over a 10-year horizon are often in excess of 100 percent and,moreover, these errors consistently exceed those of RIM by a substantial margin.This result, according to P&S, may be due to GAAP-based accounting accrualsunder RIM, which bring future cash flows forward, compared with the DCF model,which “expenses” investment outlays. Francis et al. revisit the issue of model com-parison from an ex ante perspective using VL forecasts over a 5-year horizon, andsimilarly conclude that RIM dominates over DCF. Like Francis et al., we also takean ex ante approach to study the relative performance of RIM and DCF. However,in contrast to Francis et al., we make use of VL terminal stock price forecasts incalculating terminal values for each model, thus avoiding the need either to extrap-olate such values from near-term valuation attributes or to assume an ad hocgrowth rate, which may or may not correspond to market expectations.

Three other extant empirical studies have also employed an ex ante approachto explore the valuation errors associated with RIM. Bernard (1995) uses VL fore-casts of (P − B) at the horizon five years hence to measure terminal value, andshows that the intrinsic values for RIM explain 80 percent of the cross-sectionalvariation in the level of current stock price. Abarbanell and Bernard (2000) examinethe importance that the market attaches to the present value of terminal forecasts of(P − B), and find its regression coefficient to be around 0.67, considerably below



the predicted value of unity.3 This result is consistent with the notion that VL ter-minal price forecasts contain bias/measurement error. Finally, Sougiannis andYaekura (2001) explore the valuation errors associated with several GAAP-basedRIM valuation models using I/B/E/S rather than VL forecast data. For RIM withconventional non–price-based terminal value expressions at a horizon five yearshence, they obtain median signed (absolute) valuation errors of −26 (35) percent.As we will see later, the magnitudes of these errors are comparable to our RIM errorsfor valuation estimates that do not employ VL terminal stock price forecasts.4

3. Research methodology and hypotheses development

Valuation models

In this section, we develop the two major classes of valuation models to be testedin the paper, namely, DCF and RIM, by appealing to Penman 1997. These modelsare based on the following well-known present value of expected dividend model(PVED) for an infinite horizon:

Pt = (1),

where Pt is the current market price at time t; R denotes one plus the cost of equitycapital; dt + τ denotes dividends for each future period, t + τ ; and Et indicates anexpectation conditional upon information available at time t. Penman (1997)shows that when the horizon is finite, the intrinsic value, denoted as Wt, underDDM for T periods hence is given by:

Wt(DDM) = + R−T Et(Pt + T) (2),

where Pt + T is the market’s forecasted price at the horizon, t + T. It is an ideal terminalvalue for DDM.

DCF model

The following clean surplus relation (CSR) is assumed to hold for net financialassets at time t + τ, t = 1, 2, … , T:

FAt + τ = FAt + τ − 1 + Ct + τ − It + τ + i t + τ − dt + τ (3),

where for each future period t + τ, FA denotes net financial assets (i.e., cash andmarketable securities minus debt and preferred equity) and is negative if there isnet debt; (C − I ) is operating cash flows minus capital expenditures (i.e., free cashflows generated by operating assets); and i is interest flow from net financial assets,

Rτ–Et dt τ+( )

τ 1=

∞

∑

Rτ–Et dt τ+( )

τ 1=

T

∑



which represents interest paid (earned), including preferred dividends, if net financialassets are negative (positive). Bringing dt + τ to the left-hand side of (3) and all otherexpressions to the right, and substituting for E t(d t + τ ) in equation (1), Penman(1997) derives the following version of the DCF model for an infinite horizon:

Wt(DCF) = FAt + [Ct + τ − It + τ + i t + τ − (R − 1)FAt + τ − 1] (4).

It is important to note that (4) assumes only PVED and CSR for net financialassets, and one can easily revert back to PVED by substituting in the oppositedirection. As explained by Feltham and Ohlson 1995, (4) represents the cashaccounting model where operating assets are expensed; book value is representedby current net financial assets; and “earnings” are represented by free cash flowsfrom operations, (C − I ), plus (minus) interest income (expense), i.

Penman (1997) shows that if one relaxes the assumption of risk neutrality butassumes that net financial assets are marked to market at all times, (4) becomes thefamiliar free cash flow model:

Wt(DCF) = FAt + (Ct + τ − It + τ ) (5),

where RW denotes one plus the weighted average cost of capital (i.e., WACC). Theequation states that the value of owner’s equity equals the sum of the fair values ofnet financial assets and net operating assets, with the latter represented by thepresent value of expected future free cash flows.5

Francis et al. (2000) estimate variations of (5). We prefer Penman’s version ofthe DCF (i.e., (4)) for several reasons. First, (5) requires the estimation of WACC,where the weights must be based on the estimated value of equity and debt, not oneither their book value or a target capital structure. On the other hand, (4) requiresthe equity cost of capital, thus placing DCF on an equal footing with RIM. Second,(5) assumes that FAs are marked to market and, to the extent that fair value doesnot equal book value, it introduces noise in the intrinsic value expressions. Bycomparison, (4) does not make that assumption, and implicitly corrects for any fairvalue increment on debt.6 Finally, (5) requires forecasted operating cash flows (i.e.,C − I ), which, unlike forecasts of free cash flows to common (i.e., C − I + i), arenot provided by VL. To derive C − I, one needs to remove the effects of interestexpense (income), i. This is problematic because VL does not provide forecasts of“i ” to the horizon for either debt or preferred shares.

For an arbitrary finite horizon T, Penman (1997) shows that the ideal terminalvalue for a finite horizon version of (4) is the market’s expected premium, (P − FA),at the forecast horizon. The following equation represents our DCF model employ-ing VL forecasted price in the terminal value expression:

Rτ–Et

τ 1=

∞

∑

RWτ–

Et

τ 1=

∞

∑



Wt(DCF1) = FAt + [Ct + τ − It + τ + i t + τ − (R − 1)FAt + τ − 1]

+ R−TEt(Pt + T − FAt + T) (6a).

The expression (Pt + T − FAt + T) at the horizon captures the present value of post-horizon operating cash flows because the cash accounting model expenses operat-ing assets. It also captures any post-horizon fair value increment, if net financialassets are not marked to market.

When a terminal stock price forecast is not available, it is of interest to exploreother non–price-based expressions. Following Frankel and Lee 1998, P&S 1998,and Francis et al. 2000, we employ two expressions: one assumes a simple perpe-tuity without growth and the other assumes a perpetuity with constant growth rateg = 2 percent.7 Modifying (6a) accordingly results in:


+ R−T(R − 1)−1Et[Ct + T + 1 − It + T + 1 + i t + T + 1 − (R − 1)FAt + T] (6b);


+ R−T(R − 1 − g)−1Et [Ct + T + 1 − It + T + 1 + i t + T + 1 − (R − 1)FAt + T] (6c).

We compute the numerator of the ad hoc terminal value expression as

[Ct + T + 1 −I t + T + 1 + i t + T + 1 − (R − 1)FAt + T] =(1 + g) (Ct + T − I t + T + i t + T) − (R − 1)FAt + T.

For the purposes of estimating (6a)–(6c), and (7a)–(7c) discussed next, all variablesare deflated by the number of shares outstanding at the end of forecast year.8

RIM model

Penman (1997) shows that, for a finite horizon T, the ideal terminal value for RIMis the market’s expected premium, (P − B), at the forecast horizon. This expressionrepresents the present value of post-horizon abnormal earnings (i.e., subjectivegoodwill) and reflects the joint effects of positive net present value projects andaccounting conservatism. Since VL explicitly forecasts book value five yearshence, the expected premium can be calculated to yield the following “best” con-tender from the RIM family of valuation models:

Rτ–Et

τ 1=

T

∑

Rτ–Et

τ 1=

T

∑

Rτ–Et

τ 1=

T

∑



Wt(RIM1) = Bt + ( ) + R−T Et(Pt + T − Bt + T) (7a),

where denotes abnormal income for forecast year t + τ, measured as VL’sforecasted net income minus a charge on the capital employed (i.e., R − 1 timesopening B ). The corresponding expressions that do not employ terminal priceforecasts are:

Wt(RIM0) = Bt + ( ) + R−T(R − 1)−1Et( ) (7b),

Wt(RIM2) = Bt + ( ) + R−T(R − 1 − g)−1Et( ) (7c),

where = (1 + g)Xt + T − (R − 1)Bt + T, under the assumptions of a simpleperpetuity with constant growth.

Hypotheses development

Following P&S 1998 and Francis et al. 2000, we focus on comparing the signedand absolute prediction errors across DCF and RIM. We do not consider DDM inthis paper because our price-based DCF model (i.e., (6a)) is developed directlyfrom the corresponding DDM (i.e., (2)) given the financial assets continuityaccount (i.e., (3)) for each pre-horizon year, thus guaranteeing their theoretical andempirical equivalence.9 The empirical comparison between DCF and RIM thatemploy Penman’s 1997 ideal price-based terminal value expressions (i.e., (6a) and(7a)) is, however, complicated by the presence of several additional sources ofinconsistency, which may or may not be easily avoided by the researcher, as dis-cussed in the introduction and elaborated further in section 5. The equivalence ofthese two models is not guaranteed empirically unless errors in implementing eachmodel are carefully considered and minimized. We conjecture that, in the absenceof implementation errors, the choice between DCF and RIM should be a matter ofindifference. This is formalized in our first hypothesis (stated in the null form):

HYPOTHESIS 1. Across the versions of DCF and RIM that employ VL forecastedprice in the terminal value expression, there is no difference in predictionerrors.

We next compare non–priced-based models under 0 percent and 2 percentconstant growth assumptions with the corresponding price-based models within thesame class of DCF and RIM. We expect the model that uses VL’s price forecasts in

Rτ–Et

τ 1=

T

∑ Xt τ+a

Xt τ+a

Rτ–Et

τ 1=

T

∑ Xt τ+a

Xt T 1+ +a

Rτ–Et

τ 1=

T

∑ Xt τ+a

Xt T 1+ +a

Xt T 1+ +a



the terminal value expressions (i.e., (6a) and (7a)) to beat other contenders withintheir class (i.e., (6b)– (6c) for DCF; and (7b)– (7c) for RIM). Intuitively, if theresearcher cannot observe VL’s post-horizon expectations, any non–price-basedterminal value calculated under an arbitrary growth assumption is at best ad hoc.The above discussion leads to our second hypothesis (stated in the alternative form):

HYPOTHESIS 2. Within each class of the DCF and RIM valuation models, themodel that employs VL forecasted price in the terminal value expressiongenerates the lowest prediction errors, compared with models that employnon–price-based terminal value under arbitrary (0 percent and 2 per-cent) growth assumptions.

It is worthwhile pointing out that Hypothesis 2 is also not “guaranteed” empir-ically. For example, if VL’s price forecasts are pure noise or if VL simply appliesthe reciprocal of the equity cost of capital at the horizon and multiplies this byforecasted earnings five years hence, then the forecasted price would fail to capturesubjective goodwill beyond the horizon. In this case, (7a) will have no edge over(7b) or (7c),10 and the superiority result predicted in Hypothesis 2 is generally notassured.

4. Data description and measurement issues

Data description

Our initial sample consists of 500 firms (or 2,500 firm-year observations), whichwere followed by VL over a five-year period, 1992–96, and were on both CRSPand COMPUSTAT during that time. This sample size is chosen for practical con-siderations because the forecasts of prices, book values, dividends, cash flows, andother relevant accounting valuation attributes are not available from machine-readable sources and must be hand-collected from the archived Value Line Invest-ment Survey. To draw the sample, we first obtain an intersection of 1,089 firms,excluding those in the financial services sector, from the 1996 coverage of VL,CRSP, and COMPUSTAT, and then apply a random number generating procedure.We require five years of forecast data for all firms included in the sample. Non-forecast-related historical data are extracted from the Value Line Data File. Due tomissing data in the data file, 36 firms are eliminated, 41 firms are dropped becauseVL’s annual capital investment estimates are not provided for some industries,11

and another firm is deleted because VL did not provide price forecasts for one ofthe years (i.e., 1996). This leaves us with a final sample of 422 firms (or 2,110firm-years), each with complete forecasted and historic data over the entire sampleperiod under investigation. The panel nature of the data with repeated measuresover calendar time for the same firms appeals to us, and panel data methodology(see Kmenta 1986) exploiting autocorrelations in the data will be used for formalstatistical tests.

Our sample firms are large, with mean (median) market capitalization of $4.95($1.18) billion. The minimum market capitalization is $25.80 million, and the



maximum is $16.87 billion. Firm-specific betas provided by VL range from a lowof 0.05 to a high of 2 with the mean beta given by 1.02. The equity cost of capital iscomputed based on the CAPM. The riskless rates are measured as the five-year trea-sury constant maturity rates at the beginning of the forecast month from ChicagoFederal Reserve Bank data base and the risk premiums are measured as the productof VL firm-specific betas and the approximate historical equity premium of 6percent.12 The cost of equity has a mean of 12.28 percent and the minimum andmaximum of 5.69 percent and 18.64 percent, respectively.

Measurement issues

To measure the variables described in (6a)–(6c) and (7a)–(7c) for each of the fivesample years, we take the first complete published VL forecasts, which typicallyappear in the third quarter of the firm’s fiscal year. Following Francis et al. 2000,we discount VL forecasts of the nth year’s valuation attributes by a factor of (n − 1 + f ),where f reflects the fraction of year between the market valuation date and the firstfiscal year-end.13 Since all the valuation models require book values at the date offorecast, which VL does not directly provide, we need to interpolate book values(net financial assets) to the forecast date for the RIM (DCF) models based on theirvalues at the beginning of forecast year and the VL forecasts of related current fis-cal year’s variables.14

Our conversations with VL personnel indicate that VL analysts’ predictions ofthe target stock price range, three to five years ahead, are not mechanical. Judge-ment is required of the analyst at three stages in constructing the target price range.First, judgement is used to forecast projected earnings three to five years ahead.Second, judgement is used in applying the appropriate P/E ratio to forecasted earn-ings, and the P/E ratio can deviate from the projected average P/E ratio for themarket according to the analysts’ long-term growth projections for the stock inquestion. Third, judgement is applied in selecting one of five possible range catego-ries to surround a point estimate of forecasted price, with smaller ranges associatedwith greater financial strength/safety as assessed by the VL analyst and her supervi-sors. We conclude from these conversations that the width of target stock priceranges reflects uncertainty, and that such price forecasts impound the VL analysts’growth assumptions beyond the horizon. For our purposes, we define the terminalprice forecasts, Pt + T , as the mid-point of the target price range.

VL publishes forecasts for three horizons: current fiscal year (i.e., year 1), thefollowing fiscal year (i.e., year 2), and long run (i.e., year 5). Since the internal year-by-year forecasts of valuation attributes for years 3 and 4 are not published in theValue Line Investment Survey, at the suggestion of VL analysts, we interpolate datafor these two years based on implied straight-line growth from year 2 to year 5.15 Themost recent stock price reported by VL is used as the dependent variable in our study.16

For both RIM and DCF, the researcher must confront the occasional existenceof negative terminal values. Such values can arise if either forecasted premiumsgiven terminal price forecasts or valuation attributes at the horizon are negative.We choose not to cap negative terminal values at zero because any negativeattribute at the horizon is expected to be impounded in current market price.



5. Empirical results

Descriptive statistics

Table 1 reports the relative importance of the various components of DCF andRIM. Discounted terminal value (DTV) accounts for the majority of intrinsic valuein all three versions of the DCF model (i.e., 95.38 percent, 91.81 percent, and93.19 percent for DCF1, DCF0, and DCF2, respectively).17 The importance ofDTV in the DCF models is consistent with prior literature. Copeland, Koller, andMurrin (1995), for instance, document that, for a sample of companies appraisedby McKensey and Company, non–price-based DTV amounts to 56 to 125 percentof intrinsic value. The remaining two components of DCF models tend to haveopposite signs in our data. Current book value (i.e., FAt) is, on average, negative,reflecting current net debt; whereas the present value of pre-horizon “free cashflows” coming to treasury from operations (i.e., PV) is positive.

Turning to the RIM models, DTV makes up of 52.23 percent, 20.77 percent,and 25.53 percent of intrinsic value for RIM1, RIM0, and RIM2, respectively.These percentages are considerably lower than the corresponding figures for DCF.Conversely, current book value (i.e., Bt) takes on a more significant role in all threeversions of RIM than DCF (e.g., 41.04 percent for RIM1 versus −25.71 percent forDCF1), confirming the findings of prior research that more wealth is captured invaluation attributes to the horizon under RIM than under DCF. Within the familyof RIM models, Bt is least important and DTV most important when the “ideal”terminal value is employed. For example, Bt (DTV) accounts for 41.04 percent(52.23 percent) of the intrinsic value under RIM1, compared with 68.06 percent(20.77 percent) and 63.97 percent (25.53 percent) under RIM0 and RIM2, respec-tively. However, even for RIM0 and RIM2, DTV represents more than 20 percentof the intrinsic value estimates, implying that post-horizon forecasts of abnormalearnings remain crucial to firm valuation under RIM even though, as pointed outby P&S 1998 and Francis et al. 2000, current book value brings future cash flowsforward.

Two sets of analyses are performed in this study, one based on prediction errordefined as the difference between model intrinsic value estimate and current stockprice, scaled by current stock price, and the other based on regression analysis.Panels A and B of Table 2 present the distribution of signed and absolute predic-tion errors, respectively, for the overall sample period. As is evident from thefourth column, the skewness measures are uniformly positive across all valuationmodels, implying that our data are positively skewed. For the purpose of testing thepredictions of Hypotheses 1 and 2, we therefore focus on the median, as opposedto the mean, signed and absolute prediction errors, and use non-parametric Wilcoxonsigned rank tests.

Some unusually large prediction errors are evident at both ends of the distribu-tions, especially in models for which non–price-based terminal value expressionsare employed. The prediction error analysis, in particular that involving Hypothe-sis 2, may be affected because outliers can come from different firms depending onwhether price- or non–price-based models are used.18 To assess potential prob-



TABLE 1Relative importance of components of valuation models*

DCF1 −8.46 9.98 31.39 32.91(−25.71%) (30.33%) (95.38%) (100.00%)

DCF0 −8.46 9.98 17.04 18.56(−45.58%) (53.77%) (91.81%) (100.00%)

DCF2 −8.46 9.98 20.80 22.32(−37.90%) (44.71%) (93.19%) (100.00%)

RIM1 13.53 2.22 17.22 32.97(41.04%) (6.73%) (52.23%) (100.00%)

RIM0 13.53 2.22 4.13 19.88(68.06%) (11.17%) (20.77%) (100.00%)

RIM2 13.53 2.22 5.40 21.15(63.97%) (10.50%) (25.53%) (100.00%)

Notes:

* See the appendix for a description of DCF1, DCF0, DCF2, RIM1, RIM0, and RIM2.

† FA is the net financial assets per share (i.e., cash and marketable securities minus debt and preferred equity), and B is the book value of owner’s equity per share;

‡ PV is the present value of operating cash flows to common shareholders or abnormal earnings to the horizon, on a per-share basis, under the discounted cash flows (DCF) or residual income model (RIM), respectively.

§ DTV is the discounted terminal value per share given by the last component under DCF1, DCF0, DCF2, RIM1, RIM0, and RIM2.

# IV is the intrinsic value estimates per share under DCF1, DCF0, DCF2, RIM1, RIM0, and RIM2.

Mean openingFA or B†

(% of mean IV)Mean PV‡

(% of mean IV)Mean DTV§

(% of mean IV)Mean IV#

(% of mean IV)

lems associated with outliers, we conduct the prediction error analysis with andwithout winsorizing at the 1st and 99th percentile. The results are very similarqualitatively speaking. Thus, only one set of results based on data before applyingthe winsorization procedure will be reported in the paper.

Prediction-error analyses

Results from tests of Hypothesis 1

Panel A of Table 3 reports the median intrinsic value estimates, median signedprediction errors, and pair-wise comparisons of these figures for the price-basedvaluation models over the entire sample period (1992–96) and by year. At theoverall level, the median intrinsic values of $29.181 and $29.104 for DCF1 and



TABLE 2Distribution of prediction errors

Panel A: Signed prediction errors (bias) — Overall (1992–96)*

Price-based modelsDCF1 8.42% 4.82% 0.261 1.624 8.199RIM1 8.39% 4.73% 0.269 1.557 8.094

Non–price-based modelsDCF0 −37.76% −41.34% 0.336 1.454 6.512RIM0 −34.18% −37.95% 0.275 1.613 9.370DCF2 −24.18% −30.50% 0.427 1.771 7.389RIM2 −30.26% −34.36% 0.306 1.623 8.105

Panel B: Absolute prediction errors (accuracy) — Overall (1992–96)†

Price-based modelsDCF1 19.11% 13.71% 0.197 3.203 21.069RIM1 19.54% 14.18% 0.204 3.209 20.109

Non–price-based modelsDCF0 43.90% 42.81% 0.250 0.757 3.151RIM0 38.73% 38.80% 0.207 0.873 7.409DCF2 39.68% 35.48% 0.288 2.034 11.180RIM2 37.19% 36.42% 0.217 1.156 8.541

Notes:* Signed prediction errors are calculated as ( − Pit )/Pit.

† Absolute prediction errors are calculated as | − Pit|/Pit, where Pit is the recent stock price published in the VL forecast report; and is the intrinsic value estimate per share for security i in year t calculated under M = DCF1, DCF0, DCF2, RIM1, RIM0, and RIM2, described in the appendix.

Mean (%) Median (%)Standard deviation Skewness Kurtosis

Mean (%) Median (%)Standard deviation Skewness Kurtosis

IV itM

IV itM

IV itM

RIM1, respectively, overestimate current median stock price of $28, reflectingoptimism in VL forecasts noted by Botosan 1997. For both models, the mediansigned prediction errors decline steadily over time. For example, the mediansigned prediction errors for DCF1 reduce to 1.43 percent and −1.95 percent in1995 and 1996, respectively, from the peak of 11.95 percent in 1992. Thus, VLoptimism appears to have completely abated toward the end of our sample period.These patterns are depicted in Figure 1.

For the pooled 1992–96 data, the median intrinsic value estimates and mediansigned prediction errors for DCF1 and RIM1 are all within a very small neighbor-hood of one another (i.e., $29.181 versus $29.104; 4.82 percent versus 4.73 percent).


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Nevertheless, the Wilcoxon signed rank test performed on percentage errors rejectsthe prediction of Hypothesis 1 at the 1 percent level. The sensitivity of smallmedian difference to statistical test may be partially explained by the power of testgiven the large number of observations overall, and by the fact that most (80 per-cent) of the differences are in the same direction. The support for Hypothesis 1 isconsiderably stronger when a separate analysis is performed for each of the sampleyears. In particular, none of the pair-wise comparisons in years 1992 to 1994rejects the null of no difference (i.e., Hypothesis 1) at the conventional levels ofsignificance.

The median absolute prediction errors and pair-wise comparisons based onthese errors are presented in panel B of Table 3. For both DCF1 and RIM1, theannual median absolute prediction errors decline from their highest levels in 1992to the lowest levels by the mid-point of our sample period (i.e., 1994). The trendreverses itself in the second half of the sample period. The prediction of Hypothe-sis 1 is not rejected in the last three years of the sample period (1994–96), butrejected in the first two years (1992–93). Overall, the median absolute predictionerrors are 13.71 percent and 14.18 percent for DCF1 and RIM1, respectively. TheWilcoxon signed rank test rejects Hypothesis 1 at the 1 percent level. In short, theevidence presented is largely consistent with the prediction that there is no differencein the median signed or absolute prediction errors across DCF and RIM models(Hypothesis 1), especially when analysis is conducted at the year-by-year level.

In testing Hypothesis 1, the researcher is confronted with several potentialsources of inconsistency that can lead to differences across valuation models. Wenow discuss three sources that we avoid. First, we employ Penman’s version ofDCF model (i.e., (4)) to avoid L&O’s “inconsistent discount rate error” referred toin the introduction. Thus, even if the equity cost of capital were incorrectly mea-sured, both DCF1 and RIM1 would produce the same incorrect intrinsic value soas not to affect the test of Hypothesis 1. Second, our conversations with VL per-sonnel indicate that, in the Value Line Investment Survey, forecasts of “free cash

TABLE 3 (Continued)

Notes:* Hypothesis 1 states that there is no difference in prediction errors across DCF1 and

RIM1. Wilcoxon signed rank tests are employed to test the difference in median signed/absolute prediction errors.

† Signed prediction errors are calculated as ( − Pit)/Pit and absolute prediction errors are calculated as | − Pit|/Pit, where Pit is the recent stock price published in the VL forecast report; and is the intrinsic value estimate per share for security i in year t calculated under M = DCF1, DCF0, DCF2, RIM1, RIM0, and RIM2, described in the appendix.

‡ Significant at the 1 percent level.

§ Significant at the 5 percent level.

IV itM

IV itM

IV itM



Figure 1Median signed prediction errors for price-based DCF and RIM: Years 1992 to 1996*

* Signed prediction errors are calculated as ( − Pit)/Pit , where Pit is the recent stock price published in the VL forecast report; and is the intrinsic value estimate per share for firm i in year t calculated under M = DCF1 and RIM1, described in the appendix. The graph depicts the median of signed prediction errors for all sample firms in each of the five years under investigation (1992–96).

−0.02

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19961995199419931992

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flows” typically increase working capital unless the VL analyst anticipates someother uses for the cash, such as share repurchases or retirement of long-term debt.Value Line ensures internally in their spreadsheets that all projected sources anduses of cash are reconciled through a projected statement of funds, and that CSRholds for FA. Since it is not easy for the researcher to observe where VL hasapplied funds for a particular firm-year, we create our own FA continuity schedule,starting with opening net FA and building up the next period FA using VL’s fore-casts of Ct + τ , It + τ , it + τ , and dt + τ in (3). Effectively, we generate our own fore-casts of future FA and do not use VL’s forecasted long-term debt. This procedureguarantees that CSR will hold for our version of forecasted FA, just as it does inter-nally for VL based on our discussions with VL analysts. This adjustment minimizesL&O’s so-called missing cash flows problem. Third, 301 to 770 firm-year observa-tions had negative opening book value of owners’ equity, and hence larger abnormalearnings than reported earnings under RIM1 during the forecast periods t + 1 to



t + 5. However, capping abnormal earnings at forecasted earnings for these firmswould introduce inconsistencies in comparisons with DCF. For that reason, we donot impose an upper cap on abnormal earnings. Results reported in this and thenext sections are nonetheless essentially the same qualitatively, with or without thecapping requirement. For the same reason, we also do not impose a lower boundon the two firm-year observations where RIM1 intrinsic value is negative. Onceagain, our results are not sensitive to this treatment.

We next turn to two sources of inconsistency that we do not avoid. First, forthe DCF model, it is not practical for the researcher to adjust forecasted “free cashflows” for sources or uses of cash due to working capital requirements anddeferred taxes. Regarding working capital, the cash versus non-cash componentsof forecasted working capital are not available from VL. For a typical firm in oursample, ignoring cash tied up in working capital overstates free cash flows,whereas not recognizing deferred taxes understates free cash flows. Second, forRIM, we do not force the CSR to hold when forecasted violations of CSR existbecause violations of CSR do exist in U.S. accounting principles and, therefore,should exist in expectation.19 If one were to force CSR to hold, the plug wouldhave to go to either forecasted earnings or forecasted equity infusions (i.e., nega-tive dividends). The latter treatment implies that the corresponding DCF modelvaluation attributes would have to change, leading to an unknown degree of errorin the DCF model. Since we do not adjust for these two sources of inconsistency,the empirical equivalence of DCF and RIM is not “guaranteed” to hold. Neverthe-less, even without attempting adjustments in these areas, the differences in errorsacross valuation models, reported in Table 3, are small.

Results from tests of Hypothesis 2

Panel A (B) of Table 4 presents results from testing the prediction of Hypothesis 2that the median signed (absolute) prediction errors are smaller for the price-basedvaluation models than for the corresponding non–price-based models.

For the pooled 1992–96 data, the median signed prediction errors of 4.82 per-cent (4.73 percent) for DCF1 (RIM1) are considerably closer to zero than −41.34percent (−37.95 percent) and −30.50 percent (−34.36 percent) for DCF0 (RIM0)and DCF2 (RIM2), respectively (see panel A).20 Wilcoxon signed rank tests ofpair-wise differences between the price-based and the non–price-based modelswithin the same family are all significant at the 1 percent level, supporting the pre-diction of Hypothesis 2 at the overall level. Results are similar and uniformly insupport of Hypothesis 2 when analysis is extended to each sample year. For exam-ple, focusing on the last two years when VL optimism is minimal and for whichuse of price-based models as a benchmark is most appropriate, the median signedprediction errors of 2.89 percent and −1.41 percent for RIM1 are smaller than −40.06percent and −43.32 percent (−36.27 percent and −39.98 percent) for RIM 0(RIM2), respectively, again significant at the 1 percent level. Over the same twoyears, DCF1 is also associated with considerably smaller median signed predictionerrors than DCF0 and DCF2 (1.43 percent versus −42.48 percent and −31.07 percentin 1995; −1.95 percent versus −47.81 percent and −37.86 percent in 1996).


TA
BL

E 4

Test

s of

Hyp

othe

sis

2*: M

edia

n si

gned

and

abs

olut

e pr

edic

tion

erro

rs f

or th

e pr

ice-

base

d an

d no

n–

pric

e-ba

sed

valu

atio

n m

odel

s†

Pan

el A

: M

edia

n si

gned

pre

dict

ion

erro

rs (

bias

) —

Ove

rall

and

by y

ear

Cur

rent

sto

ck p

rice

2826

2628

2932

DC

F129

.181

4.82

27.8

7311

.95

27.5

745.

8629

.274

5.19

30.1

121.

4331

.513

−1.9

5D

CF0

15.7

68−4

1.34

16.4

78−3

3.84

14.3

03−4

0.25

15.5

52−4

2.77

16.1

03−4

2.48

17.0

84−4

7.81

DC

F219

.062

−30.

5019

.880

−18.

4416

.683

−30.

7418

.382

−32.

6219

.283

−31.

0720

.348

−37.

86Te

sts

of H

ypot

hesi

s 2

DC

F1-D

CF0

44.0

0‡43

.24‡

45.6

8‡44

.59‡

42.4

2‡42

.55‡

DC

F1-D

CF2

33.1

7‡29

.19‡

34.5

0‡35

.28‡

31.7

1‡33

.32‡

DC

F0-D

CF2

−10.

67‡

13.9

2‡−1

0.28

‡−1

0.06

‡−1

0.25

‡−9

.52‡

RIM

129

.104

4.73

28.1

2611

.72

27.4

435.

8428

.994

4.60

30.3

302.

8931

.479

−1.4

1R

IM0

17.0

42−3

7.95

17.9

98−2

7.17

15.2

12−3

7.52

16.6

47−3

9.04

17.2

38−4

0.06

18.3

47−4

3.32

RIM

217

.918

−34.

3619

.170

−21.

7015

.775

−34.

5817

.460

−35.

8018

.189

−36.

2719

.636

−39.

98Te

sts

of H

ypot

hesi

s 2

RIM

1-R

IM0

40.8

4‡38

.42‡

43.4

2‡42

.21‡

39.5

3‡40

.72‡

RIM

1-R

IM2

37.3

8‡32

.67‡

40.7

9‡39

.04‡

36.8

9‡37

.23‡

RIM

0-R

IM2

−3.3

7‡−5

.23‡

−3.0

7‡−2

.91‡

−3.1

1‡−3

.26‡

(The

tabl

e is

con

tinue

d on

the

next

pag

e.)

1992

–96

1992

1993

1994

1995

1996

Med

ian,

$M

edia

n,%

Med

ian,

$M

edia

n,%

Med

ian,

$M

edia

n,%

Med

ian,

$M

edia

n,%

Med

ian,

$M

edia

n,%

Med

ian,

$M

edia

n,%



TAB

LE

4 (

Con

tinue

d)

Pan

el B

: M

edia

n ab

solu

te p

redi

ctio

n er

rors

(ac

cura

cy)

— O

vera

ll an

d by

yea

r

Cur

rent

sto

ck p

rice

2826

2628

2932

DC

F129

.181

13.7

127

.873

14.7

727

.574

14.2

429

.274

12.4

930

.112

13.5

631

.513

13.8

2D

CF0

15.7

6842

.81

16.4

7836

.87

14.3

0341

.19

15.5

5243

.60

16.1

0342

.87

17.0

8448

.64

DC

F219

.062

35.4

819

.880

30.1

516

.683

34.2

918

.382

35.3

819

.283

35.6

120

.348

40.0

2Te

sts

of H

ypot

hesi

s 2

DC

F1-D

CF0

−28.

11‡

−21.

25‡

−26.

41‡

−30.

75‡

−28.

21‡

−33.

20‡

DC

F1-D

CF2

−20.

32‡

−13.

97‡

−17.

66‡

−22.

41‡

−21.

04‡

−24.

91‡

DC

F0-D

CF2

7.96

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83‡

7.93

‡7.

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7.67

‡8.

15‡

RIM

129

.104

14.1

828

.126

15.5

627

.443

14.8

228

.994

13.0

830

.330

14.0

431

.479

13.4

2R

IM0

17.0

4238

.80

17.9

9829

.88

15.2

1238

.24

16.6

4739

.24

17.2

3840

.72

18.3

4743

.39

RIM

217

.918

36.4

219

.170

29.1

115

.775

36.2

517

.460

37.1

018

.189

38.6

319

.636

40.1

1Te

sts

of H

ypot

hesi

s 2

RIM

1-R

IM0

−25.

55‡

−13.

09‡

−25.

97‡

−27.

18‡

−26.

58‡

−29.

91‡

RIM

1-R

IM2

−22.

62‡

−10.

90‡

−21.

67‡

−24.

12‡

−25.

32‡

−26.

79‡

RIM

0-R

IM2

2.61

‡3.

22‡

2.39

‡2.

36‡

2.47

‡2.

76‡

(The

tabl

e is

con

tinue

d on

the

next

pag

e.)

1992

–96

1992

1993

1994

1995

1996

Med

ian,

$M

edia

n,%

Med

ian,

$M

edia

n,%

Med

ian,

$M

edia

n,%

Med

ian,

$M

edia

n,%

Med

ian,

$M

edia

n,%

Med

ian,

$M

edia

n,%



Turning to accuracy, for the entire sample period, the median absolute predictionerrors for DCF1 and RIM1 are significantly lower than those for the correspondingnon–price-based models. The contrast for DCF is 13.71 percent versus 42.81 per-cent and 35.48 percent, and that for RIM is 14.18 percent versus 38.80 percent and36.42 percent (see panel B), lending strong support for Hypothesis 2. The resultsare equally strong at the year-by-year level.

Evidence on the relative performance of RIM versus DCF with ad hoc growthassumptions in the terminal value expression is mixed. At an assumed growth rateof 0 percent, RIM is less biased and more accurate than DCF overall (i.e., −37.95percent versus −41.34 percent; 38.80 percent versus 42.81 percent); whereas theconverse is true when the growth rate is assumed to be 2 percent (i.e., −34.36 per-cent versus −30.50 percent; 36.42 percent versus 35.48 percent). Similar patternscan also be found in each of the five sample years. These results are to be con-trasted with analogous pair-wise comparisons between RIM and DCF when theideal terminal price forecasts are employed. As reported under the heading “Resultsfrom tests of Hypothesis 1”, above, RIM1 does not dominate, nor is it dominatedby DCF1 for most of the annual comparisons of median signed and absolute pre-diction errors. Thus, the conclusion by P&S 1998 and Francis et al. 2000 that RIMoutperforms DCF would appear to be quite sensitive to the growth assumptionmade about valuation attributes and the way terminal values are measured.

As sensitivity tests of Hypothesis 2, we repeat the analysis under the alterna-tive, albeit similarly ad hoc, growth assumptions of 4 percent, 6 percent, 8 percent,and 10 percent for DCF employed in Francis et al. 2000. The results indicate that themedian absolute prediction errors for DCF1 continue to be lower than the corre-sponding ad hoc growth models. The median differences are −17.41 percent, −24.20percent, −58.98 percent, and −154.40 percent, respectively, all significant at the 1percent level. For RIM, we use Gebhardt, Lee, and Swaminatham’s 2001 fade-rateprocedure to generate the alternative ad hoc growth assumption. For each samplefirm-year observation, the linear fade rate is defined as the rate at which a firm’sabnormal return on equity at the horizon will converge to the industry average evenly

TABLE 4 (Continued)

Notes:* Hypothesis 2 states that the terminal value expression that employs VL’s forecasted

price will have the lowest prediction errors within each class of the DCF and RIM models. Wilcoxon signed rank tests are employed to test the difference in median signed/absolute prediction errors.

† Signed prediction errors are calculated as ( − Pit)/Pit and absolute prediction errors are calculated as | − Pit|/Pit, where Pit is the recent stock price published in the VL forecast report; and is the intrinsic value estimate per share for security i in year t calculated under M = DCF1, DCF0, DCF2, RIM1, RIM0, and RIM2, described in the appendix.


IV itM

IV itM

IV itM



over a seven-year period beyond the forecast horizon. The median difference inabsolute prediction errors between RIM1 and the fade-rate-based RIM model(denoted RIMf) is −35.82 percent, in favor of RIM1. The corresponding mediansigned difference (i.e., RIM1 − RIMf) is 52.07 percent, implying that RIMf seri-ously understates the post-horizon goodwill projected by VL.

Taken together, these results are strongly in support of the prediction ofHypothesis 2, and suggest that the researcher should exercise care in interpretingresults based on models that employ ad hoc terminal value expressions, becauseintrinsic value estimates in these models can be severely downward biased. Thisobservation applies to studies such as Frankel and Lee 1998, who use a simple per-petuity expression for their RIM terminal values to identify mispriced securitiesand profitable trading strategies; and Gebhardt et al. 2001, who use a simple fade-rate procedure for their RIM terminal values in order to solve for a firm’s ex antecost of capital implied by the RIM intrinsic value estimates and current stock price.

As with tests of Hypothesis 1, the researcher needs to deal with several poten-tial sources of inconsistency in testing Hypothesis 2. First, we adopt the approachrecommended by L&O 2001 to extrapolate valuation attributes in the first yearbeyond the forecast horizon (see section 3, above). However, we also repeat theanalysis using the approach commonly employed in the “horse race” literature byredefining year t + 6 abnormal earnings as year t + 5 abnormal earnings multiplied by(1 + g) (see P&S 1998 and Francis et al. 2000). The results (not reported in a table)are qualitatively the same across these two extrapolation methods. For example,focusing on accuracy, the median absolute prediction errors for RIM2 and DCF2now become 37.25 percent and 37.42 percent, compared with the correspondingfigures of 36.42 percent and 35.48 percent reported previously in panel B of Table4. The prediction of Hypothesis 2 is once again strongly supported at the 1 percentlevel, implying that our earlier conclusion about the superiority of models usingVL terminal price forecasts over non–price-based models within the same familyare robust to the manner in which ad hoc growth rates are applied to the terminalvalue expressions. Second, 8 (49) firm-year observations have negative intrinsicvalues under RIM0 (DCF0) and 9 (34) under RIM2 (DCF2). For these firms,unless negative intrinsic values are capped at zero, comparing across the price-based and non–price-based models would overstate the difference due to limited lia-bility constraints. Notwithstanding this capping requirement, it should be notedthat all the results continue to hold when the restriction is relaxed. Third, firmsmight have reached a steady state prior to the horizon potentially affecting tests ofHypothesis 2. To rule out this possibility, we delete 202 observations whose abnor-mal earnings change signs from positive to negative before the horizon and repeatthe analysis presented in Table 4. The results (not reported in a table) are similarqualitatively. For example, differences in the median absolute prediction errors are−27.09 percent, −18.93 percent, −24.65 percent, and −21.90 percent for DCF1 −DCF0, DCF1 − DCF2, RIM1 − RIM0, and RIM1 − RIM2, respectively. Wilcoxonsigned rank tests again all support Hypothesis 2 at the 1 percent level.



Regression analyses

Panels A and B of Table 5 report results from the pooled GLS panel regressions ofcontemporaneous stock prices on intrinsic value estimates for DCF and RIM models,respectively. For this analysis and that reported in Table 6, we use the GLS proce-dure because standard tests reject homoscedasticity of model residuals obtainedfrom OLS regressions using share-deflated variables.21 The GLS procedure trans-forms the data to correct for heteroscedasticity and removes autocorrelation from theresiduals (Kmenta 1986). While GLS does not correct for cross-sectional correlationin residuals, any such correlation is unlikely to represent a serious departure fromstandard assumptions, given modest calendar and industry clustering in our sample.

Several results from Table 5 confirm the impressions obtained previously.First, as a benchmark model, the results for DCF1 are striking. While the slopecoefficient of 0.966 differs significantly from a theoretical prediction of unity at the1 percent level, the R2 of 93.71 percent suggests that the measurement error result-ing from using VL terminal price forecasts as a proxy for market expectations ismodest. Second, the R2s of 93.71 percent and 93.04 percent for the DCF1 andRIM1 models are quite close, implying that these models apparently have similarability to explain cross-sectional variation in current stock price. To test for thepair-wise difference in R2s, we compute the Vuong Z-statistic (Dechow 1994) forDCF1 versus RIM1 and cannot reject the null of no difference at the 5 percentlevel.22 This result lends further support for the prediction of Hypothesis 1 that,with ideal terminal value expressions, the choice of valuation models is a matter ofindifference. Third, the R2s are considerably higher for the price-based models,compared with their non – price-based counterparts. For the DCF models, theformer is 93.71 percent, and the latter are 67.95 percent and 60.46 percent forDCF0 and DCF2, respectively. The corresponding figures for RIM are 93.04 per-cent versus 79.65 percent and 77.02 percent, respectively. Thus, both price-basedvaluation models appear to be far more successful in explaining the variability ofcurrent stock price than the non–price-based models within the same family, aresult consistent with the prediction of Hypothesis 2. Fourth, the R2s for the non–price-based RIM models are considerably higher than those for the non–price-basedDCF models (i.e., 79.65 percent versus 67.95 percent and 77.02 percent versus 60.46percent, based on the 0 percent and 2 percent growth assumptions, respectively),implying that RIM is superior to DCF in situations where terminal price forecastsare not available.

Panels A and B of Table 6 present evidence on the incremental explanatorypower of various components of intrinsic value estimates for the DCF and RIMmodels, respectively. Comparing across variants within the same family of DCFand RIM valuation models, we find that the overall R2 is at its highest level inDCF1 and RIM1 (i.e., 93.40 percent versus 67.68 percent and 63.66 percent forDCF; 92.79 percent versus 81.11 percent and 80.52 percent for RIM), establishingonce again the superiority of price-based models over their non–price-based coun-terparts (i.e., Hypothesis 2).




TAB

LE

5

Pool

ed G

LS

pane

l reg

ress

ion

of c

onte

mpo

rane

ous

stoc

k pr

ices

on

intr

insi

c va

lue

estim

ates

*

Pan

el A

Inte

rcep

t0.

162

1.10

115

.604

52.2

72‡

16.1

6150

.076

‡

IV0.

966

176.

740‡

−6.2

45‡

0.89

966

.692

‡−7

.485

‡0.

706

56.6

38‡

−23.

643‡

R2

93.7

1 %

67.9

5 %

60.4

6 %

Pan

el B

Inte

rcep

t0.

598

3.88

6‡9.

943

34.7

96‡

11.3

4138

.305

‡

IV0.

950

167.

520‡

−8.7

41‡

1.10

790

.630

‡8.

753‡

0.97

183

.851

‡−2

.478

‡

R2

93.0

4 %

79.6

5 %

77.0

2 %

Not

es:

*M

odel

: Pit =

a0

+ a 1

+ e i

t. T

he s

lope

coe

ffici

ent o

n ea

ch o

f th

e in

trin

sic

valu

e es

timat

es is

pre

dict

ed to

be

1, w

here

is th

e in

trin

sic

valu

e es

timat

e pe

r sh

are

for

firm

i in

yea

r t c

alcu

late

d un

der

M =

DC

F1, D

CF0

, DC

F2, R

IM1,

RIM

0, a

nd R

IM2,

des

crib

ed in

the

appe

ndix

.

†D

TV

is th

e di

scou

nted

term

inal

val

ue p

er s

hare

giv

en b

y th

e la

st c

ompo

nent

of

valu

atio

n m

odel

s de

scri

bed

abov

e.

‡Si

gnifi

cant

at t

he 1

per

cent

leve

l.

Pric

e-ba

sed

DT

V†

Non

–pr

ice-

base

d D

TV

† , g

= 0

%N

on–

pric

e-ba

sed

DT

V† ,

g =

2%

Coe

ffici

ent

t-st

atis

tics

H0:

aj =

0t-

stat

istic

sH

0: a

j = 1

Coe

ffici

ent

t-st

atis

tics

H0:

aj =

0t-

stat

istic

s H

0: a

j = 1

Coe

ffici

ent

t-st

atis

tics

H0:

aj =

0t-

stat

istic

s H

0: a

j = 1

DC

F1D

CF0

DC

F2

Pric

e-ba

sed

DT

V†

Non

–pr

ice-

base

d D

TV

† , g

= 0

%N

on–

pric

e-ba

sed

DT

V† ,

g =

2%

Coe

ffici

ent

t-st

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H0:

aj =

0t-

stat

istic

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0: a

j = 1

Coe

ffici

ent

t-st

atis

tics

H0:

aj =

0t-

stat

istic

s H

0: a

j = 1

Coe

ffici

ent

t-st

atis

tics

H0:

aj =

0t-

stat

istic

s H

0: a

j = 1

RIM

1R

IM0

RIM

2

IVitM

IVitM

TA
BL

E 6

Pool

ed G

LS

pane

l reg

ress

ion

of c

onte

mpo

rane

ous

stoc

k pr

ices

on

the

com

pone

nts

of in

trin

sic

valu

e es

timat

es*

Pan

el A

Inte

rcep

t0.

038

0.25

715

.443

49.0

50‡

16.1

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86.9

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15.6

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58.2

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2.39

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1.12

829

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290‡

15.4

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DT

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−8.2

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760

27.7

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16.0

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Pan

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3.14

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30.7

49‡

8.99

030

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TV

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0.63

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0.45

717

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R2

92.7

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80.5

2%

(The

tabl

e is

con

tinue

d on

the

next

pag

e.)

Pric

e-ba

sed

DT

VN

on–

pric

e-ba

sed

DT

V, g

= 0

%N

on–

pric

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DT

V, g

= 2

%

Coe

ffici

ent

t-st

at.

H0:

α j =

0

t-st

at.

H0:

α j =

1In

crem

enta

lR

2†C

oeffi

cien

t

t-st

at.

H0:

α j =

0

t-st

at.

H0:

α j =

1In

crem

enta

lR

2†C

oeffi

cien

t

t-st

at.

H0:

α j =

0

t-st

at.

H0:

α j =

1In

crem

enta

lR

2†

DC

F1D

CF0

DC

F2

Pric

e-ba

sed

DT

VN

on–

pric

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sed

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V, g

= 0

%N

on–

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DT

V, g

= 2

%

Coe

ffici

ent

t-st

at.

H0:

α j =

0

t-st

at.

H0:

α j =

1In

crem

enta

lR

2†C

oeffi

cien

t

t-st

at.

H0:

α j =

0

t-st

at.

H0:

α j =

1In

crem

enta

lR

2†C

oeffi

cien

t

t-st

at.

H0:

α j =

0

t-st

at.

H0:

α j =

1In

crem

enta

lR

2†

RIM

1R

IM0

RIM

2



At the component level, the incremental explanatory power of DTV is highestwhen VL price forecasts are used in the terminal value calculations. For instance,DTV explains 45.81 percent (15.38 percent) of the cross-sectional variations incontemporaneous stock prices in DCF1 (RIM1), but only 20.09 percent (3.70 per-cent) and 16.07 percent (3.11 percent) for DCF0 (RIM0) and DCF2 (RIM2),respectively. These results imply that VL forecasts of (P − FA) or (P − B) are farless noisy than the non–price-based DTVs in capturing post-horizon goodwill,confirming the impression from Table 1 that DTV accounts for the lion’s share ofintrinsic value estimates in the price-based valuation models. In both DCF andRIM, the coefficients on DTV are much closer to the theoretical prediction of unityin the price-based models than in the non–price-based models (i.e., 0.942 versus0.760 and 0.530 for DCF; 0.945 versus 0.630 and 0.457 for RIM). However, thetheoretical prediction of unity is rejected for all the slope coefficients at the 1 percentlevel.

When the comparisons are made across families of valuation models, theoverall R2s appear to be similar when VL terminal price forecasts are employed(i.e., 93.40 percent and 92.79 percent for DCF1 and RIM1, respectively). A Vuongtest fails to reject the null of no difference in R2 between DCF1 and RIM1 at theconventional levels of significance. This result is consistent with the prediction ofHypothesis 1. Similar to the evidence presented in Table 5, the non–price-basedRIM models continue to have higher overall R2 than the corresponding DCF,regardless of the growth assumption (i.e., 81.11 percent versus 67.68 percent given0 percent growth; 80.52 percent versus 63.66 percent given 2 percent growth).

TABLE 6 (Continued)

Notes:* Model for DCF is Pit = α 0 + α1FAit + α 2PVit + α 3DTVit + εit and model for RIM is

Pit = α 0 + α1Bit + α2PVit + α 3DTVit + εit , where Pit is the recent stock price published in the VL forecast report; FA is the net financial assets per share (i.e., cash and marketable securities minus debt and preferred equity); B is the book value of owner’s equity per share; PV is the present value of operating cash flows to common shareholders or abnormal earnings to the horizon, on a per-share basis, under the discounted cash flows (DCF) or residual income model (RIM), respectively; and DTV is the discounted terminal value per share given by the last component under DCF1, DCF0, DCF2, RIM1, RIM0, and RIM2.

† Incremental R2 is calculated as the difference between R2 for the full model and R2 for the model excluding the variable in question.


§ Significant at the 5 percent level.



Sensitivity analyses

Analysis based on VL’s uncertainty about future stock prices

As discussed in section 4, the target price range at the forecast horizon reflectsVL’s uncertainty about future stock prices. In particular, uncertainty is directlyrelated to the width of the range. A priori, one would expect to see larger predictionerrors and a diminished edge of the price-based valuation models over those thatemploy non–price-based terminal value expressions, when VL is less certain aboutthe future. To gain some insight into this issue and provide indirect evidence thatVL target price forecasts are judgemental in nature, we rank our sample observa-tions pooled over the 1992–96 period in ascending order according to the degreeof uncertainty facing VL, where uncertainty is measured as the difference betweenthe two endpoints of the range, scaled by the mid-point.

Focusing on accuracy, we first compute the median absolute prediction errorsfor the top (i.e., most certain) and bottom (i.e., least certain) quartiles. The figuresfor DCF1 and RIM1 are 12.40 percent versus 16.22 percent and 12.43 percent versus16.64 percent, respectively. Wilcoxon two-sample tests of pair-wise comparisonsacross the top and bottom quartiles for each of the two price-based models are allsignificant at the 1 percent level, implying that VL target price forecasts are lessrepresentative of the investor beliefs impounded in the current market price asuncertainty increases.

Next, we compute the difference in the median absolute prediction errorsbetween DCF1 and DCF0, and RIM1 and RIM0 within the same quartile. Thedifferences for the top and bottom quartiles are −29.14 percent and −22.99 per-cent (−27.18 percent and −18.23 percent) for DCF1 − DCF0 (RIM1 − RIM0),respectively. A negative difference reflects greater representativeness of the price-based valuation model, compared with the corresponding ad hoc 0 percent growthmodel. We then contrast the pair-wise differences for the same family across thetop and bottom quartiles using a Wilcoxon two-sample test, and find it to be signif-icant for both DCF and RIM models at the 1 percent level. The result is similar forinterquartile comparison of RIM1 − RIM2, whereas an analogous comparison ofDCF1 − DCF2 is not statistically significant at any conventional level. Theseresults once again suggest a generally declining representativeness edge of price-based valuation models over their non–price-based counterparts when VL facesgreater uncertainty about the future, confirming our earlier understanding based onconversations with VL analysts that VL price forecasts are judgemental, rather thanmechanical, in nature.

Analysis based on Fama-French industry cost of equity

Following the convention in the literature, we have addressed the issue of risk bydiscounting a stream of future flows of valuation attributes (i.e., cash flows andabnormal earnings) at a risk-adjusted discount rate. As discussed in section 4, eachfirm’s risk premium is calculated as the product of VL firm-specific beta and anassumed market premium. Feltham and Ohlson (1999) point out that this approachis ad hoc and lacks theoretical foundation. The conceptually preferred method



would involve adjusting valuation attributes for risk and then discounting theresulting expressions at a riskless rate. However, implementing the certainty equiv-alence approach advocated by Feltham and Ohlson is difficult in practice.

As an alternative, we reperform the analysis using Fama and French’s 1997industry costs of equity. This requires that we first classify our sample firms intoone of the 48 industries described in Appendix A of Fama and French (179–81),and then use industry risk premiums from the five-year rolling three-factor model(see last column, Table 7 of Fama and French, 172–3). The results (not reported ina table) are very similar to those reported previously in Tables 3–6, and providecomfort that the findings of this study are unlikely to be driven by the way we capturerisk.

6. Conclusion

Prior studies by Penman and Sougiannis 1998 and Francis et al. 2000 have com-pared the bias and accuracy of the non–price-based DCF and RIM models, meas-ured in terms of the signed and absolute prediction errors, respectively, andconcluded that RIM outperforms DCF. In this study, we provide evidence to showthat these findings need not hold when Penman’s 1997 theoretically “ideal” termi-nal value for each model is employed. Using Value Line terminal stock price fore-casts at the horizon to proxy for such values, we explore the empirical equivalenceof DCF and RIM over a five-year valuation horizon under the assumptions that anymeasurement error in VL price forecasts is “neutral” across these valuation mod-els, and that we have avoided the errors that can impede a comparison of suchmodels. For the overall sample, the median absolute prediction errors are 13.71percent and 14.18 percent for DCF1 and RIM1, respectively. Thus, focusing onaccuracy, RIM does not dominate DCF when the ideal terminal values are employed.

Contrasting intrinsic values for models employing terminal price forecasts withthose that do not, we find that, for both DCF and RIM, the price-based valuationmodels outperform the corresponding non–price-based models by a wide margin.Of course, using VL price forecasts as the appropriate benchmark is invalid if suchforecasts are optimistic. However, even for the last two years of our sample (1995–96)when the optimism in VL price forecasts has abated to a negligible level, our mediansigned prediction error evidence continues to indicate a serious downward biaswhen ad hoc terminal value expressions are used. These results imply that research-ers who study the ex ante cost of capital or trading strategies using ad hoc terminalvalue expressions for RIM should exercise care in interpreting their results.

Replacing VL terminal price forecasts with conventional terminal valueexpressions using ad hoc growth estimates, similar to those employed by P&S1998 and Francis et al. 2000, we are able to replicate their findings that RIM out-performs DCF. For example, when regressing current stock prices on intrinsic val-ues, the R2 is highest in RIM, compared with DCF (e.g., 79.65 percent versus67.95 percent, and 77.02 percent versus 60.46 percent under 0 percent and 2 per-cent growth assumptions, respectively). The superiority of RIM over DCF whenthe ideal terminal value is not available is explained by P&S 1998 as follows: cur-rent book values of owner’s equity bring future cash flows forward and leave rela-



tively little value to be captured in the conventional terminal value expressions;whereas the DCF model expenses operating assets and defers most of the value tobe captured at the horizon. For example, under a 0 percent (2 percent) growthassumption, 20.77 percent (25.53 percent) of intrinsic value for RIM is derivedfrom discounted terminal value, and the corresponding figure for DCF is 91.81percent (93.19 percent).

Any “horse race” between RIM and DCF may be biased against DCF becauseof the inherent limitations in estimating the Copeland et al. 1995 version of thefinance free cash flow model, an approach employed by Francis et al. 2000 using VLdata. To address this issue, we estimate a version of DCF introduced by Penman1997. This alternative specification is better suited to VL’s data because the valuationattribute, free cash flows to common, is available from VL and there is no need toestimate the WACC. Nevertheless, we caution that implementing Penman’s versionof DCF empirically using VL data may still contain measurement errors because VLdoes not provide forecasts of either deferred income taxes or cash tied up in workingcapital. Given these practical limitations of estimating DCF, it is quite remarkablethat we were able to establish the approximate equivalence between DCF1 andRIM1.

For students of financial statement analysis, our paper contains several impor-tant messages. We agree with P&S 1998 and Francis et al. 2000 that RIM outper-forms DCF when ideal terminal values are not available. However, we also showthat these models are empirically equivalent given ideal terminal values. Thus, inour view, the main focus of valuation analysis should be improving forecasts ofattributes beyond a finite horizon. Post-horizon forecasts of free cash flows orabnormal earnings can easily articulate across valuation approaches and ultimatelyarticulate back to the benchmark model of forecasting the present value ofexpected dividends. A reliable “set” of post-horizon forecasts of valuationattributes for DCF and RIM gives the analyst the key to valuation, namely, a reli-able price forecast at the horizon. Hence, the dilemma over which valuation modelto use is replaced by the challenge of forecasting post-horizon valuation attributes.

This study has focused on the pricing errors and viewed market efficiency as amaintained assumption. As an avenue for future research, tests for equivalencecould be conducted with future excess returns. Under the null of equivalence, valu-ation models using ideal terminal value expressions should generate mispricingsignals (i.e., intrinsic value minus price) that yield identical excess returns whentrading strategies are implemented.



Appendix

Summary of valuation models and notations

Valuation models

DCF1: Wt(DCF1) = FAt + [Ct + τ − It + τ + i t + τ − (R − 1)FAt + τ − 1]

+ R−TEt(Pt + T − FAt + T)

DCF0: Wt(DCF0) = FAt + [Ct + τ − It + τ + i t + τ − (R − 1)FAt + τ − 1]

+ R−T(R − 1)−1Et[Ct + T + 1 − It + T + 1 + i t + T + 1 − (R − 1)FAt + T]

DCF2: Wt (DCF2) = FAt + [Ct + τ − It + τ + i t + τ − (R − 1)FAt + τ − 1]

+ R−T(R − 1 − g)−1Et [Ct + T + 1 − It + T + 1 + i t + T + 1 − (R − 1)FAt + T]

RIM1: Wt(RIM1) = Bt + ( ) + R−TEt(Pt + T − Bt + T)

RIM0: Wt(RIM0) = Bt + ( ) + R−T(R − 1)−1Et( )

RIM2: Wt(RIM2) = Bt + ( ) + R−T(R − 1 − g)−1Et( )

Notations

Wt = Intrinsic value estimates per share under DCF1, DCF0, DCF2, RIM1, RIM0, and RIM2.

R = One plus the cost of equity.

Pt + T = VL’s forecasted price at the horizon, t + T.

Ct +τ = Operating cash flows, on a per-share basis, for forecast year t + τ.

It +τ = Capital expenditures, on a per-share basis, for forecast year t + τ.

i t +τ = Interest flow from net financial assets for forecast year t + τ, on a per-share basis. It represents interest paid (earned), including preferred dividends, if net financial assets are negative (positive).

Rτ–Et

τ 1=

T

∑

Rτ–Et

τ 1=

T

∑

Rτ–Et

τ 1=

T

∑

Rτ–Et

τ 1=

T

∑ Xt τ+a

Rτ–Et

τ 1=

T

∑ Xt τ+a

Xt T 1+ +a

Rτ–Et

τ 1=

T

∑ Xt τ+a

Xt T 1+ +a



= Abnormal income, on a per-share basis.

FAt = Net financial assets per share (i.e., cash and marketable securities minus debt and preferred equity).

Bt = Book value of owner’s equity per share.

In addition, the numerator of the terminal value expression for the DCF0/DCF2 and RIM0/RIM2 models is given by:

Ct + T + 1 − It + T + 1 + it + T + 1 − (R − 1)FAt + T = (1 + g)(Ct + T − It + T + i t + T)

− (R − 1)FAt + T,

and

= (1 + g) − (R − 1)Bt + T ,

respectively.

Endnotes1. The substitution “works” because both DCF and RIM are accounting systems (cash

versus accrual accounting) that obey a clean surplus relation. However, the substitution can just as easily occur in the opposite direction such that one ends up back with PVED. The choice between these three models, for infinite valuation horizons, is a matter of indifference.

2. Some caveats are in order. First, as discussed in section 3, VL forecasts cash flows to common, not operating, cash flows. Second, VL’s definition of cash flows ignores deferred income taxes and changes in working capital. These limitations could bias model comparisons against the DCF model.

3. The 0.67 estimate pertains to the sum of present value of forecasted (P − B) and forecasted abnormal earnings for the last three years of the VL forecast horizon. When the second component is separated, the (unreported) valuation coefficient on terminal forecasts of (P − B), according to Abarbanell and Bernard 2000, is only “slightly higher”.

4. The version of our RIM models that is closest to Sougiannis and Yaekura 2001 is RIM2, which assumes a 2 percent growth rate. As reported in section 5, the median signed and absolute prediction errors for our RIM2 model are −34.36 percent and 36.42 percent, respectively, comparable to those documented by Sougiannis and Yaekura using I/B/E/S data.

5. See Proposition 1 of Feltham and Ohlson 1995 for a reconciliation of the RIM and DCF models when infinite horizons and risk neutrality are assumed.

6. The correction is evident since “i” in (4) denotes the interest expense (income) that will be reported at date t + τ .

7. In both cases, the firm is assumed to have reached a steady state at the horizon. The 2 percent growth rate approximates the rate of inflation during our sample period.

Xt τ+a

Xt T 1+ +a

Xt T+



8. Implicitly, we assume that the residual cash flows from financial assets grow at the same rate as that generated by operating assets. If financial assets were marked to market, expected financial residual cash flows would be zero, and the terminal value would depend only on operating cash flows.

9. The results for the DDM model (not reported in a table) are in fact exactly the same as those under DCF1, which appear in Tables 3–6. See section 5 for an elaboration.

10. To see this, note that if VL simply employs the reciprocal of the equity cost of capital as a forecasted P/E ratio at the horizon, (7a) will collapse to (7b) because (Pt + 5 − Bt + 5) = Xt + 6/re − Bt + 5 = (Xt + 6 − reBt + 5)/re = /re, under the assumption that Pt + 5 = Xt + 6/re.

11. Sectors affected include retail stores and airlines.12. When the VL firm-specific beta is missing, the average VL industry beta at the two-

digit SIC level is used. The historic market premium of 6 percent is appropriate, according to Ibbotson and Sinquefield 1983.

13. For most of our sample firms, f ’s are given by (1/4), implying that the forecast is generally made in the third quarter.

14. Specifically, the first period abnormal earnings for RIM, covering a fraction of the year from forecast (i.e., evaluation) date to the end of forecast year, are = f − [(1 + r) f − 1]Btq , where Btq = Bt + (1 − f )(Xt + 1 − Dt + 1). For DCF, the first period residual financial income is = f (Ct + 1 − It + 1) − [(1 + r) f − 1]FAtq, where FAtq = FAt + (1 − f )(Ct + 1 − It + 1 − Dt + 1). The notation is as defined in the text and summarized in the appendix.

15. VL forecasts to be interpolated using this procedure include cash flows, capital spending, number of common shares outstanding, dividends, and tax rates. In order to preserve CSR in years 3 and 4, we assume that earnings for these two years are equal. Appealing to CSR for years 3 to 5 and solving for Xt + 3 (or equivalently Xt + 4), we get Xt + 3 = Xt + 4 = 1⁄2(Bt + 5 − Xt + 5 + dt + 5 − Bt + 2 + dt + 3 + dt + 4).

16. We use the most recent VL stock price prior to the forecast date as the dependent variable because it represents the market’s evaluation of the firm at the time when VL generates its forecasts. At that time, the conditioning information set of the market and that of VL are approximately synchronous in time. Allowing the passage of time so that market price impounds VL forecasts would introduce a price influenced by subsequent information not available to VL at the forecast date and hence confound inferences.

17. These percentages are very similar to that for DDM (not reported in a table) where 92.28 percent of intrinsic value comes from DTV, implying that dividend payments to the horizon per se are only value relevant at the margin because they represent wealth distribution rather than wealth creation.

18. The impact on the test of Hypothesis 1 is minimal because there is substantial (i.e., 76 percent) overlap in the firms falling in the extreme distributions of DCF1 and RIM1 models.

19. Note that 258 (or 12.27 percent) of our 2,110 sample observations do not satisfy CSR for book values within ±5 percent of book values. This is consistent with Bushee 2001, who reports that for his sample VL’s expectational data “satisfy” a similar CSR condition about 90 percent of the time.

Xt 6+a

Xt 1+a

Xt 1+Yt 1+

a



20. The corresponding median signed prediction errors in Francis et al. 2000 are −42.7 percent and −28.2 percent for DCF0 and RIM0, respectively. They do not report results for DCF2 and RIM2.

21. The results presented in both tables are based on a subset of the original sample, after deleting 35 observations (or seven firms) with studentized residuals exceeding an absolute value of 2.5.

22. As discussed earlier, the Kmenta 1986 GLS procedure is essentially OLS after transforming the data to remove autocorrelation and heteroscedasticity. Since the Vuong test is appropriate for OLS, it is also appropriate for residuals arising from the final-stage regression.

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