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The Ohlson model of evaluation of companies: tutorial for use/O modelo Ohlson de avaliacao de empresas: tutorial para utilizacao.

I. INTRODUCTION

Evaluation of companies is one of the principal demands in research about capital markets (KOTHARI, 2001). Bodie and Merton (2002) and Damodaran (1999) highlight that the ability of evaluating assets with precision is at the heart of the theory of finances because many personal and business decisions can be made by the selection of alternatives that maximize the value. Fernandez (2001) states that the evaluation can be used for various purposes amongst which: to determine the initial price of an IPO (Initial Public Offering); to serve as a parameter of comparison of the shares negotiated in stock exchanges, to quantify the creation of value that is attributable to the executives of the company (and thus give them bonuses); to help in the strategic decision making (decision to continue in the business, to sell, expand, merge or buy other companies).

A series of relevant questions can apply in the task of evaluating an investment: market efficiency, forecasts of analysts and cost of opportunity are some of them. In some models there are attempts to capture the interaction of these questions in evaluation formulas, with methodological approaches that vary in degree of complexity (ii). As to this aspect, Ohlson (1995) presented a formulation derived from the classical conceptions that used accounts variables in the function of evaluation. The structuring was baptized Ohlson Model (MO) and had great impact in the academic research about capital markets.

Acquainted with the intense discussions about this model in foreign literature, the Ohlson model still is an incipient subject in Brazil (LOPES, 2001). Exceptions repose in some few works with predominantly quantitative focus and that in the majority of cases do not consider that which is the innovation proportioned by the model: the premise of the linear informational dynamics. In this sense the article makes an incursion into the Ohlson model with the intuit of proportioning better comprehension of that which it represents and of the way that the variables interact in the evaluation function.

The rest of the study is found organized as follows: section 2 offers the theoretical basis, section 3 describes the methodology applied, section 4 focuses on the Ohlson model (structuring and entries demanded); section 5 demonstrates the extensions to the model and section 6 concludes the work.

II. THEORETICAL BASIS

The theory of finances describes the value of the company in terms of expected future dividends (PENMAN; SOUGIANNIS, 1998), being the model of discount of dividends (MDD) the basic and theoretically correct approach of evaluation (PLENBORG, 2000). Its formal representation is given by:

[p.sub.t] = [[infinity].summation over ([tau] = 1)] [R.sup.-[tau]] [E.sub.t] ([[??].sub.t+[tau]]) (1)

where:

[p.sub.t] is the market value of the company on date t;

[[??].sub.t+[tau]] is assumed to represent the net dividends in t + [tau]

R is the discount rate r (rate free of risk) plus "1", indicated as a constant;

[E.sub.t] means the operator of expectation based on the information available on this date t.

The formula focuses the problem of evaluation in the perspective of the investor: on buying a part of the net worth of the company, the investor expects to receive dividends referent to this portion. The value of the fraction that belongs to him must be equal to the present value of the flow of dividends (ANG; LIU, 1998). With this construction the MDD constitutes the traditional focus for evaluation of companies in the economic and finances literature (ANG; LIU, 1998), being used as foundations in the formulation of other models, as for example the evaluation by the residual profit (ALR). For Lo and Lys (2000), the ALR reposes on the simple hypothesis that the value of the company represents the present value of all future dividends.

The model of evaluation by the residual profit was largely ignored in specialized literature. Its reappearance constitutes a major contribution to modern accounting (LUNDHOLM, 1995). By the use of profits, accountable value of the PL and the relationship Clean Surplus, the MDD is re-written as a model of discount of accountable numbers. In its most far reaching form the model expresses the value of the company as the sum of its capital investments and the present value discounted from the residual profit of its future activities.. Thus,

[p.sub.t] = [b.sub.t] + [[infinity].summation over ([tau] = 1)][R.sup.-[tau]] [E.sub.t] ([x.sup.a.sub.t+[tau]] ) (2)

where:

[b.sub.t] is assumed to represent the accountable value of the PL on date t;

[x.sup.a.sub.t+[tau]] denotes the residual profits in the period t + [tau].

Equation (2) shows that the value of the company can be divided into two parts: one accounts measure of capital invested - [b.sub.t] - and a measure of the value of the expected residual profits--[[infinity].summation over ([tau]=1)] [R.sup.-[tau]] [E.sub.t] ([x.sup.a.sub.t+[tau]]). This last parcel is defined as the present value of the flows of the future economic results still not incorporated into the net worth current accounting. If the firm obtains future results at the same rate as its desired remuneration of the capital (represented by the discount rate r), then the present value of the future residual profits will be zero. In other words, for the companies that do not create or destroy wealth, the variable of relevance for the evaluation will only be its accountable value of the net worth.

In turn, the residual profit of the period t is defined as the amount that the firm gains in excess of the discount rate applied on the accountable value of the PL of the previous period (t - 1). The terminology was motivated by the concept that "normal" profit must be related to the "normal" return on capital invested at the start of the period, that is, the accountable value of the PL on. the date "t-1" (OHLSON, 1995). In this way the "residual" profit is interpreted as the profit (iii) diminished from the charge on the use of capital.

[x.sup.a.sub.t] = [x.sub.t] -r([b.sub.t-1]) (3)

where r is the discount rate and [x.sub.t] the accountable profit (t -1,t).

As described, the concept imposed by equation (3) permits one to conclude that a positive value of residual profit indicates a lucrative period for the company in the measure in which the accountable rate of return exceeds the capital cost of the firm.

To derive ALR from the MDD, two additional premises are necessary (LO; LYS, 2000). The first refers to the adoption of an accounts system that satisfies the relationship Clean Surplus (Clean Surplus Relation--CSR). The CSR is a restriction in the relationship between accountable profits (x), accountable value of the PL (b) and net dividends (d) in the period t (Myers, 1999). Essentially, CSR is a condition imposed so that all the net worth variations transit through the result. Its mathematical notation is given by:

[b.sub.t] = [b.sub.t-1] + [x.sub.t] - [d.sub.t] (4)

This representation of profits is a great advance over the previous constructions (LUNDHOLM, 1995). The formula ties profits and accountable value of the PL in the same equation and implies that the goodwill is equal to the present value of the expected future residual profits (OHLSON, 1995). A consequence of its adoption in ALR is the independence in relation to a specific accounting system. Given a flow of future dividends, the values of [b.sub.t] and of [x.sub.t] can be taken by any random numbers. The assertive is sustained in the fact that [b.sub.t] is updated according to equation (4) and the relationship of evaluation in equation (2) will take charge of producing the present value of the flow of dividends (DECHOW et al., 1999, p. 4).

The second premise to derive the ALR from the MDD is a condition of regularity that imposes that an accountable value of the PL increases at a lesser rate than R.

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

The ALR model connects the evaluation of companies to observable accountable data apart from basing itself on simple mathematical constructions (LO, LYS, 2000). The study promoted by Ohlson (1995) characterizes a model of residual profit similar to the ALR. In spite of the original ALR anteceding the MO by many decades, Ohlson offered the possibility of repositioning the focus of the accounts research on evaluation of companies establishing a formal connection between the ALR and propositions provided by an additional structure denominated linear information dynamic (DIL).

III. METHOLDOLOGY AND SOURCE OF DATA

As to the objectives, the article classifies itself as exploratory research. Beuren (2003, p. 80) highlights that one seeks, with the exploratory study, "[... ] to know the matter with greater depth, so as to make it clearer [...]" and adds: "[... ] to explore a subject means to gather more knowledge [...], as well as to seek new dimensions up to then unknown." (BEUREN, 2003, p. 81). Pinsonneault and Kraemer (1993 apud HOPPEN et al., 1996) highlight that the exploratory research is an elucidative way to analyze new concepts. The study maintains such orientations: it addresses a subject still little explored in national literature and critically analyzes the model in its applicability and empirical testability.

As to the procedures, bibliographical research was used. Cervo and Bervian (1983) teach that the bibliographical research:
   [...] explains a problem from the theoretical references published
   in documents. It can be done independently or as part of
   descriptive or experimental research. Both the cases seek to know
   and analyze the cultural or scientific contributions of the past,
   existent about a determined matter, theme or problem.


In bibliographical research all referential published serves as a source of consultation: articles from periodicals, magazines, books, theses etc (BEUREN, 2003). Given the scarce national literature existent about the Ohlson model, the research was essentially based on foreign publications, notably periodicals (iv) and books. Additionally, a search was made on the world network of computers--Internet--involving key-words about the theme (v).

As to the approach of the problem, the article classifies itself as qualitative research. Beuren (2003, p. 92) highlights that:
   In the qualitative research deeper analyses are conceived in
   relation to the phenomenon that is being studied. The qualitative
   approach aims at highlighting characteristics not observed by means
   of a quantitative study, seeing the superficiality of the latter.


Van Maanen (1983 apud HOPPEN et al., 1996) teaches that the qualitative methodologies are constituted by a set of interpretative techniques. Hoppen et al. (1996) advocate that the qualitative research is complex for being based on words and not on numbers. Now Richardson (1999) highlights that the difference between qualitative and quantitative research is that the latter employs statistical instruments as the basis of the process of analysis of the problem whereas the other does not have this appeal.

IV. THE OHLSON MODEL

4.1 Structuring

Considering the existent theory, Prof. James Ohlson saw the possibility of structuring a model of evaluation sustained by the relationship of clear profit (CSR), where accountable variables had an outstanding role. He orientated himself in the model of evaluation by the residual profit and established 3 premises: (i) the MDD determines the market value considering the neutrality to the risk; (ii) traditional accountancy that satisfies CSR is applied; (iii) the MO defines the stochastic behavior of [x.sup.a.sub.t]. In (i), the premise considers the use of the present value of the future dividends discounted jointly with the property of irrelevance of the dividends to define the share prices. Now in (ii), formula (4) guarantees the consistence of the determination of profit independently of the accounting system adopted.

For the stochastic behavior of [x.sup.a.sub.t] some considerations are necessary. Ohlson (1995) and Lundholm (1995) emphasize that the empirical implications of the model critically depend on this last premise, related to the informational dynamics of the residual profits. Its function is to put restrictions in the Standard model of discount of dividends. Seen from an empirical perspective, the firm continues being evaluated by the MDD with the differential of the nature of the relationship between the current information and the discounted value of the future dividends being established. The stochastic process that defines the third premise is known as Linear Information Dynamics, or dynamics of linear information (DIL) and is given by the equations:

[[??].sup.a.sub.t+1] = [omega][x.sup.a.sub.t] + [v.sub.t] + [[??].sub.1,t+1] (5)

[[??].sub.t+1] = [gamma][v.sub.t] + [[??].sub.2,t+1] (6)

where [x.sup.a.sub.t] is the abnormal profit (or residual profit) for the period "t"; [v.sub.t] means "other information " about expected future residual profits that are observed at the end of period "t" but were still not recognized by the accounting; [omega] and [gamma] are parameters of persistence; [[??].sub.1] and [[??].sub.2] represent the terms of stochastic errors assumed for having mean zero and normal distribution.

The DIL represents the great contribution of Ohlson for the research of evaluation of companies (FUKUI, 2001). Its construction is based on the presupposition that the information about the future residual profits is obtained both from the past series of the abnormal profits and of data still not captured by the accounting (MCCRAE; NILSSON, 2001). The two dynamic equations are combined with CSR to guarantee that all the relevant events relating to the value of the company are absorbed by the profits and accountable value of the PL (OHLSON, 1995). One assumes that [x.sup.a.sub.t] and [v.sub.t] follow a self regressive process of a single interval and that the parameters of persistence - [omega] and [gamma]- are both restricted for being not negative and less than 1.

As to the "Other information", Lundholm (1995) teaches that they refer to non accountable information that proportion a chock in the residual profits in future periods. Ohlson (1995) assumes that [v.sub.t] must be considered as a summary of the relevant events for the evaluation of the company that will still cause an impact on the financial statements. Based on the ALR and on equations (5) and (6), Ohlson obtains the function of evaluation:

[p.sub.t] = [b.sub.t] + [[alpha].sub.1][x.sup.a.sub.t] + [[alpha].sub.2][v.sub.t] (7)

where [[alpha].sub.1] = [omega] / (R - [omega]) and [[alpha].sub.2] = R / (R - [omega]) (R - [gamma]).

With these constructions Ohlson imposed an additional structure in the ALR so that the evaluation could be expressed as a function of the contemporaneous accountable data and no longer only in predictions (LEE, 1999 e LO; LYS, 2000). Differently to some traditional models (MDD and Discounted Cash Flow), the evaluation formula of Ohlson--given by equation (7)--does not require explicit forecasts of future dividends nor of additional premises of calculation of the terminal value (DECHOW et al., 1999).

Two observations related to the coefficients [[alpha].sub.1] and [[alpha].sub.2] help to understand the functionality of the model. For [omega]>0, the two coefficients are positive simply because the predictions [E.sub.t] [[x.sup.a.sub.t+[tau]]], for any [tau]>1, relate positively with [x.sup.a.sub.t] and [v.sub.t]. The extreme case of [omega] = 0 implies that [E.sub.t] [[x.sup.a.sub.t+[tau]]] is independent of [x.sup.a.sub.t] and therefore [p.sub.t] cannot depend on [x.sup.a.sub.t] (OHLSON, 1995). Additionally, the functions [[alpha].sub.1] ([omega]) and [[alpha].sub.2]([onega], [gamma]) react in an increasing way to their arguments, that is, high values of [omega] and [gamma] make [p.sub.t] more sensitive to the realizations of [x.sup.a.sub.] e [v.sub.t].

The MO still incorporates properties of Modigliani and Miller (1961), which are: (i) dividends affect the market value on the dollar-to-dollar basis, implying the premise of the irrelevance of the payment of dividends; (ii) the dividends paid in the current period would negatively influence the expected future profits. Combined, the two properties indicate that the dividends reduce the accountable value of the PL but do not influence the current profit (OHLSON, 1995).

4.2 Entries Required

In the determination of the parameters of the Ohlson model, some of the necessary data is promptly available whereas others must be established. Specifically, the model depends on: (i) three variables: the accountable value of the PL in the current period - [b.sub.t], profits in the current period - [x.sub.t] - and other information in the current period - [v.sub.t]; (ii) three parameters: [omega] and [gamma], which are parameters of persistence, and r, which is the discount rate. Accounts reports--such as the Patrimonial Balance Sheet, Income Statement of the Period and Statement of Changes in the Net Worth--supply the basis for the fixing of the first two variables ([b.sub.t] and [x.sub.t]). The remaining variable ([v.sub.t]) and the three parameters are more difficult to be measured.

Ohlson (1995) offers little or no orientation as to how to obtain the variable [v.sub.t] and the parameters of persistence [omega] and [gamma]. The task therefore remained relegated to future research. In this context diverse methodologies or proxies were suggested in academic works that tested the MO.

4.2.1 Establishing the Discount Rate (r)

In the task of evaluation it is necessary to identify a discount rate that converts flows that will be realized (or one expects they will be realized) into present values. There are various ways of measuring r and the literature about the theme is extensive. Approaches include the cost of own capital, the average pondered cost of capital, the rate of return on the PL or on the asset, amongst others. The detailed discussion of each one of the possible focuses to determine the discount transcends the objective o this article. (vi).

The MO assumes that r is defined in a non stochastic way, considering neutrality to the risk and homogenous beliefs (OHLSON, 1995, p. 665). The discount rate used in various empirical works on the Ohlson model is the rate of return of the Net Worth (DECHOW et al., 1999; FRANKEL; LEE, 1999). Martins (1998) reminds us that this procedure is a debatable point since the investors have difference opinions with respect to the minimum profitability expected for the company.

4.2.2 Establishing Other Information (vt)

Kothari (2001) reminds us that the current performance of the company (such as presented in the accounts reports) is an important, but not the sole, source of information for the evaluation of the market value of the company. Dechow et al. (1999) remind us that for some time the academic literature has recognized that the share prices reflect information about future profits that are not contained in the current profits. Such information cannot be observed directly (OHLSON, 2001, p. 112). Candidates for this "other information" ([v.sub.t]) are new patents, approval of laws for a new medicament in pharmaceutical companies, long term contracts, amongst others (MYERS, 1999). Attempts to incorporate [v.sub.t] within the analysis of evaluation go back at least to the year of 1980 with the work of Beaver et al. (1980).

Ohlson (1995) defines "other information" as a scale variable, however, he does not concretely establish its analytical content. Recently the very Ohlson (2001, p. 112) referred to [v.sub.t] as a "mysterious" variable. The lack of definition of the variable "other information" caused many researchers to neglect its use in the tests on the MO (BEAVER, 1999, p. 38). As to this aspect, Hand (2001, p. 122) highlights that up to 1998 almost all empirical research on the MO disdained the informational content of [v.sub.t]. The few articles that did not leave "aside" the variable "other information" chose an intuitive path instead of a formal construction (examples include AMIR and LEV, 1996 apud HAND, 2001 and MYERS, 1999).

Ohlson (2001) sustains that although there may be an analytical interest in not specifying the value of [v.sub.t], such procedure reduces the empirical content of the MO. He also highlights that consensual forecasts of analysts constitute a reasonable tool to measure the expected future profits and that there is no reasons to eliminate [v.sub.t] from the model since the variable can be based on observable data (vii). Hand (2001) adds that to consider [v.sub.t] equal to zero is to make the "heroic" assertive that the accounts data publicly available are sufficient to explain the share prices.

4.2.3 Establishing the parameters of Persistence ([omega] and [gamma])

The linear dynamics presented by Ohlson (1995) define the relationship between current and future information using a self regressive process of the first order--AR (1). The residual profit of the following period ([x.sup.a.sub.t+1]) is a function of the residual profit of the current period (adjusted by a coefficient of correction denominated parameter of persistence), other information ([v.sub.t]) and a term of error ([[epsilon].sub.1,1+1]). In turn, other information of the following period ([v.sub.t+1]) is a function of other information of the current period (also adjusted by a coefficient of correction) and a term of error ([[epsilon].sub.=2,t+1]). The parameter of persistence of residual profits is indicated by the notation [omega] and [gamma] and the parameter of persistence of other information.

Ohlson does not establish criteria to obtain [omega] or [gamma], restricting himself to declaring that the economic medium and the accounts principles of the company determine the exogenous parameters [omega] and [gamma] (OHLSON, 1995, p. 686). Also institutes that such parameters must not be negative or greater than 1 (one). Such parameters are directly used in the determination of the coefficients of the function of evaluation proposed by Ohlson (1995), as seen in equation (7). The coefficient [[alpha].sub.1] is a function of [omega] and [[alpha].sub.2] is a function of [omega] and [gamma].

In a recent article that addresses the empirical perspective of its model, Ohlson (2001, p. 115) declares that researchers must try to estimate the value of [omega] and [gamma], without indicating how this could or should be done. The work of Dechow et al. (1999) is referenced by Ohlson as one of the empirical studies of the MO that evaluates the attributes of the model in a closer way (OHLSON, 2001, p. 108). In the establishing of the parameters of persistence, Dechow et al. (1999, p. 7) consider the historical sample estimates of [omega] and [gamma].

4.2.4 Establishing the Variables [b.sub.t] and [x.sub.t]

Ohlson (1995) uses well known concepts obtained from accounts reports such as the profit ([x.sub.t]) and the value of the net worth (bt). However, for use of the variables [x.sub.t] and [b.sub.t], the MO imposes a restriction of the relationship Clean Surplus (CSR) (viii), that has direct reflex on the quality of the accounts data.

4.2.5 Source of Data

Implications of regulatory nature determine at times the requirement of publication of accounts statements (ix). Companies and specialized periodicals disclose information about the macroeconomic environment and rates of return, amongst other data of interest. Information providers keep current and historical data as well as forecasts of companies and of market segments.

The availability of computational data bases (relating to the financial information of the companies) stimulated rapid growth in accounting research in the capital market (BROWN, 2001). The United States of America (USA) was pioneer in the construction of these types of data bases (BROWN, 2001). In foreign literaturex, one sees the frequent use of the following sources of data (xi):

1. Forecast of Profits: In the USA there are various entities that undertake to provide the estimate of future profits of companies. Value Line has published its estimates since the decade of the 70's. Standard & Poor's has published its forecasts weekly from 1967 to 1987, in a bulletin called Earnings Forecaster. Other companies that make forecasts of profits are: Institutional Brokers Estimate System (I/B/E/S), originally published by Lynch, Jones and Ryan, and Zacks Investment Research (The Icarus Service).

2. Accounts and Financial Data: COMPUSTAT offers historical data (from 1987) of approximately 22,000 companies headquartered in the USA (active or not). Now the Center for Research in Security Prices (CRSP) is a center of financial research of the University of Chicago that has a data bank of the share market (prices, indexes etc) of companies negotiated in the principal North American Stock Exchanges (NASDAQ, AMEX, NYSE).

4.3 Hypothetical example

The example was developed in the attempt to reproduce an application of the Ohlson model. It should be highlighted that the data and the environment imagined are hypothetical and therefore subject to the limitations inherent to the specifications of this species. One sought to privilege the didactic aspect in detriment to a more rigorous specification (greater horizons of forecast and of the temporal series of profits and net worth, inclusion of forecast of the administration etc).

The scenario where the illations are developed, part of the existence of a metallurgical company, Carol Inc., that has been participating in the industry of metals and laminates for 20 years. An efficient market is admitted in semi-strong form. For the segment of activities an average rate of return on own capital of 7% was seen. Additionally, the following information is supplied in TABLE 1:

The net worth of the company was $100 in the period t-6. Taking the existent information as basis one can obtain the results shown in TABLE 2:

The historical series of TABLE 2 was used for the calculation of the parameter of persistence [omega]. One sees the existence of residual profits in all the periods and their persistence, on average, was approximately 98% in relation to the immediately previous period.

In period t, the company promoted the implantation of a new boiler apart from a training program for the reduction of the waste matter of production, and work accidents. The administration is confident that such actions will have positive repercussion in the productivity of the company. Based on this information the analysts forecast an additional result of $2 per period in Carol Inc. However, it is known that the information of the analysts has a bias (mean) to below -18%. The variable [v.sub.t] was calculated as being $ 2.36 and the parameter of persistence [gamma] equal to one.

The calculation of the coefficients of the formula of evaluation--equation (7)-- returned a value of 10.89 for [[alpha].sub.1] and 169.84 for [[alpha].sub.2]. By the formula the value of the company would be $562.5:

[p.sub.t] =121,5 + (10,89 x 3,69)+(169,84 x 2,36)

[p.sub.t] =562,5

The example offers a notion of how the parameters and variables involved in the Ohlson modeling interact. The formula of evaluation returned the intrinsic value (xii) of the company by the Ohlson model (1995). The comparison of this with the respective market value would be the next step to identify the degree of response offered by the MO for the scenario imagined (xiii).

4.4 Extensions of the Model

Researchers have gone deep into the theoretical study of the MO, with the aim of offering a more consistent basis or to propose modifications in the underlying theory of the Ohlson model. Examples include the treatment of Dirty Surplus items in the model of evaluation (LO; LYS, 2000); the inclusion of more periods in the self regressive process (OTA, 2000); the incorporation of a stochastic rate of interest and aversion to risk (ANG; LIU, 1998); the structuring of a non linear informational dynamic (BIDDLE et al., 2000) etc.

Of the work related to the theory of the MO, those elaborated by the very Prof. James Ohlson, individually or in partnership with other researchers, are highlighted.

--Conservatism, Operational Assets and Growth of the PL: concomitant with the publication of the article that established the structuring of the MO, James Ohlson offered an extension of his model, conceived jointly with Prof. Gerald Feltham. Up to the moment the work of Feltham and Ohlson (1995) represents the most notorious extension of the MO and sometimes is referenced as if it were him (LOPES, 2001). The Feltham-Ohlson model (1995)--MFO--provides a differenced treatment of financial and operational assets for the purposes of evaluation. This separation is done due to the fact that the accountancy for the historical cost differs systematically from the fair value. The dynamic information of the MFO differ from those instituted in the MO, highlighting the inclusion of a coefficient that measures the degree of conservatism of the accountancy and another that defines the parameter of growth of the accountable value of the PL. To reduce the bias contained in the accountable profit (xiv), MFO assumes the premise that the residual profits for financial assets will always be equal to zero. Thus one can simplify the model to focus exclusively on the operational assets. The simplification done, no modification is required for MDD, CSR or ALR. The informational dynamics of the MFO are different than the MO. Whereas this latter counts on only two DILxv, the MFO establishes four;

--Transitory Profits: Ohlson (1999) makes an analysis of the concept of transitory profits, their impact on the evaluation of the company using the ALR and their difference in relation to the other items of profits. He argues that the accounts theory and analysts of accounts reports recognize that some sources of profits can be characterized as transitory and that they need to be separated or eliminated from the income statement of the period. The informational dynamics and the formula of evaluation were modified to include transitory profits, proportioning a way of dealing with this species of profit to estimate the value of the companies;

--Stochastic Interest Rate: the underlying theory of the Ohlson model simplified the role of the risk in the function of evaluation, assuming that the investors are neutral to the risk and interest rates are fixed and non stochastic. Recently, Feltham and Ohlson (1999) demonstrated analytically that it is possible to incorporate the risk both in the MO and in the MFO. The procedure consists of substituting expected future residual profits for equivalent certainties based on the aversion to the risk by the investor between the date and possible events. The pricing of the risk will depend on the appropriate set of information referent to the events and possible dates of the future residual profits, to obtain the equivalent certainties. The study of Feltham and Ohlson (1999), however, is silent in the demonstration of how the investors and researchers can obtain this set of information. The work of Gode and Ohlson (2000) also generalizes the MO to include stochastic interest rates basing itself on the fact that the changes in the interest rates are relevant because they modify perceptions of the long term profits. The most recent study (identified) on the application of the risk in the model of Ohlson is of Baginski and Wahlen (2003).

--Depreciation: Feltham and Ohlson (1996) examined the impact of the policy of depreciation of the company in the relationship between the accounts numbers and the market value of the company. At the start of the discussions the authors warn that the policy of depreciation affects the accountable numbers but does not have effect on the market value of the company. Specifically, whereas the accounting policy must affect the representation of the information received by the investors, Feltham and Ohlson (1996) assume that it does not affect the information relevant value received. The study identified policies of depreciation that provide unbiased or conservative accounting, that is, the goodwill not registered is equal or exceeds "zero" on average respectively. It was also demonstrated that the economic profits are equal (on average) to the accountable profits if the accountancy is not biased or if there is no increase in the value of the PL.

V. CONCLUSIONS

This work proposes to analyze the Ohlson model being that the task consisted of identifying the origin of the model, raising the underlying theory, verifying the entries demanded, to structure a hypothetical example to demonstrate the logic involved in the internal consistency of the linear informational dynamics and finally to identify the state of the art.. During this course diverse points were identified and debated. Part of them is found presented ahead under the title of ascertainments:

1. There is no consensus in the academic literature about the appropriate method to measure the parameters of persistence ([omega] and [gamma]).

2. There are propositions of improving the original conception of the MO by means of extensions to the model. The approach of the conservatism, growth, risk and transitory profits already constituted the list of studies that focalize on the theory relating to the Ohlson model.

3. The Ohlson model propitiated a series of contributions in the academic literature about capital markets: relit the debate around the evaluation by residual profits in the research of evaluation; gave support so that the accounts numbers could be used in models of evaluation; adopted a more desirable focus on the distribution of wealth for an orientation directed to the creation of value for the company; intensified the interest in studies of value relevance that connect accounting variables (accountable value of the PL and profits, principally) the models of evaluation of companies and orientated opportunities for future research as for example studies that focalize variables and parameters of the Ohlson model.

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Cesar Medeiros Cupertino

University of Brasilia

Paulo Roberto Barbosa Lustosa

University of Brasilia

(i) This article weas presented at the 4th USP Congress of Contollership and Accounting.

(ii) One sees the existence of simple models (of the uni-varied way or random- walk) and sophisticated models (of the multi-varied type and self regressive processes of multiple order).

(iii) In this case the ample or far reaching profit (comprehensive income).

(iv) As to the periodicals, the research included the consultation, amongst others, of the following: Contemporary Accounting Research; Journal of Finance; The Accounting Review; Journal of Accounting, Auditing and Finance; Journal of Accounting and Economics; Journal of Accounting Research; Journal of Business.

(v) Some of the terms conssulted were: Residual Income Valuation; Linear Information Model; Linear Information Dynamics; Ohlson's Model; Edwards-Bell-Ohlson; EBO.

(vi) Examples of some approaches (model of three factors and rate of return by industry) can be obtained in the works of Fama and French (1997, 1998).

(vii) Forecasts of analysts for example.

(viii) Described in equation (4).

(ix) In Brazil in the case of limited liability corporations of open capital, this requirement can be conferred in art. 289 of Law 6.404/76 and with the new wording given by Law no. 9.457, of 5.5.1997, which sets forth thus: "The publications ordered by the present Law will be done in the official organ of the Union or the State of the Federal District, according to the place in which the head office of the company is situated, and in another neewspaper of large circulation published in the place in which the head office of the company is situated ".

(x) Particularly North American

(xi) All the providers cited are companies headquartered in the USA.

(xii) According to Myers (1999), "intrinsic value is equal to the present value of the expected future dividends indiferently to the policy of payment of dividends or the quality of the accountable numbers as long as the relationship Clean Surplus is observed ". (our translation and highlighting)

(xiii) Myers (1999) suggests the use of the market value as benchmark for the intrinsic value of the company. In the example, obviously, the degree of response of the Ohlson model to the value of the company (by the market) cannot be identified since it is a question of a hypothetical company.

(xiv) Resulting from the delay in the recognition of economic events by the accountancy.

(xv) See equations (5) and (6).
TABLE 1
Available date of Carol Inc.

                                         Temporal Series
                       t-5    t-4    t-3    t-2    t-1

Profits                10.0   10.1   10.3   10.5   10.7
Dividends              6.0    6.0    6.0    6.0    6.0
Forecast of profit *   8.3    8.4    8.5    8.5    8,6

Note:

* The forecasts ofprofits refer to consensual estimates of analysts.

TABLE 2 Calculated Data of Carol Inc.

                                                    Temporal Series
                                                     t-5     t-4

Net Worth *                                         104.0   108.1
([b.sub.t] = [b.sub.t-1] + [x.sub.t] - [d.sub.t])

Normal Profit **                                    6.00    6.24
([x.sub.t] = [b.sub.t] X 0,07)

Residual Profit                                     4.00    3.86
([x.sup.a.sub.t] = [x.sub.t] - [x.sub.t])

Persistence Residual Profits ***                            0.97
([delta] = [x.sup.a.sub.t] / [x.sup.a.sub.t-1])

Error of Forecast ****                              -0.18   -0.17
(Forecast--Observed) /
Observed

Return on PL (ROE)                                  0.10    0.09
(ROE = [x.sub.t] / [b.sub.t])

ROE Residual *****                                  0.04    0.03
([ROE.sup.res] = ROE - r)

Dividend Payment Rate (k)                           0.60    0.59
(k = [d.sub.t] / [x.sub.t])

                                                    Temporal Series
                                                     t-3     t-2

Net Worth *                                         112.3   116.8
([b.sub.t] = [b.sub.t-1] + [x.sub.t] - [d.sub.t])

Normal Profit **                                    6.49    6.74
([x.sub.t] = [b.sub.t] X 0,07)

Residual Profit                                     3.76    3.76
([x.sup.a.sub.t] = [x.sub.t] - [x.sub.t])

Persistence Residual Profits ***                    0.98    1.00
([delta] = [x.sup.a.sub.t] / [x.sup.a.sub.t-1])

Error of Forecast ****                              -0.17   -0.19
(Forecast--Observed) /
Observed

Return on PL (ROE)                                  0.09    0.09
(ROE = [x.sub.t] / [b.sub.t])

ROE Residual *****                                  0.03    0.03
([ROE.sup.res] = ROE - r)

Dividend Payment Rate (k)                           0.59    0.57
(k = [d.sub.t] / [x.sub.t])

                                                    Temporal Series
                                                          t-1

Net Worth *                                              121.5
([b.sub.t] = [b.sub.t-1] + [x.sub.t] - [d.sub.t])

Normal Profit **                                         7.01
([x.sub.t] = [b.sub.t] X 0,07)

Residual Profit                                          3.69
([x.sup.a.sub.t] = [x.sub.t] - [x.sub.t])

Persistence Residual Profits ***                         0.98
([delta] = [x.sup.a.sub.t] / [x.sup.a.sub.t-1])

Error of Forecast ****                                   -0.20
(Forecast--Observed) /
Observed

Return on PL (ROE)                                       0.09
(ROE = [x.sub.t] / [b.sub.t])

ROE Residual *****                                       0.03
([ROE.sup.res] = ROE - r)

Dividend Payment Rate (k)                                0.56
(k = [d.sub.t] / [x.sub.t])

Notes: * Calculated in accordance with the relationship Clean
Surplus--see equation (4).

** The notation [x.sub.t] was used for normal profit.

*** The notation [delta] was used for the persistence in residual
profits.

**** Calculated in accordance with the methodology suggested by
Francis et al. (2000).

***** roe residual was defined as ROEres and the discount rate as "r".


I. INTRODUCAO

Avaliacao de empresas e uma das principais demandas na pesquisa sobre mercado de capitais (KOTHARI, 2001). Bodie e Merton (2002) e Damodaran (1999) ressaltam que a habilidade de se avaliar ativos com precisao esta no cerne da teoria de financas, porque muitas decisoes pessoais e empresariais podem ser feitas pela "selecao de alternativas que maximizam o valor. Fernandez (2001) afirma que a avaliacao pode ser utilizada para varios propositos, entre eles: determinar o preco inicial da acao em uma IPO (Initial Public Offering); servir como parametro de comparacao das acoes negociadas em bolsas; quantificar a criacao de valor que e atribuivel aos executivos da empresa (e assim bonifica-los); auxiliar na tomada de decisoes estrategicas (decisao de continuar no negocio, vender, expandir, fundir ou comprar outras companhias).

Uma serie de questoes relevantes pode incidir na tarefa de se avaliar um investimento: eficiencia de mercado, previsoes de analistas e custo de oportunidade sao algumas delas. Em alguns modelos, ha tentativas de capturar a interacao dessas questoes em formulas de avaliacao, com abordagens metodologicas que variam em grau de complexidade (ii). Quanto a esse aspecto, Ohlson (1995) apresentou uma formulacao derivada de concepcoes classicas, que utilizava variaveis contabeis na funcao de avaliacao. A estruturacao foi batizada de Modelo de Ohlson (MO) e teve um grande impacto na pesquisa academica sobre mercado de capitais.

A par das intensas discussoes sobre esse modelo na literatura estrangeira, o modelo de Ohlson ainda e um assunto incipiente no Brasil (LOPES, 2001). Excecoes repousam em alguns poucos trabalhos, com enfoque predominantemente quantitativo e que na maioria dos casos nao consideram aquilo que e a inovacao proporcionada pelo modelo: a premissa das dinamicas informacionais lineares. Nesse sentido, o artigo realiza uma incursao no modelo de Ohlson, com o intuito de proporcionar uma melhor compreensao daquilo que ele representa e da maneira como as variaveis se interagem na funcao de avaliacao.

O restante do estudo encontra-se organizado como segue: a secao 2 oferece a fundamentacao teorica, a secao 3 descreve a metodologia aplicada, a secao 4 enfoca o modelo de Ohlson (estruturacao e entradas exigidas); a secao 5 demonstra extensoes ao modelo e a secao 6 conclui o trabalho.

II. FUNDAMENTACAO TEORICA

A teoria de financas descreve o valor da empresa em termos de dividendos futuros esperados (PENMAN; SOUGIANNIS, 1998), sendo o modelo de desconto de dividendos (MDD) a abordagem basica e teoricamente correta de avaliacao (PLENBORG, 2000). Sua representacao formal e dada por:

[p.sub.t] = [[infinity].summation over ([tau] = 1)] [R.sup.-[tau]] [E.sub.t]([[??].sub.t+[tau]])

onde:

[p.sub.t] e o valor de mercado da empresa na data t;

[[??].sub.t + [tau]] e assumido para representar os dividendos liquidos em t + [tau],

R e a taxa de desconto r (taxa livre de risco) mais "1", indicado como uma constante; [E.sub.t] significa o operador de expectativa baseado nas informacoes disponiveis na data t.

A formula focaliza o problema da avaliacao na perspectiva do investidor: ao comprar uma parte do patrimonio liquido da empresa, o investidor espera receber dividendos referentes a essa parcela. O valor da fracao que lhe pertence deve ser igual ao valor presente do fluxo de dividendos (ANG; LIU, 1998). Com essa construcao, o MDD constitui o enfoque tradicional para avaliacao de empresas na literatura economica e de financas (ANG; LIU, 1998), sendo utilizado como fundamentos na formulacao de outros modelos, como por exemplo, a avaliacao pelo lucro residual (ALR). Para Lo e Lys (2000), a ALR repousa na simples hipotese de que o valor da empresa representa o valor presente de todos os dividendos futuros.

O modelo de avaliacao pelo lucro residual foi largamente ignorado na literatura especializada. Seu ressurgimento constitui a maior contribuicao para a contabilidade moderna (LUNDHOLM, 1995). Pelo uso de lucros, valor contabil do PL e a relacao Clean Surplus, o MDD e reescrito como um modelo de desconto de numeros contabeis. Na sua forma mais abrangente, o modelo expressa o valor da empresa como a soma de seus investimentos de capital e o valor presente descontado do lucro residual de suas atividades futuras. Assim,

[p.sub.t] = [b.sub.t] + [[infinity].summation over ([tau] = 1)] [R.sup.-[tau]] [E.sub.t] ([x.sup.a.sub.t + [tau]]) (2)

onde:

[b.sub.t] e assumido para representar o valor contabil do PL na data t;

[x.sup.a.sub.t + [tau]] denota os lucros residuais no periodo t + [tau].

A equacao (2) mostra que o valor da empresa pode ser dividido em duas partes: uma medida contabil de capital investido - [b.sub.t] - e uma medida do valor dos lucros residuais esperados - [[infinity].summation over ([tau] = 1)] [E.sub.t] ([x.sup.a.sub.t + [tau])]. Essa ultima parcela e definida como o valor presente dos fluxos dos resultados economicos futuros ainda nao incorporados ao patrimonio liquido contabil corrente. Se a firma obtem resultados futuros a mesma taxa da sua remuneracao desejada do capital (representado pela taxa de desconto r), entao o valor presente dos lucros residuais futuros sera zero. Em outras palavras, para as empresas que nao criam nem destroem riqueza, a variavel de relevancia para avaliacao sera somente seu valor contabil do patrimonio liquido.

Por sua vez, o lucro residual do periodo t e definido como o montante que a firma ganha em excesso a taxa de desconto aplicada sobre o valor contabil do PL do periodo anterior (t - 1). A terminologia foi motivada pelo conceito de que o lucro "normal" deve ser relacionado com o retorno "normal" sobre o capital investido no inicio do periodo, isto e, o valor contabil do PL na data "t-1" (OHLSON, 1995). Sendo assim, o lucro "residual" e interpretado como o lucro (iii) diminuido do encargo sobre o uso de capital.

[x.sup.a.sub.t] = [x.sub.t] - r([b.sub.t-1]) (3)

onde r e a taxa de desconto e xt o lucro contabil (t - 1,t).

Como descrito, o conceito imposto pela equacao (3) permite concluir que um valor positivo de lucro residual indica um periodo lucrativo para empresa, na medida em que a taxa de retorno contabil excede o custo de capital da firma.

Para derivar ALR do MDD, duas premissas adicionais sao necessarias (LO; LYS, 2000). A primeira refere-se a adocao de um sistema contabil que satisfaca a relacao Clean Surplus (Clean Surplus Relation--CSR). A CSR e uma restricao na relacao entre lucros contabeis (x), valor contabil do PL (b) e dividendos liquidos (d) no periodo t (Myers, 1999). Essencialmente, CSR e uma condicao imposta para que todas as variacoes patrimoniais transitem pelo resultado. Sua notacao matematica e dada por:

[b.sub.t] = [b.sub.t-1] + [x.sub.t] - [d.sub.t] (4)

Essa representacao de lucros e um grande avanco sobre construcoes anteriores (LUNDHOLM, 1995). A formula amarra lucros e valor contabil do PL na mesma equacao e implica que o goodwill e igual ao valor presente dos lucros residuais futuros esperados (OHLSON, 1995). Uma consequencia da sua adocao na ALR e a independencia em relacao a um sistema de contabilidade especifico. Dado um fluxo de dividendos futuros, os valores de [b.sub.t] e de [x.sub.t] podem ser tomados por numeros randomicos quaisquer. A assertiva e sustentada no fato de que [b.sub.t] e atualizado de acordo com a equacao (4) e a relacao de avaliacao na equacao (2) se encarregara de produzir o valor presente do fluxo de dividendos (DECHOW et al., 1999, p. 4).

A segunda premissa para derivar a ALR do MDD e uma condicao de regularidade, que impoe que o valor contabil do PL cresce a uma taxa menor que R.

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

O modelo ALR liga a avaliacao de empresas a dados contabeis observaveis, alem de se apoiar em construcoes matematicas simples (LO, LYS, 2000). O estudo promovido por Ohlson (1995) caracteriza um modelo de lucro residual similar a ALR. Apesar da ALR original anteceder o MO em muitas decadas, Ohlson ofereceu a possibilidade de reposicionar o foco da pesquisa contabil sobre avaliacao de empresas, estabelecendo uma ligacao formal entre a ALR e proposicoes providas por uma estrutura adicional denominada dinamica das informacoes lineares (DIL).

III. METODOLOGIA E FONTE DE DADOS

Quanto aos objetivos, o artigo enquadra-se como pesquisa exploratoria. Beuren (2003, p. 80) salienta que se busca, com o estudo exploratorio, "[...] conhecer com maior profundidade o assunto, de modo a torna-lo mais claro [...]" e complementa: "[...] explorar um assunto significa reunir mais conhecimento [...], bem como buscar novas dimensoes ate entao nao conhecidas." (BEUREN, 2003, p. 81). Pinsonneault e Kraemer (1993 apud HOPPEN et al., 1996) salientam que a pesquisa exploratoria e um modo elucidativo para se analisar novos conceitos. O estudo mantem tais orientacoes: aborda um assunto ainda pouco explorado na literatura nacional e analisa criticamente o modelo na sua aplicabilidade e testabilidade empirica.

Quanto aos procedimentos, utilizou-se a pesquisa bibliografica. Cervo e Bervian (1983) ensinam que a pesquisa bibliografica:
   [...] explica um problema a partir de referenciais teoricos
   publicados em documentos. Pode ser realizada independentemente ou
   como parte da pesquisa descritiva ou experimental. Ambos os casos
   buscam conhecer e analisar as contribuicoes culturais ou
   cientificas do passado existentes sobre um determinado assunto,
   tema ou problema.


Na pesquisa bibliografica, todo referencial publicado serve como fonte de consulta: artigos de periodicos, revistas, livros, teses etc (BEUREN, 2003). Dada a escassa literatura nacional existente sobre o modelo de Ohlson, a pesquisa baseou-se essencialmente em publicacoes estrangeiras, notadamente periodicos (iv) e livros. Adicionalmente, foi realizada busca na rede mundial de computadores--Internet--envolvendo palavras-chave sobre o tema (v).

Quanto a abordagem do problema, o artigo enquadra-se como pesquisa qualitativa. Beuren (2003, p. 92) salienta que:
   Na pesquisa qualitativa concebem-se analises mais profundas em
   relacao ao fenomeno que esta sendo estudado. A abordagem
   qualitativa visa destacar caracteristicas nao observadas por meio
   de um estudo quantitativo, haja vista a superficialidade deste
   ultimo.


Van Maanen (1983 apud HOPPEN et al., 1996) ensina que as metodologias qualitativas sao constituidas por um conjunto de tecnicas interpretativas. Hoppen et al. (1996) advogam que a pesquisa qualitativa e complexa por ser baseada em palavras e nao em numeros. Ja Richardson (1999) ressalta que a diferenca entre a pesquisa qualitativa e a quantitativa e que a ultima emprega instrumentos estatisticos como base do processo de analise do problema, enquanto que a outra nao tem esse apelo.

IV. O MODELO DE OHLSON

4.1 Estruturacao

Considerando a teoria existente, o Prof. James Ohlson vislumbrou a possibilidade de estruturar um modelo de avaliacao, sustentado pela relacao de lucro limpo (CSR), onde variaveis contabeis tivessem papel destacado. Orientou-se no modelo de avaliacao pelo lucro residual e estatuiu 3 premissas: (i) o MDD determina o valor de mercado, considerando a neutralidade ao risco; (ii) aplica-se a contabilidade tradicional que satisfaca CSR; (iii) o MO define o comportamento estocastico de [x.sup.a.sub.t] . Em (i), a premissa considera a utilizacao do valor presente dos dividendos futuros descontados em conjunto com a propriedade de irrelevancia dos dividendos para definir o preco de acoes. Ja em (ii), a formula (4) garante a consistencia da determinacao do lucro, independente do sistema de contabilidade adotado.

Para o comportamento estocastico de [x.sup.a.sub.t] sao necessarias algumas consideracoes. Ohlson (1995) e Lundholm (1995) enfatizam que as implicacoes empiricas do modelo dependem criticamente dessa ultima premissa, relacionada as dinamicas informacionais dos lucros residuais. Sua funcao e colocar restricoes no modelo padrao de desconto de dividendos. Visto de uma perspectiva empirica, a firma continua sendo avaliada pelo MDD, com o diferencial de ser estabelecida a natureza da relacao entre informacoes correntes e o valor descontado dos dividendos futuros. O processo estocastico que define a terceira premissa e conhecido como Linear Information Dynamics, ou dinamica das informacoes lineares (DIL) e e dado pelas equacoes:

[[??].sup.a.sub.t+1] = [omega][x.sup.a.sub.t] + [v.sub.t] + [[??].sub.1,t+1] (5)

[[??].sub.t+1] = [[gamma]v.sub.t] + [[??].sub.2,t+1] (6)

onde [x.sup.a.sub.t] e o lucro anormal (ou lucro residual) para o periodo "t"; [v.sub.t] significa "outras informacoes" sobre lucros residuais futuros esperados que sao observadas no final do periodo "t" mas ainda nao foram reconhecidas pela contabilidade; [omega] e [gamma] sao parametros de persistencia; [[??].sub.1] e [[??].sub.2] representam os termos de erros estocasticos, assumidos para terem media zero e distribuicao normal.

A DIL representa a grande contribuicao de Ohlson para a pesquisa de avaliacao de empresas (FUKUI, 2001). Sua construcao esta baseada no pressuposto de que as informacoes sobre lucros residuais futuros sao obtidas tanto da serie passada dos lucros anormais quanto de dados ainda nao capturados pela contabilidade (MCCRAE; NILSSON, 2001). As duas equacoes dinamicas sao combinadas com CSR para garantir que todos os eventos relevantes relacionados ao valor da empresa sejam absorvidos pelos lucros e valor contabil do PL (OHLSON, 1995). Assume-se que [x.sup.a.sub.t] e [v.sub.t] seguem um processo autoregressivo de um unico intervalo e que os parametros de persistencia--[omega] e gamma--sao ambos restringidos para serem nao negativos e menores que 1.

Quanto as "Outras informacoes", Lundholm (1995) ensina que se referem a informacoes nao contabeis que proporcionam um choque nos lucros residuais em periodos futuros. Ohlson (1995) assume que [v.sub.t] deve ser considerada como um resumo dos eventos relevantes para a avaliacao da empresa que ainda causarao impacto sobre as demonstracoes financeiras. Baseado na ALR e nas equacoes (5) e (6), Ohlson obtem a funcao de avaliacao:

[P.sub.t] = [b.sub.t] + [[alpha].sub.1][x.sup.a.sub.t] + [[alpha].sub.2][v.sub.t] (7)

onde [[alpha].sub.1] = [omega]/(R - [omega]) e [[alpha].sub.2] = R/(R - [omega])(R - [alpha]).

Com essas construcoes, Ohlson impos uma estrutura adicional na ALR para que a avaliacao pudesse ser expressa como uma funcao de dados contabeis contemporaneos e nao mais somente em predicoes (LEE, 1999 e LO; LYS, 2000). Diferentemente de alguns modelos tradicionais (MDD e Fluxo de Caixa Descontado), a formula de avaliacao de Ohlson - dada pela equacao (7)--nao requer previsoes explicitas de dividendos futuros nem de premissas adicionais de calculo do valor terminal (DECHOW et al., 1999).

Duas observacoes relacionadas com os coeficientes [[alpha].sub.1] e [[alpha].sub.2] ajudam a entender a funcionalidade do modelo. Para [omega] > 0, os dois coeficientes sao positivos simplesmente porque as predicoes [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], para qualquer [tau] > 1, relacionam-se positivamente com [x.sup.a.sub.t] e [v.sub.t]. O caso extremo de [omega] = 0 implica que [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] e independente de xat e entao pt nao pode depender de [x.sup.a.sub.t] (OHLSON, 1995). Adicionalmente, as funcoes [[alpha].sub.1] ([omega]) e [[alpha].sub.2] ([omega], [gamma]) reagem de forma crescente aos seus argumentos, isto e, altos valores de [omega] e [gamma] fazem com que [p.sub.t] seja mais sensivel para as realizacoes de [x.sup.t.sub.a] e [v.sub.t].

O MO ainda incorpora propriedades de Modigliani e Miller (1961), quais sejam: (i) dividendos afetam o valor de mercado na base dolar-a-dolar, implicando na premissa da irrelevancia do pagamento de dividendos; (ii) os dividendos pagos no periodo corrente influenciam negativamente os lucros futuros esperados. Combinadas, as duas propriedades indicam que os dividendos reduzem o valor contabil do PL, mas nao influenciam o lucro corrente (OHLSON, 1995).

4.2 Entradas Requeridas

Na determinacao dos parametros e variaveis do modelo de Ohlson, alguns dos dados necessarios estao prontamente disponiveis, enquanto outros devem ser estabelecidos. Especificamente, o modelo depende de: (i) tres variaveis: valor contabil do PL no periodo Corrente--[b.sub.t] , lucros no periodo corrente--[x.sub.t]--e outras informacoes no periodo corrente--[v.sub.t]; (ii) tres parametros: [omega] e [gamma], que sao parametros de persistencia, e r, que e a taxa de desconto. Relatorios contabeis--como o Balanco Patrimonial, Demonstracao do Resultado do Exercicio e Demonstracao das Mutacoes do Patrimonio Liquido--fornecem a base para fixacao das duas primeiras variaveis ([b.sub.t] e [x.sub.t]). A variavel remanescente ([v.sub.t]) e os tres parametros sao mais dificeis de serem mensurados.

Ohlson (1995) oferece pouca ou nenhuma orientacao de como obter a variavel vt e os parametros de persistencia [omega] e [gamma]. A tarefa ficou, portanto, relegada a pesquisas futuras. Nesse contexto, diversas metodologias ou proxies foram sugeridas em trabalhos academicos que testaram o MO.

4.2.1 Estabelecendo a Taxa de Desconto (r)

Na tarefa de avaliacao, faz-se necessario identificar uma taxa de desconto que converta fluxos que se realizarao (ou espera-se que se realizem) em valores presentes. Ha varias formas de mensurar r e a literatura sobre o tema e extensa. Abordagens incluem o custo do capital proprio, o custo medio ponderado de capital, a taxa de retorno sobre o PL ou sobre o ativo, entre outras. A discussao detalhada de cada um dos enfoques possiveis para determinar a taxa de desconto transcende ao objetivo desse artigo (vi).

O MO assume que r e definida de forma nao estocastica, considerando neutralidade ao risco e crencas homogeneas (OHLSON, 1995, p. 665). A taxa de desconto utilizada em varios trabalhos empiricos sobre o modelo de Ohlson e a taxa de retorno do patrimonio liquido (DECHOW et al., 1999; FRANKEL; LEE, 1999). Martins (1998) lembra que esse procedimento e um ponto discutivel, uma vez que investidores tem opinioes diferentes a respeito da rentabilidade minima esperada para a empresa.

4.2.2 Estabelecendo Outras Informacoes ([v.sub.t])

Kothari (2001) lembra que o desempenho corrente da empresa (tal como apresentado nos relatorios contabeis) e uma importante, mas nao a unica fonte de informacoes para a avaliacao do valor de mercado da empresa. Dechow et al. (1999) lembram que ha tempo a literatura academica reconhece que os precos de acoes refletem informacoes sobre lucros futuros que nao estao contidas nos lucros correntes. Tais informacoes nao podem ser observadas diretamente (OHLSON, 2001, p. 112). Candidatos para essas "outras informacoes" ([v.sub.t]) sao novas patentes, aprovacao de leis para um novo medicamento em companhias farmaceuticas, contratos de longo prazo, entre outros (MYERS, 1999). Tentativas de incorporar [v.sub.t] dentro da analise de avaliacao remonta, no minimo, ao ano de 1980, com o trabalho de Beaver et al. (1980).

Ohlson (1995) define "outras informacoes" como uma variavel escalar, porem nao estabelece concretamente seu conteudo analitico. Recentemente, o proprio Ohlson (2001, p. 112) se referiu a [v.sub.t] como variavel "misteriosa". A indefinicao da variavel "outras informacoes" fez com que muitos pesquisadores negligenciassem sua utilizacao nos testes sobre o MO (BEAVER, 1999, p. 38). Quanto a esse aspecto, Hand (2001, p. 122) ressalta que, ate 1998, quase toda pesquisa empirica sobre o MO desprezava o conteudo informacional de [v.sub.t]. Os poucos artigos que nao deixaram "de lado" a variavel "outras informacoes" escolheram um caminho intuitivo ao inves de uma construcao formal (exemplos incluem AMIR e LEV, 1996 apud HAND, 2001 e MYERS, 1999).

Ohlson (2001) sustenta que, embora possa haver um interesse analitico de nao se especificar o valor de [v.sub.t], tal procedimento reduz o conteudo empirico do MO. Ressalta ainda que previsoes consensuadas de analistas constituem uma ferramenta razoavel para mensurar os lucros futuros esperados e que nao ha motivo para se eliminar [v.sub.t] do modelo, uma vez que a variavel pode se apoiar em dados observaveis (vii). Hand (2001) acrescenta que considerar [v.sub.t] igual a zero e fazer a "heroica" assertiva de que os dados contabeis publicamente disponiveis sao suficientes para explicar o comportamento do preco de acoes.

4.2.3 Estabelecendo os Parametros de Persistencia ([omega] e [gamma])

As dinamicas lineares apresentadas por Ohlson (1995) definem a relacao entre informacoes correntes e futuras, utilizando um processo autoregressivo de primeira ordem--AR (1). O lucro residual do periodo seguinte ([x.sup.t.sub.a+1]) e uma funcao do lucro residual do periodo corrente (ajustado por um coeficiente de correcao denominado parametro de persistencia), outras informacoes ([v.sub.t]) e um termo de erro ([[epsilon].sub.2,t+1]).Por sua vez, outras informacoes do periodo seguinte ([v.sub.t+1]) sao uma funcao de outras informacoes do periodo corrente (tambem ajustadas por um coeficiente de correcao) e um termo de erro ([[epsilon].sub.2,t+1]). O parametro de persistencia de lucros residuais e indicado pela notacao [omega] e [gamma] e o parametro de persistencia de outras informacoes.

Ohlson nao estabelece criterios para obter [omega] ou [gamma], restringindo-se a declarar que o meio economico e os principios contabeis da empresa determinam os parametros exogenos [omega] e [gamma] (OHLSON, 1995, p. 686). Institui ainda que tais parametros nao devem ser negativos ou maiores que 1 (um). Tais parametros sao utilizados diretamente na determinacao dos coeficientes da funcao de avaliacao proposta por Ohlson (1995), conforme verificado na equacao (7). O coeficiente [[alpha].sub.1] e funcao de [omega] e [[alpha].sub.2] e funcao de [omega] e [gamma].

Em recente artigo que aborda a perspectiva empirica de seu modelo, Ohlson (2001, p. 115) declara que pesquisadores devem tentar estimar o valor de [omega] e [gamma], sem indicar como isto poderia ou deveria ser feito. O trabalho de Dechow et al. (1999) e referenciado por Ohlson como um dos estudos empiricos do MO que avalia de forma mais aproximada os atributos do modelo (OHLSON, 2001, p. 108). No estabelecimento dos parametros de persistencia, Dechow et al. (1999, p. 7) considera as estimativas amostrais historicas de [omega] e [gamma].

4.2.4 Estabelecendo as Variaveis [b.sub.t] e [x.sub.t]

Ohlson (1995) utiliza conceitos bem conhecidos, obtidos de relatorios contabeis, tais como o lucro ([x.sub.t]) e o valor do patrimonio liquido ([b.sub.t]). Contudo, para utilizacao das variaveis

[x.sub.t] e [b.sub.t], o MO impoe a restricao da relacao Clean Surplus (CSR) (viii), que tem reflexo direto na qualidade dos dados contabeis.

4.2.5 Fonte de Dados

Implicacoes de natureza regulatoria determinam, por vezes, a exigibilidade de publicacao de demonstrativos contabeisix. Empresas e periodicos especializados divulgam informacoes sobre o ambiente macroeconomico, taxas de retorno, entre outros dados de interesse. Provedores de informacao mantem dados atuais e historicos, bem como previsoes de empresas e de segmentos de mercado.

A disponibilidade de bases de dados computacionais (relacionadas as informacoes financeiras das empresas) estimulou um rapido crescimento na pesquisa contabil em mercado de capitais (BROWN, 2001). Os Estados Unidos da America (EUA) foram pioneiros na construcao desses tipos de bases de dados (BROWN, 2001). Na literatura estrangeirax, percebe-se a utilizacao frequente das seguintes fontes de dados (xi):

1. Previsao de Lucros: Nos EUA ha varias entidades que se encarregam de prover a estimativa de lucros futuros de empresas. A Value Line publica suas estimativas desde a decada de 70. A Standard & Poor's publicou suas previsoes semanalmente de 1967 a 1987, no boletim chamado Earnings Forecaster. Outras empresas que fazem previsoes de lucros sao: Institutional Brokers Estimate System (I/B/E/S), originalmente publicada pela Lynch, Jones e Ryan, e a Zacks Investment Research (The Icarus Service).

2. Dados Contabeis e Financeiros: a COMPUSTAT oferece dados historicos (a partir de 1987) de aproximadamente 22.000 empresas sediadas nos EUA (em atividade ou nao). Ja o Center for Research in Security Prices (CRSP) e um centro de pesquisa financeira da Universidade de Chicago que possui um banco de dados do mercado de acoes (precos, indices etc) de empresas negociadas nas principais bolsas norte-americanas (NASDAQ, AMEX, NYSE).

4.3 Exemplo hipotetico

O exemplo foi desenvolvido na tentativa de reproduzir uma aplicacao do modelo de Ohlson. Cabe ressaltar que os dados e o ambiente imaginado sao hipoteticos e, portanto, sujeitos as limitacoes inerentes das especificacoes dessa especie. Procurou-se privilegiar o aspecto didatico em detrimento de uma especificacao mais rigorosa (horizontes maiores de previsao e de series temporais de lucros e patrimonio liquido, inclusao de previsao da administracao etc).

O cenario, onde sao desenvolvidas as ilacoes, parte da existencia de uma empresa metalurgica, a Carol Inc., que participa da industria de metais e laminados ha 20 anos. Admite-se um mercado eficiente, na forma semiforte. Para o segmento de atividades, foi verificada uma taxa media de retorno sobre o capital proprio de 7%. Adicionalmente, na TABELA 1 sao fornecidas as seguintes informacoes:

O patrimonio liquido da empresa era de $100 no periodo t-6. Tomando por base as informacoes existentes, pode-se obter os resultados constantes na TABELA 2:

A serie historica da TABELA 2 foi utilizada para o calculo do parametro de persistencia [omega]. Verifica-se a existencia de lucros residuais em todos os periodos e sua persistencia foi, em media, de aproximadamente 98% em relacao ao periodo imediatamente anterior.

No periodo t, a empresa promoveu a implantacao de uma nova caldeira, alem de um programa de treinamento para diminuicao dos refugos de producao e acidentes de trabalho. A administracao esta confiante que tais acoes irao repercutir de forma positiva na produtividade da empresa. Com base nessa informacao, os analistas previram um resultado adicional de $2 por periodo na Carol Inc. No entanto, sabe-se que a informacao dos analistas tem um vies (medio) para baixo de -18%. A variavel [v.sub.t] foi calculada como sendo $2,36 e o parametro de persistencia [gamma] igual a um.

O calculo dos coeficientes da formula de avaliacao--equacao (7)--retornaram um valor de 10,89 para [[alpha].sub.1] e de 169,84 para [[alpha].sub.2.] Pela formula, o valor da empresa seria de $562,5:

[p.sub.t] = 121,5 + (10,89 X 3,69) + (169,84 x 2,36)

[p.sub.t] = 562,5

O exemplo oferece uma nocao de como se interagem os parametros e variaveis envolvidos na modelagem de Ohlson. A formula de avaliacao retornou o valor intrinsecoxii da empresa pelo modelo de Ohlson (1995). A comparacao deste com o respectivo valor de mercado seria o proximo passo para se identificar o grau de resposta oferecido pelo MO para o cenario imaginado (xiii).

4.4 Extensoes do Modelo

Pesquisadores tem aprofundado no estudo teorico do MO, visando oferecer embasamento mais consistente ou propor modificacoes na teoria subjacente ao modelo de Ohlson. Exemplos incluem o tratamento de itens Dirty Surplus no modelo de avaliacao (LO; LYS, 2000); a inclusao de mais periodos no processo autoregressivo (OTA, 2000); a incorporacao de taxa de juros estocastica e aversao ao risco (ANG; LIU, 1998); a estruturacao de uma dinamica informacional nao linear (BIDDLE et al., 2000) etc.

Dos trabalhos relacionados a teoria do MO, destacam-se aqueles elaborados pelo proprio Prof. James Ohlson, individualmente ou em parceria com outros pesquisadores.

--Conservadorismo, Ativos Operacionais e Crescimento do PL: concomitante a publicacao do artigo que estabeleceu a estruturacao do MO, James Ohlson ofereceu uma extensao de seu modelo, concebida em conjunto com o Prof. Gerald Feltham. Ate o momento, o trabalho de Feltham e Ohlson (1995) representa a extensao mais notoria do MO e algumas vezes e referenciado como se fosse o proprio (LOPES, 2001). O modelo Feltham-Ohlson (1995)--MFO--prove um tratamento diferenciado de ativos financeiros e operacionais para fins de avaliacao. Essa separacao e feita devido ao fato de que a contabilidade pelo custo historico difere sistematicamente do fair value. As informacoes dinamicas de MFO diferem daquelas instituidas no MO, destacando-se a inclusao de um coeficiente que mede o grau de conservadorismo da contabilidade e outro que define o parametro de crescimento do valor contabil do PL. Para reduzir o vies contido no lucro contabil (xiv), MFO assume a premissa de que os lucros residuais para ativos financeiros serao sempre iguais a zero. Pode-se, assim, simplificar o modelo para focalizar exclusivamente os ativos operacionais. Feita a simplificacao, nenhuma modificacao e requerida para MDD, CSR ou ALR. As dinamicas informacionais do MFO sao diferentes do MO. Enquanto este ultimo conta com somente duas DILxv, o MFO estabelece quatro;

--Lucros Transitorios: Ohlson (1999) realiza uma analise do conceito de lucros transitorios, seu impacto na avaliacao de empresas usando a ALR e sua diferenca em relacao aos demais itens de lucros. Argumenta que a teoria contabil e analistas de relatorios contabeis reconhecem que algumas fontes de lucros podem ser caracterizadas como transitorias e que precisam ser apartadas ou eliminadas do demonstrativo do resultado do exercicio. As dinamicas informacionais e a formula de avaliacao foram modificadas para incluir lucros transitorios, proporcionando uma forma de se tratar essa especie de lucro para estimar o valor das empresas;

--Taxa de Juros Estocastica: a teoria subjacente ao modelo de Ohlson simplifica o papel do risco na funcao de avaliacao, assumindo que os investidores sao neutros ao risco e taxas de juros sao fixas e nao estocasticas. Recentemente, Feltham e Ohlson (1999) demonstraram analiticamente que e possivel incorporar o risco tanto no MO quanto no MFO. O procedimento consiste em substituir lucros residuais futuros esperados para certezas equivalentes, baseadas na aversao ao risco pelo investidor entre as datas e eventos possiveis. A precificacao do risco ira depender do conjunto apropriado das informacoes referentes aos eventos e datas possiveis dos lucros residuais futuros, para auferir as certezas equivalentes. O estudo de Feltham e Ohlson (1999), entretanto, silencia-se na demonstracao de como os investidores e pesquisadores podem obter esse conjunto de informacoes. O trabalho de Gode e Ohlson (2000) tambem generaliza o MO para incluir taxas de juros estocasticas, fundamentando-se no fato de que as mudancas nas taxas de juros sao relevantes porque modificam percepcoes sobre lucros a longo prazo. O estudo (identificado) mais recente sobre a aplicacao do risco no modelo de Ohlson e de Baginski e Wahlen (2003).

--Depreciacao: Feltham e Ohlson (1996) examinaram o impacto da politica de depreciacao da empresa na relacao entre os numeros contabeis e o valor de mercado da empresa. No inicio das discussoes, os autores advertem que a politica de depreciacao afeta os numeros contabeis, mas nao tem efeito no valor de mercado da empresa. Especificamente, enquanto a politica contabil deve afetar a representacao das informacoes recebidas pelos investidores, Feltham e Ohlson (1996) assumem que ela nao afeta a informacao value relevant recebida. O estudo identificou politicas de depreciacao que proveem contabilidade nao viesada ou conservadora, isto e, o goodwill nao registrado e igual ou excede a "zero" na media, respectivamente. Tambem foi demonstrado que os lucros economicos sao iguais (na media) aos lucros contabeis se a contabilidade for nao viesada ou se nao houver crescimento no valor do PL.

V. CONCLUSOES

Esse trabalho se propos a analisar o modelo de Ohlson, sendo que a tarefa consistiu em identificar da origem do modelo, levantar a teoria subjacente, verificar as entradas exigidas, estruturar um exemplo hipotetico para demonstrar a logica envolvida na consistencia interna das dinamicas informacionais lineares e, por fim, identificar o estado da arte. Nesse percurso, foram identificados e debatidos diversos pontos. Parte deles encontra-se a seguir apresentados, a titulo de constatacoes:

1. Nao ha consenso na literatura academica sobre o metodo apropriado de mensurar os parametros de persistencia ([omega] e [gamma]).

2. Ha proposicoes de aperfeicoamento da concepcao original do MO por meio de extensoes ao modelo. A abordagem do conservadorismo, crescimento, risco, lucros transitorios ja constitui pauta dos estudos que focalizam a teoria relacionada ao modelo de Ohlson.

3. O modelo de Ohlson propiciou uma serie de contribuicoes na literatura academica sobre mercados de capitais: reacendeu o debate em torno da avaliacao pelo lucro residual na pesquisa de avaliacao; deu um suporte para que os numeros contabeis pudessem ser utilizados em modelos de avaliacao; adotou um enfoque mais desejavel, da distribuicao de riqueza para uma orientacao voltada para a criacao de valor para a empresa; intensificou o interesse em estudos de value relevance que ligam variaveis contabeis (valor contabil do PL e lucros, principalmente) a modelos de avaliacao de empresas; orientou oportunidades de pesquisa futura, como, por exemplo, estudos que focalizam variaveis e parametros do modelo de Ohlson.

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PENMAN, S. H.; SOUGIANNIS, T. A Comparison of Dividend, Cash Flow, and Earnings Approaches to Equity Valuation. Contemporary Accounting Research, v. 15, n. 3, fall, p. 343-383, 1998.

PLENBORG, T. Firm Valuation: Comparing the residual income and discounted cash flow approaches. [S.l.]: Social Science Research Network, 2000. Disponivel em: <http://papers.ssrn.com>. Acesso em 30 out. 2002, 08:54:20.

RICHARDSON, R. J. Pesquisa Social: Metodos e Tecnicas. 3 ed. Sao Paulo: Atlas, 1999.

Cesar Medeiros Cupertino

Universidade de Brasilia

Paulo Roberto Barbosa Lustosa

Universidade de Brasilia

(i) Este artigo foi apresentado no 4 Congresso USP de Controladoria e Contabilidade.

(ii) Verifica-se a existencia de modelos simples (do tipo linear univariado ou random-walk) e modelos sofisticados (do tipo multivariado e processos autoregressivos de multipla ordem).

(iii) Nesse caso, o lucro amplo ou abrangente (comprehensive income). Brazilian Business Review

(iv) Quanto aos periodicos, a pesquisa incluiu a consulta, dentre outros, dos seguintes: Contemporary Accounting Research; Journal of Finance; The Accounting Review; Journal of Accounting, Auditing and Finance; Journal of Accounting and Economics; Journal of Accounting Research; Journal of Business.

(v) Alguns dos termos consultados foram: Residual Income Valuation; Linear Information Model; Linear Information Dynamics; Ohlson 's Model; Edwards-Bell-Ohlson; EBO.

(vi) Exemplos de algumas abordagens (modelo de tres fatores e taxa de retorno por industria) podem ser obtidos nos trabalhos de Fama e French (1997, 1998).

(vii) Previsoes de analistas, por exemplo. Brazilian Business Review

(viii) Descrita na equacao (4).

(ix) No Brasil, no caso das sociedades anonimas de capital aberto, essa exigibilidade pode ser conferida no art. 289 da Lei 6.404/76 e com a nova redacao dada pela Lei no. 9.457, de 5.5.1997, que assim dispoe: "As publicacoes ordenadas pela presente Lei serao feitas no orgao oficial da Uniao ou do Estado ou do Distrito Federal, conforme o lugar em que esteja situada a sede da companhia, e em outro jornal de grande circulacao editado na localidade em que esta situada a sede da companhia".

(x) Particularmente norte-americana.

(xi) Todos os provedores citados sao de empresas sediadas nos EUA.

(xii) Segundo Myers (1999), "valor intrinseco e igual ao valor presente dos dividendos futuros esperados, indiferentemente da politica de pagamento de dividendo ou da qualidade dos numeros contabeis, contanto que a relacao Clean Surplus seja observada". (traducao e grifo nossos)

(xiii) Myers (1999) sugere a utilizacao do valor de mercado como benchmark para o valor intrinseco da empresa. No exemplo, obviamente, o grau de resposta do modelo de Ohlson ao valor da empresa (pelo mercado) nao pode ser identificado, uma vez que se trata de uma empresa hipotetica.

(xiv) Decorrente do atraso no reconhecimento de eventos economicos pela contabilidade.

(xv) Vide equacoes (5) e (6).
TABELA 1 Dados disponiveis da Carol Inc.

                                    Serie Temporal

                      t-5    t-4    t-3    t-2    t-1

Lucros                10,0   10,1   10,3   10,5   10,7
Dividendos            6,0    6,0    6,0    6,0    6,0
Previsao de Lucro*    8,3    8,4    8,5    8,5    8,6

Nota:

* As previsoes de lucros referem-se a estimativas consensuadas de
analistas.

TABELA 2
Dados Calculados da Carol Inc.

                                     Serie Temporal

                                       t-5       t-4         t-3

Patrimonio Liquido*                   104,0     108,1       112,3
([b.sub.t] = [b.sub.t]-1 +
[x.sub.t] - [d.sub.t])

Lucro Normal**                        6,00       6,24       6,49
([x.sub.t] = [b.sub.t]
X 0,07)

Lucro Residual                        4,00       3,86       3,76
([x.sup.a.sub.t] = [x.sub.t] -
[x.sup.'.sub.t])

Persistencia Lucros Residuais***                 0,97       0,98
([delta] = [x.sup.a.sub.t]
+ [x.sub.t]a-1)

Erro de Previsao****                  -0,18     -0,17       -0,17
(Previsto--Observado)/Observado

Retorno sobre o PL (ROE)              0,10       0,09       0,09
(ROE = [x.sub.t]/[b.sub.t])

ROE Residual*****                     0,04       0,03       0,03
([ROE.sup.res] = ROE - r)

Taxa Pagamento Dividendos             0,60       0,59       0,59
(k)
(k = [d.sub.t] + [x.sub.t])

                                     Serie Temporal

                                        t-2        t-1

Patrimonio Liquido*                    116,8      121,5
([b.sub.t] = [b.sub.t]-1 +
[x.sub.t] - [d.sub.t])

Lucro Normal**                         6,74        7,01
([x.sub.t] = [b.sub.t]
X 0,07)

Lucro Residual                         3,76        3,69
([x.sup.a.sub.t] = [x.sub.t] -
[x.sup.'.sub.t])

Persistencia Lucros Residuais***       1,00        0,98
([delta] = [x.sup.a.sub.t]
+ [x.sub.t]a-1)

Erro de Previsao****                   -0,19      -0,20
(Previsto--Observado)/Observado

Retorno sobre o PL (ROE)               0,09        0,09
(ROE = [x.sub.t]/[b.sub.t])

ROE Residual*****                      0,03        0,03
([ROE.sup.res] = ROE - r)

Taxa Pagamento Dividendos              0,57        0,56
(k)
(k = [d.sub.t] + [x.sub.t])

Notas:

* Calculado de acordo com a relacao Clean Surplus--vide equacao
(4).

** Foi utilizada a notacao xt para lucro normal.

*** Foi utilizada a notacao o para a persistencia em lucros residuais.

**** Calculado de acordo com a metodologia sugerida por Francis et al.
(2000).

***** roe residual foi definido como ROEres e a taxa de desconto
como "r".
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Author:Cupertino, Cesar Medeiros; Lustosa, Paulo Roberto Barbosa
Publication:Brazilian Business Review
Date:Jan 1, 2004
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