Comparison of the Ohlson and Feltham-Ohlson Models for Equity
Valuation: Evidence from the British Telecommunications Sector
S. N. Spilioti
Athens University of Economics and Business, Department of Business
Administration, Patission 76, 10434, Athens, Greece
G. A. Karathanassis
Athens University of Economics and Business, Department of Business
Administration, Patission 76, 10434, Athens, Greece
Abstract
Ohlson (1995) and Feltham and Ohlson (1995) provide a consistent framework for
the valuation of accounting numbers, the latter capturing different properties of
operating and financial assets. We test the empirical validity of these valuation
models for the telecommunications’ sector of the British equity market using panel
data techniques. Our empirical findings are not supportive of either model. We
interpret our findings as evidence of strong competition in the British
telecommunications’ sector.
Keywords:
Equity valuation, Clean surplus accounting, Book value, abnormal
earnings, Operating assets, Financial assets.
JEL Classification:
G1.
1
1. Introduction
Traditional equity valuation models discount expected future dividends in order to
arrive at a theoretically correct intrinsic value, which will be then compared to the
current market price (Gordon (1959)). However, in their studies (Peasnell (1982),
Ohlson (1995) and Feltham and Ohlson (1995)) suggest that security prices should be
determined by book value and discounted future abnormal earnings. The Ohlson
(1995) and Feltham and Ohlson (FO) (1995), models are landmark works in financial
accounting. These models provide a consistent framework for the valuation of
accounting numbers. FO show how a valuation model can be used to capture different
properties of different assets classes, such as operating and financial assets. They also
use their model to illustrate the effect of conservative accounting on the relation
between equity value, accounting book value and future earnings. Compared to the
traditional valuation models, the Ohlson and FO formulation is superior for empirical
purposes as it focuses on the relation between share price and accounting numbers. It
is a valuable contribution highlighting the role of stock price fundamentals such as net
worth, earnings and growth forecasts. The fact that value can be computed over a few
years by forecasting book value and earnings may turn out to be a significant
achievement in the theory of investment. Previous empirical studies (see section 2
below) find that these alternative valuation models are reliable for the purpose of
equity valuation.
The Ohlson approach to share valuation relies heavily on the present value of
expected abnormal earnings. In a fully competitive market, however, abnormal
earnings are expected to be zero. In that case, excess returns should not exist and their
influence on share prices should be eliminated. In this paper, we compare empirically
2
the explainability of Ohlson’s equity valuation model with that of FO approach, using
data from the highly competitive telecommunications sector of the London Stock
Exchange for the period 2000-2005. We use panel data techniques overcoming a
number of frequently encountered estimation problems.
Our empirical findings suggest that abnormal earnings, abnormal operating earnings
and operating assets are not a significant determinant of share prices in this sector. We
interpret this as evidence of a high degree of competition in the British
telecommunications sector. The rest of this paper is organized as follows. Section 2
discusses previous literature, section 3 presents the data and methodology, section 4
presents our empirical findings. Finally, section 5 concludes the paper.
2. Literature review
Share valuation models are important both to academics and practitioners. Interest in
the determinants of share prices dates back to the days when the first organized stock
exchanges were set up. According to the traditional valuation theory the price of a
share is equal to the present value of the stream of dividends, expected from the share
over its entire life (see for example Williams (1938), Gordon (1959)). Modigliani and
Miller (1961), assuming perfect capital markets, rational behavior, and perfect
certainty, argued for the Investment Opportunities Approach, according to which the
factors that affect the security price are the expected dividends, the growth rate in
expected dividends, and factors that proxy for the risk of the security. Alternatively,
one could use expected earnings and expected growth rate in earnings instead of
dividends. The results of empirical studies (see for example, Durand (1955), Gordon
3
(1959), Fisher (1961), Friend and Puckett (1964), Bower and Bower (1969), Keenan
(1970), Karathanassis and Tzoannos (1977), Karathanassis and Philippas (1988), Rees
(1997), Giner and Rees (1999), Akbar and Stark (2003), Ghezzi and Piccardi (2003),
Foerster and Sapp (2005), Rutterford (2004), Nasseh and Strauss (2004), Hand and
Landsman (2005), indicate that the main explanatory variables of equity prices are
dividends, earnings, retained earnings, size, variability in earnings, and debt to equity
ratio.
Ohlson (1990, 1991, 1995) suggest that, as long as forecasts of earnings, book values
and dividends follow clean surplus accounting ( bvt  bvt 1  xt  d t ), security prices
should be determined by book value and discounted future abnormal earnings:

Pt  bvt   R f i Et [ xtai ]
(1)
i 1
where, dt denotes the dividend per share at time t; Pt denotes the share price at time t,
bvt denotes the book value per share at time t, Et represents the expectations operator
at time t, xti represents abnormal earnings per share in period t  i and Rf is 1 plus
the risk free.
Finally, Ohlson assumes linear information dynamics, that is, abnormal earnings can
be estimated with linear regression analysis. Then, the abnormal earnings for period
t+1 are defined as:
xta1  xta  vt   1t 1
(2)
4
where the non-accounting information for period t+1 is defined as:
vt 1  vt   2t 1
(3)
If these assumptions hold the price of a security is defined as:
Pt  bvt  a1 xta  a2 vt
(4)
where
a1  [ /( R f   )]  0 , and a2  [ R f /( R f   )( R f   )]  0
This specification has three advantages. Firstly, special emphasis is given to book
value, thus avoiding any economic hypotheses about future cash flows. Secondly, the
treatment of investments is such that they are treated as a balance sheet factor and not
one that reduces cash flows (Penman and Sougiannis (1998)). Thirdly, as Bernard
(1995) has shown, for shorter horizons the Ohlson formulation is more suitable than
the dividends valuation model, as the latter underestimates share value. Previous
empirical studies find that book value and discounted future abnormal earnings have
an important role to play in the determination of equity prices (see for example,
Bernard (1995), Lundholm (1995), Frankel and Lee (1998), Lee and Swaminathan
(1998), Penman and Sougiannis (1998), Dechow, Hutton and Sloan (1999), Myers
(1999), Barth, Beaver, Hand and Landsman (1999), Francis, Ohlson and Oswald
(2000) ), Karathanassis and Spilioti (2003)).
Building on the foundation established by Ohlson (1995), FO (1995) model the
relation between a firm’s market value and accounting data concerning operating and
financial activities within a clean surplus context. We summarize the basic
assumptions and observations related to FΟ model. The notation is as follows:
5
fat = financial assets (net of financial liabilities), date t
oat = operating assets (net of operating liabilities), date t
ox t = operating earnings for period (t-1,t)
it = income due to financial activities, for period (t-1,t)
bvt  fat  oat = book value, date t
xt  it  oxt = net earnings
Pt = market value, date t
ct = (free) cash flows, date t
R f = risk free interest rate plus one
d t = net dividends
xta  xt  R f 1bvt 1 = residual earnings
oxta  oxt  R f  1oat = residual operating earnings, date t
The model is based on four assumptions described by equation (5) to (8) below:
1. Pt equals PVED

Pt   R f  Et d t  
(5)
 1
2. Clean surplus accounting:
fat  fat 1  it  d t  ct  (Financial assets relation) (6a)
oat  oat 1  oxt  ct (Operating assets relation)
(6b)
3. Net interest relation
i  R f  1 fat 1
(7)
6
4. Linear information dynamics
oxta1  11oxta  12oat  v1t   1t 1
(8)
oat 1  22oat  v2t   2t 1
v1t 1   1v2t   3t 1
v2t 1   2 v2t   4t 1
where vkt represents other information relevant in the forecasting of future abnormal
earnings. FO impose the following a priori restrictions on the parameters, 11 , 12 ,
22 ,  1 ,  2 , in linear information model:
(i)
h 1
h  1,2,3 , (ii) 0  11  1, (iii) 1   22  R f , (iv) 12  0
Given these assumptions FO formulation shows that:
Pt  bvt  1oxta   2oat  vt
(9)
where
1  11 / RF  11
 2  12 RF /RF  22 RF  11  and
  1 ,  2   RF /RF  11 RF   1 , 2 /RF   2 
Taking a similar approach, Liu and Ohlson (1999) develops empirical implications of
the FO (1995) model. The key issue concerns how one conceptualizes a firm’s
expected growth to explain its market value when the model also includes more basic
7
accounting measures reflecting its current performance. It is shown that market value
can be expressed in terms of : (i) financial assets with a coefficient of one, (ii) the
expected change in operating earnings with a non-negative coefficient, (iii) the
expected operating earnings with a positive coefficient, (iv) current (net) operating
assets with a no-negative coefficient, and, (v) the expected change in (net) operating
assets with a non negative coefficient. One identifies the measure of a firms expected
growth by normalizing the last variable with current (net) operating assets. The
variable will be relevant if and only if the accounting is conservative. Myers (2000)
critiques the above paper and concludes that Liu and Ohlson (1999) provide
empirically testable models and interpretations of the resulting coefficients in terms of
the underlying information dynamics. Their analysis and practical suggestions
regarding empirical proxies should make the FO model more accessible to empirical
researchers. On the other hand, Popova (2003) presents a case study of Microsoft
Corporation (for the period 1992-2002), where the company is valued separately by
both Ohlson (1995) and FO (1995) equity valuations models and under different
settings of the input data with the purpose to compare the extent to which the models
deal with accounting distortions. The study focuses particularly on the impact of
deviations from the clean-surplus principle and comments on other deficiencies in the
publicly available accounting data. The FO model was found more suited to cope with
such accounting problems, while the Ohlson valuation produced considerably
understated estimates of common equity. The case study also indicated that
deficiencies in the reporting of employee stock option compensation, investment and
derivatives might produce major inconsistencies in the examined valuation
frameworks and distort their results. In addition, Callen and Segal (2005) tests the FO
model by transforming the undefined ‘other information’ variables into expectational
8
variables, as suggested by Liu and Ohlson (2000). The data cover a sample of U.S
stocks for the period 1990-2001. The signs of the estimated coefficients conform to
the model’s predictions using panel data techniques, non-parametric estimation,
reverse regressions and portfolio regressions. The tests reject the Ohlson model in
favor of FO. Nevertheless, the estimated leverage coefficient takes a value of three
instead of one for most variations of the model. Also, the 1-year-ahead price
predictions of the FO model are no more accurate than those of the Ohlson model or a
naïve earnings valuation model. In conclusion, Inchausti (2006) empirically analyses
the adequacy of the valuation framework developed by Ohlson (1995) and FO (1995),
using conditions with different degree of complexity. The less sophisticated
conditions only include the fundamental accounting variables, book value and
earnings, while the more complex ones also include additional variables in order to
take into account the parameter “other information”. The sample contains nonfinancial companies listed in the Madrid Stock Exchange and indicates the period
1991-1999. The results suggest that Ohlson (1995) outperforms the other models,
given that the value obtained in the empirical tests is consistent with its theoretical
assumptions and implies lower prediction errors regarded the abnormal earnings
component. As for those based on FO (1995), the “conservatism parameter” produces
conflictive results because it is not able to capture all the effects of accounting
conservatism.
3. Data and Methodology
Our empirical analysis is based on data from the London Stock Exchange, available
from DataStream, covering the period between 2000 and 2005. The data is expressed
9
in nominal values and annual frequency. Our sample includes companies from the
British telecommunications sector.
Previous research on equity valuation has typically used either time-series or crosssection methods. Both methodologies, however, have a number of drawbacks. For
example, time-series analysis is subject to autocorrelation and multicolinearity
problems; on the other hand, cross-section analysis is subject to heteroscedasticity
problems and often fails to detect the dynamic factors that may affect the dependent
variable. We use a combination of time-series and cross-section data (panel data
analysis) a procedure that avoids the problems mentioned above and, in addition, has
a number of advantages. For example, a panel data approach not only provides
efficient and unbiased estimators but also a larger number of degrees of freedom
allowing researchers to overcome the restrictive assumptions of the linear regression
model (see e.g Baltagi and Raj (1992) and Maddala (1987)). Our econometric model
can be represented as follows:
K
Yit     i  t    K X Kit   it
(10)
K 1
i  1,......, N
t  1,......., T
where Yit is the value of the dependent variable for the cross section i at time t, XKit is
the value of the Kth explanatory variable for the cross section i at time t, μi is an
unobserved cross-section effect, λi is an unobserved time effect and εi is the
unobserved overall remainder. Equation (10) can be estimated either under the
10
assumption that μi and λi are fixed so that
N
 i  0 and
i 1
T

i 1
t
 0 , or under the
assumption that μi and λi are random variables. The first case describes the well
known Dummy Variable Model or the Covariance Model, while the second case
describes the Error Components Model (see among others Kmenta (1971), Griffiths et
al. (1993), Hsiao (1986), Wallace and Hussein (1969)).
Researchers are often faced with the problem of choosing among the two approaches
as it cannot be known beforehand whether the μi and λi terms are random or fixed. The
Error Components Model will lead to unbiased, consistent, and asymptotically
efficient estimators only if the orthogonality assumption holds, i.e. that the
explanatory variables are uncorrelated with the cross-section and time-series effects.
If that is not true, the Covariance Model estimators will still be consistent, since they
are not affected by the orthogonality condition (see for details Madalla (1971) and
Mundlack (1978)). To examine whether the explanatory variables are uncorrelated
with the cross-section and time-series effects one can apply the testing procedure
developed by Hausman (1978) where the null hypothesis is that the Error Components
Model is correctly specified, i.e. that μi and λi are uncorrelated with the explanatory
variables, XKit. The test statistic, m, is defined as equation (11) below
m  ( ˆ FE  ˆGLS )( Mˆ 1  Mˆ 0 )1 ( ˆ FE  ˆGLS )
(11)
where βGLS is the generalized-least square Error Component Model estimator, βFE is
the ordinary least square Dummy Variable Model estimator, M1 is the covariance
11
matrix of βFE, and M0 is the covariance matrix of βGLS. This m-statistic has an
asymptotic  k2 distribution. Accepting the null hypothesis suggests the use of the
generalized least square estimator. Rejecting the null hypothesis indicates the use of
the Covariance Model approach.
We estimate equation (10) defining the dependent variable to be the arithmetic
average of monthly average closing equity prices. We specify the right-hand side of
equation (10) in two alternative ways, representing the Ohlson (1995) and FO (1995)
valuation approaches. Concerning the Ohlson valuation model we used as
independent variables, book value (BV) and abnormal earnings (AE). BV is the
owners’ equity over the number of stocks in circulation, and AE is the difference
between current earnings and the opportunity cost of capital. The opportunity cost of
capital is defined as the previous period’s BV times the cost of capital (that is, the 3month treasury bill). Alternatively, for the specification representing the FO valuation
model, we have defined as independent variables, book value (BV), operating assets
(OA) and abnormal operating earnings (AOE). OA is the operating assets net of
operating liabilities (accounts receivables, inventory, etc.) and AOE is the difference
between current operating earnings and the previous period’s OA times the cost of
capital (that is the 3-month treasury bill).
Ohlson suggests that for the model to be correctly specified we should obtain a
positive relationship between AE and prices. We also, theoretically, expect a positive
relationship between BV and prices. According to the FO specification we expect a
positive relationship between BV, OA, AOE and prices.
12
4. Empirical findings
As a first step in the analysis we examine which approach is appropriate for the
estimation of equation (10). To this end we apply the Hausman (1978) criterion
discussed above. Table 1 reports the results of the estimation of the Hausman (1978)
test. Concerning the Ohlson valuation model, the results seem to suggest that the
cross-section and time-series effects can be considered as random variables. In other
words, μi and λi are uncorrelated with the explanatory variables, XKit, in which case the
Error Components Model is correctly specified and thus, we proceed with its
estimation. Alternatively, for the specification representing the FO valuation model,
the results appear to suggest that the cross-section and time-series effects can be
considered as fixed variables which means that we can proceed with the estimation
using the Covariance Model.
[INSERT TABLE 1]
According to the theoretical relationships predicted by the Ohlson valuation model we
expect both book value and abnormal earnings to be positively related to share prices.
Our empirical findings (reported in table 2) are not in accordance with the theoretical
predictions for the abnormal earnings coefficient. Thus, our ex-ante expectations are
empirically validated only for the variable of book value since this variable has a
positive and significant influence on share prices. On the other hand, according to the
FO model we expect book value, abnormal operating earnings and operating assets to
be positively related to share prices. Our empirical findings for abnormal operating
earnings and operating assets are not in accordance with the theoretical predictions.
13
Either the ex-ante relationships are empirically validated only for book value. Table 2
suggests that the Ohlson valuation model explains 20% of the variability of the
dependent variable while FO valuation model explains a similar proportion (27%).
[INSERT TABLE 2]
5. Conclusions
Previous studies suggest that changes in security prices are explained by book value
and discounted future abnormal earnings (Ohlson (1995) and FO (1995)). This paper,
attempted empirically to compare the explainability of Ohlson’s equity valuation
model with that of FO approach employing data from the London Stock Exchange
and panel data analysis. More specifically, we examine the behavior of equity prices
in the British telecommunications sector for the period 2000-2005.
Our empirical findings are not supportive of the Ohlson and FO valuation models in
the context of the British telecommunications sector. The regression coefficients of
abnormal earnings, abnormal operating earnings and operating assets are statistcally
insignificant and have an incorect sign. These empirical findings are not surprising
given the highly competitive nature of the British telecommunications sector: Our
findings suggest that as competition forces abnormal earnings to zero, the influence of
excess returns on share prices is eliminated.
14
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18
Table 1
Telecommunications Sector
m-statistic
p -value
df
Model 1
1.95
0.38
2
Model 2
10.12
0.02
3
Notes to Table 1
Model 1: the Ohlson (1995) valuation model
Model 2: the Feltham and Ohlson valuation model
Null hypothesis: the Error Components Model is correctly specified
m-statistic: Hausman’s (1978) test statistic
df: degrees of freedom
p-value at 95% confidence level
19
Table 2
Telecommunications Sector
Independent
Variables
Model 1
CONSTANT
0.80
(1.06)
BV
0.02
(3.42) *
AE
-0.01
(-0.61)
Model 2
0.02
(2.30) *
OA
-5.01E-10
(-1.39)
AOE
-4.01E-10
(-1.92)
R2
0.20
0.27
D-W
1.19
1.35
RSS
648.95
486.99
Notes to Table 2:
BV: Book Value per share
AE: Abnormal Earnings per share
OA: Operating Assets per share
AOE: Abnormal Operating Earnings per share
t-statistics appear in parentheses
* denotes significance at the 5%
D-W denotes the Durbin-Watson statistic
RSS denotes the Residuals Sum of Squares
20