Implied Cost of Capital over the Last 20 Years*
N K†M G

Graduate School of Business Administration
KOBE UNIVERSITY

Graduate School of Business Administration
KOBE UNIVERSITY

ABSTRACTe purpose of this paper is to estimate an alternative implied cost of capital, as inferredfrom a valuation model, and to attempt to compare its validity. We compare the following
major five models: 1) a model proposed by Gebhardt et al. (2001); 2) a model suggested
by Ohlson and Juettner-Nauroth (2005); 3) an expected earnings to price ratio (EP ratio);4) a PEG ratio; and 5) a modified PEG ratio (the last two being proposed by Easton(2004)). For the criteria of valuation in this study, we focused on the following two points:
first, a significant correlation with the risk factors consistent with the expected signs and,second, that the coefficients have the expected sign and that the adjusted R-square ishigh in the multivariate models that regress the cost of capital on the risk factors. As aresult, we conclude that the PEG and modified PEG ratios are superior to other models.
Furthermore, we suggest that the correlation between the cost of capital and the risk factors
varies, depending on the periods. Although Gode and Mohanram (2003) pointed out thatthe difference in the cost of capital by industry is important, this study shows that thedifference in the time series of the cost of capital is more important in Japan.
JEL Classification: M; M4; M41
Key Words: Implied Cost of Capital; PEG Ratio; Modified PEG Ratio; Risk Factors

1. Introduction
e purpose of this paper is to estimate an alternative implied cost of capital as inferred from* e authors appreciate the helpful comments and suggestions received from the participants of 2010 American Accounting
Associations Research Interaction Forum Session. e authors disclosed receipt of the following financial support for the research,authorship, and/or publication of this article: Masatoshi Goto and Norio Kitagawa gratefully acknowledge the financial support
from the Grant-in-Aid for Scientific Research (#21330110) from the Ministry of Education, Culture, Sports, Science andTechnology of Japan.
† Corresponding Author. Address Kobe University, 2-1 Rokkodai, Nada, Kobe 657-8501, JAPAN.
Telephone +81-78-803-6992 E-mail kitagawa@b.kobe-u.ac.jp
Received July 4, 2011; accepted September 9, 2011

Copyright©2011 Research Institute for Economics & Business Administration - Kobe University.

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e Japanese Accounting Review, 1 (2011), 71-104

a valuation model, and to attempt to compare its validity. e cost of capital is “the cost necessary
to anchor shareholders to the company” from the company’s point of view, and “expected returns on
capital investment” from the shareholders’ point of view. Cost of capital can be calculated by adding
a risk premium to a risk-free rate, but the risk premium cannot be directly observed. us, somearguments have ensued about inferring the cost of capital, and thus far, the argument has focusedon the following two approaches. One is the ex post approach using realized returns, which are
estimated by a capital asset pricing model (CAPM) or the three-factor model of Fama and French(1992, 1993). Another is the ex ante approach using a residual income model and an abnormal
earnings growth valuation model. Since the cost of capital estimated with the latter approach reflects
the cost implicitly expected by market participants at the time of capital investment, it is often called
an “implied cost of capital.” In this study, we focus on the implied cost of capital.
In recent years, many studies using the implied cost of capital have been published, and thevalidity of the implied cost of capital has been suggested in many studies (e.g., Lee et al. 2009; Pastor
et al. 2008).1 However, alternative models exist for estimating the implied cost of capital, as wellas various assumptions. us, we are interested in which of the models is the most appropriate for
estimating the cost of capital. In this paper, we compare the following five major models: 1) a model
proposed by Gebhardt et al. (2001); 2) one suggested by Ohlson and Juettner-Nauroth (2005); 3) an
expected earnings to price ratio (EP ratio); 4) a PEG ratio; and 5) a modified PEG ratio (the lasttwo being proposed by Easton (2004)). For the criteria of valuation in this study, we focused on thefollowing two points: first, a significant correlation with the risk factors consistent with the expected
signs and, second, that the coefficients have the expected sign and that the adjusted R-square is highin the multivariate models that regress the cost of capital on the risk factors. As a result, we conclude
that the PEG ratio and modified PEG ratio are superior to other models, and that their validity
varies, depending on the periods.
is paper makes several contributions as follows. First, it is the first study in which the implied
cost of capital is compared in terms of a correlation with risk factors in Japan. As there have been only
a few studies in Japan focusing on the implied cost of capital, it has not been fully clarified which isthe best model for inferring the cost of capital. In this paper, we show that the PEG and modified
PEG ratios are the most appropriate for an analysis of the cost of capital in Japan. Second, this paper
presents the evidence in terms of a comparison with U. S. analysis results. While prior studies (e.g.,Gode and Mohanram 2003) suggest the superiority of a cost of capital inferred from the Gebhardt
et al. (2001) model, this paper indicates that the cost of capital inferred from the PEG and modified
PEG models reflects risks more appropriately. Finally, in this paper, we suggest that the correlation
between the cost of capital and risk factors varies, depending on the time period. Although Gode andMohanram (2003) pointed out that the difference in the cost of capital by industry is important, it
is shown that the difference in cost of capital by time series is more important in Japan. e models
considering abnormal earnings growth—such as the Ohlson and Juettner-Nauroth (2005) model,
PEG ratio, and modified PEG ratio—have become more weakly correlated with risk factors since
the second half of the 1990s. On the contrary, the correlation between the model inferred from
Gebhardt et al. (2001) and the risk factors becomes stronger. In general, the results of our analysis
present beneficial evidence about the superiority of the model for inferring the implied cost of capitalin a Japanese environment.
1

Elton (1999, p. 1199) pointed out that a risk premium estimated by using a realized return is not appropriate as a benchmark of
expected return because it is often lower than the risk-free rate. However, a few studies point out that the implied cost of capital isbiased.

Kitagawa and Gotoh: Implied Cost of Capital over the Last 20 Years73

is paper proceeds as follows. In section 2, we review prior studies that compare the alternative
costs of capital. Section 3 presents the research design. In particular, we explain five models for
estimating the cost of capital, and seven risk factors. Section 4 shows the sample and descriptive
statistics. e analysis results are reported in section 5. Finally, in section 6 we summarize theconclusions.

2. Prior Studies
Many researchers have studied the relationship between various variables and the implied cost ofcapital. For example, the relationship between the cost of capital and the below-mentioned variables
is analyzed: the disclosure level of the IR (investor relations) and environmental information (e.g.,
Botosan 1997; Botosan and Plumlee 2002; Espinosa and Tronbetta 2007; Francis et al. 2005; Francis
et al. 2008; Hail 2002; Otogawa 2000; Suda et al. 2004; Chujo 2006), earnings attributes (e.g.,
Bhattacharya et al. 2003; Francis et al. 2004; Verdi 2006; McInnis 2010), precision of analyst forecasts(e.g., Botosan et al. 2004; Otogawa and Muramiya 2006), precision of management earnings forecast(e.g., Muramiya 2006), restatement of financial statements (e.g., Hribar and Jenkins 2004; Xu et al.
2006), the effect of the Sarbanes-Oxley Act (e.g., Ashbaugh-Skaife et al. 2009; Beneish et al. 2008;
Hammersley et al. 2008; Ogneva et al. 2007), and the effect of Regulation Fair Disclosure (e.g., Chenet al. 2010).
In addition, some studies have analyzed the impacts of adopting international accounting
standards (e.g., Cuijpers and Buijink 2005; Daske 2006; Christensen et al. 2007; Daske et al. 2008,2011; Karamanou and Nishiotis 2009; Dargenidou et al. 2006; Li 2010), securities regulation forinvestor protection (e.g., Hail and Leuz 2006), and various tax factors (e.g., Dhaliwal et al. 2005,
2006, 2007) on the cost of capital. Several studies show evidence that some auditing factors affectthe cost of capital: for example, the auditor independence (e.g., Hope et al. 2009; Khurana andRaman 2006) and the size of the auditing firms (“Big Four” and “Non-big Four”) (e.g., Khurana andRaman 2004). In finance research, there are studies that examine the relationship with the structureof corporate governance (e.g., Ashbaugh-Skaife et al. 2005; Guedhami and Mishra 2010), types ofshareholder rights (e.g., Cheng et al. 2006, 2008; Chen et al. 2011), cross-listings (e.g., Hail and Leuz
2009), and diversification strategy of firms (e.g., Inoue and Noma 2007), as well as those that haveexamined the validity of using an implied cost of capital in an investment strategy (e.g., Desrosiers etal. 2007; Esterer and Schrder 2006).
However, estimations of the implied cost of capital in these preceding studies were not carriedout with identical models. ere are many estimation models for the cost of capital according toassumptions regarding earnings growth and dividends, as well as forecast periods. Prior studies havegenerally used the following models: 1) the Gebhardt et al. (2001) model, the Claus and omas(2001) model, and the Gordon and Gordon (1997) model, based on a residual income model; 2)
the Ohlson and Juettner-Nauroth (2005) model, called the abnormal earnings growth valuation
model; and 3) the PEG ratio and modified PEG ratio, which are one form of an abnormal earnings
growth valuation model, both suggested by Easton (2004). ese models will be presented in section
3. Here, we are interested in which model would be the most appropriate to estimate the cost ofcapital. As stated above, since the true value of the cost of capital is not observable, it is not possible
to compare them easily. erefore, the preceding studies compare these models in establishing many
valuation criteria. To be more specific, the cost of capital is evaluated by measuring the correlation

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e Japanese Accounting Review, 1 (2011), 71-104

with observable risk factors and realized stock returns. In other words, a cost of capital that shows
expected signs and a higher correlation with risk factors and realized stock returns is regarded as
desirable. However, the evidence of these studies is not consistent.
For example, Gode and Mohanram (2003) compared the costs of capital derived from themodels of Ohlson and Juettner-Nauroth (2005), Gebhardt et al. (2001), and Liu et al. (2002). ey
compared costs of capital using the following three methods. First, they examined the correlation
with risk factors. Second, they examined the correlation with a risk premium computed bymultiplying a realized value of risk factors and a coefficient obtained with a regression of the risk
premium in the previous year on risk factors in the previous year. ird, they examined the correlation
with a realized stock return. As a result, they show that all costs of capital have a positive correlation
with conventional risk factors (such as earnings volatility, variability in stock returns, and leverage),and that they have a negative correlation with analysts’ coverage. In particular, cost of capital asderived from the Gebhardt et al. (2001) model has a higher correlation with risk factors than that of
the Ohlson and Juettner-Nauroth (2005) model. erefore, Gode and Mohanram conclude that the
Gebhardt et al. (2001) model is superior to the Ohlson and Juettner-Nauroth (2005) model.2
In contrast, Botosan and Plumlee (2005) compare the costs of capital by focusing on differencesin assumptions of terminal value. ey infer the cost of capital from five models proposed by Botosan
and Plumlee (2002), Gebhardt et al. (2001), Gordon and Gordon (1997), Gode and Mohanram(2003), and Easton (2004).3 ey also measure the correlation with such risk factors as market beta,
leverage, information risks, market value, book-to-market ratio, and growth in expected earnings. As
a result, they suggest that the models presented in Botosan and Plumlee (2002) and in Easton (2004)
show the most consistent correlation with risk factors. Meanwhile, they point out that the cost ofcapital as inferred from the model of Gebhardt et al. (2001) does not show a consistent correlation
with risk factors.
Easton and Monahan (2005) compare the costs of capital in terms of a correlation with realized
stock returns. ey show that all costs of capital derived from seven types of models for analysis
have a negative correlation with realized stock returns, contrary to expectation. Consequently, they
conclude that an implied cost of capital is less reliable as a proxy for expected return. However,they also noted the following two points. First, if analysts’ consensus regarding a long-term growthforecast is low, the reliability of the cost of capital as inferred from the model of Claus and omas(2001) becomes higher. Second, when ex post analysts’ forecast error is low, all costs of capital have apositive correlation, as expected. In other words, their result suggests that the superiority of the costof capital is dependent on the analysts’ forecast error.
Guay et al. (2006) compare the significance of slope coefficients, obtained with a regressionof future realized stock returns, to cost of capital. ey use the cost of capital inferred from eachmodel proposed by Gebhardt et al. (2001), Claus and omas (2001), Gordon and Gordon (1997),
Ohlson and Juettner-Nauroth (2005), and Easton (2004). ey measure realized stock returns fromone year ahead to three years ahead. e result shows that any costs of capital have a low correlation
However, because the result varies depending on whether loss firms are included in the calculation of the industry median (Gebhardt
et al. 2001) or not (Liu et al. 2002), it is necessary to interpret the superiority of the residual income model to a limited extent. On
the contrary, Gode and Mohanram (2003) conclude that the cost of capital inferred from Ohlson and Juettner-Nauroth (2005)
shows a more robust result.
3
Assumptions regarding terminal value in each study are as follows: 1) Botosan and Plumlee (2002): analysts’ forecast on terminal
value is equal to a market forecast; 2) Gebhardt et al. (2001): ROE (return on equity) exceeding the prediction horizon converges
on industry median. 3) Gordon and Gordon (1997): ROE exceeding the prediction horizon approximates a cost of capital. 4)Gode and Mohanram (2003): Corporate abnormal earnings growth converges on the economic level if exceeding the forecasts
horizon; 5) Easton (2004): Corporate abnormal earnings growth is zero if exceeding the forecast horizon.
2

Kitagawa and Gotoh: Implied Cost of Capital over the Last 20 Years75

with future stock returns. However, they point out that the cost of capital inferred from the modelof Gebhardt et al. (2001) shows a relatively high correlation, and it is an appropriate benchmark forforecasting future stock returns.
Chen et al. (2004) compare the costs of capital inferred from the models of Gebhardt et al.
(2001) and Ohlson and Juettner-Nauroth (2005) in seven countries (U.S., U.K., Australia, Canada,
Japan, Germany, and France). As a result, they show that, under a circumstance in which a clean
surplus relationship is maintained in financial reporting, the cost of capital derived from the model ofGebhardt et al. (2001) is more reliable. ey also show that, under a circumstance in which the clean
surplus relationship is not necessarily maintained, the model of Ohlson and Juettner-Nauroth (2005)
estimates a more reliable cost of capital.
As for the implied costs of capital discussed above, consistent results have not necessarily beenobtained. In this study, we attempt to additional empirical evidence for these studies, using data fromJapanese companies.

3. Research Design
As stated above, many alternative models are used to estimate an implied cost of capital. ey
are generally classified into two types—one based on the residual income model, such as that from
Gebhardt et al. (2001), and the one based on abnormal earnings growth valuation, such as the Ohlson
and Juettner-Nauroth (2005) model. We focus on these two models, and summarize their differences.
Both are commonly based on a discounted dividend model, but there are some differences as follows.4
One difference is an assumption regarding the clean surplus relationship. As seen in theexpression below, the model proposed by Gebhardt et al. (2001) requires information on shareholders’equity, in addition to dividends, current stock prices, and earnings forecasts. Meanwhile, the model
proposed by Ohlson and Juettner-Nauroth (2005) uses only dividends, current stock prices, andexpected returns, but does not need information on shareholders’ equity. e Gebhardt et al. (2001)
model requires assuming a clean surplus relationship so as to compute the forecasted shareholders’equity. However, the Ohlson and Juettner-Nauroth (2005) model is not necessarily based on theassumption of a clean surplus relationship.
Another difference is the use of long-term forecast data. Gebhardt et al. (2001) model needs
forecasted ROEs over 12 years ahead and a future dividend payout ratio as information for a longterm forecast. In order to estimate forecasted ROEs over 12 terms, the Gebhardt et al. (2001) model
hypothesizes that ROE will converge on the industry median in the long term.5 erefore, thenumerical value of the industry median affects the forecasted ROE. Meanwhile, the Ohlson andJuettner-Nauroth (2005) model involves only the short-term forecasted ROE for two years ahead,
and the long-term forecast depends only on γ in the expression, EPSt+1 = γ EPSt. Consequently, theindustry median of ROE is not required.
In this study, we are interested in how an estimated cost of capital is influenced by thesedifferences between the two models. Based on preceding studies, such as those of Gode andMohanram (2003) and Botosan and Plumlee (2005), we compare costs of capital using the following
two methods. First, we compute risk factors considered to be generally supported, and compare the45Features of both models are further described in Ohlson and Gao (2006), Easton (2009), and other papers.
e validity of said hypothesis is shown in Nissim and Penman (2001) and other papers. However, as with Fairfield et al. (2009),
some studies point out that profitability converges on a median of the entire industry of companies.

e Japanese Accounting Review, 1 (2011), 71-104

76

correlation with the cost of capital. Second, we compare the signs of coefficients and the explanatory
power of the models by estimating a multiple regression model in which the cost of capital is adependent variable and a risk factor is an independent variable. In this study, we consider that thehigher the correlation is with the risk factors, or the higher an adjusted R-square is with the expected
sign of the coefficient of the multiple regression model, the more the cost of capital is presumablyreflecting risks. Next, we explain the estimation model for the cost of the capital and risk factors usedin this paper.
3.1 Inferring the Cost of Capital
3.1.1 e Gebhardt et al. (2001) Model
As mentioned above, the Gebhardt et al. (2001) model for inferring the cost of capital is basedon the residual income model, and it can be represented by equation (1) below. Where P0 is a stock
price at 0; BVPSt is forecasted book value per share at period t; FROEt is forecasted ROE at periodt; and x denotes the cost of capital. As forecasted future earnings are available to a limited extent, theforecasted earnings and the earnings growth ratio are used explicitly for three years. e values after
this period are assumed to converge on an industry median. e forecast period of 12 years is adopted
in this case.

11 FROE ��x
FROE����x
FROE����x
FROE�����xi�
BVPS���
BVPS��� Σ
BVPSi����
BVPS��
�i����x�
����x�
����x�
x ����x���i��
(1)
11 FROE ��x
FROE�����xi�
VPS��� Σ
BVPSi����
BVPS��
����x�ix ����x���i��P��= BVPS���e Gebhardt et al. (2001) model requires forecasted values of ROE, book value per share, anddividend per share. e forecasted ROEs for one year and two years ahead are computed by using
the forecasted earnings per share (EPS: reported by IBES). erefore, when the forecasted EPS at
the fiscal year t is defined as FEPSt, the forecasted ROE for i years ahead is expressed as FEPSt+i/ BVPSt+i –1. e forecasted earnings for three years ahead, FEPS3, are computed by multiplying theforecasted earnings for two years ahead, FEPS2 , and the long-term growth reported by IBES aroundthe same time of this forecasted value. From 4 years to 12 years ahead, a constant amount is deducted
every year, from the forecasted value for 3 years ahead to the median of the industry to which thecompany belongs. Here, the industry median is the median of the values in the industry to which thecompany belongs (the Nikkei industry code is used here) as experienced over the past 10 years up
to the current year. To be more specific, the industry median is obtained by computing a median foreach year over the past 10 years, then calculating the median of that 10-year period. It is incorporated
into the model from the viewpoint of measuring how much profitability the company may have inthe future by using the industry median.
e forecasted book value per share, BVPS1, is obtained by using the clean surplus relationship,
adding the forecasted EPS in the next year to the current book value per share, BVPS 0, andsubtracting the forecasted dividend per share, DPS1. In other words, the forecasted book value for the
fiscal year t is expressed by the following equation: BVPSt = BVPSt-1 + FEPSt – DPSt. At this time, thenecessary forecasted dividend per share is computed by using a dividend payout ratio.
Specifically, on the assumption that the dividend payout ratio is invariable, the forecasted
dividend is computed by multiplying the dividend payout ratio calculated in the current year and theKitagawa and Gotoh: Implied Cost of Capital over the Last 20 Years

77

forecasted EPS. Consequently, the expression to calculate the forecasted dividend per share for the
fiscal year t is FEPSt ·DPS0 / EPS0.
e cost of capital is computed by solving the above polynomial equation for x. is polynomial
equation may have multiple solutions, and we solve using the Muller method.6
3.1.2 e Ohlson and Juettner-Nauroth (2005) Modele Ohlson and Juettner-Nauroth (2005) model is expressed as equation (2). e definitionof variables is the same as in Gebhardt et al. (2001). Although γ plays an important role in thisexpression, how to decide its value is not definitively shown, even in Ohlson and Juettner-Nauroth(2005). ey infer that, taking the value of EPS for example, the value is EPSt+1 = γEPSt, where γ>1.7
In this study, we assume that γ is 1.03.8

where

x = A + A2 +

�

(

)

� FEPS2
FEPS1
��– (� –1)
P0
FEPS1

DPS�
A � γ ����
�
P�

�

(2)

3.1.3 e Modified PEG Ratio, PEG Ratio, and EP Ratio in Easton (2004)
In this study, we also examine the modified PEG ratio and the PEG ratio proposed by Easton(2004) in order to weigh the impacts of γ and the dividends involved in Ohlson and Juettner-Nauroth(2005). e modified PEG ratio can be expressed by equation (3).9 As seen in this expression, amodified PEG ratio is obtained by hypothesizing γ = 1 based on the condition that the abnormal
earnings growth in the Ohlson and Juettner-Nauroth (2005) model is constant. Furthermore, thePEG ratio is based on the assumption of DPS = 0, in addition to the assumption in the modified
PEG ratio. e PEG ratio can be expressed by equation (4).
x=

FEPS2 + xDPS1 – FEPS1
P0

(3)

x=

FEPS2 – FEPS1
P0(4)

We also examine the EP ratio, which is also regarded as a form of the abnormal earnings growthvaluation model and is computed by equation (5). e EP ratio assumes that the abnormal earnings
e Muller method is described in general textbooks to explain the algorithm. Here, we refer to Scientific and Engineering
Computation by Hayato Togawa, SAIENSU-SHA Co., Ltd., 1992. In addition to the Muller method, this equation can also
be solved with the Newton method and the Traub method. e solution of a nonlinear equation can be computed, but it is notpossible to limit oneself to only one solution; it is just one of many solutions. Under the Muller method, in cases where multiple
solutions are obtained, the smallest one is adopted.
7However, if γ > 1, the future value of EPS calculated by EPSt+1= γ EPSt diverges.
8
Ohlson and Juettner-Nauroth (2005) stated that it is possible to unify γ of all firms within the range of 1.03-1.05. ey explain as
follows (p. 359): “Perhaps the most logical interpretation is that the limit growth should correspond to the very long-run steadystate in which a firm’s growth in expected earnings equals the growth in expected GNP. It follows that one can argue that γ shouldbe the same for all firms in the range of 1.03 to 1.05.”
9
Some preceding studies modify the model by using the forecasted earnings for four and five terms ahead (e.g., Botosan and
Plumlee 2005). However, since few companies announce the forecasted earnings for four and five terms ahead, this estimation
model is used here.
6

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e Japanese Accounting Review, 1 (2011), 71-104

growth = 0. In other words, the EP ratio is a model implying that, if forecasted earnings for the next
year are available, a satisfactory corporate evaluation is possible.
x=

FEPS1
P0

(5)

3.2 Measuring Risk Factors
In this study, we adopt the following seven risk factors: 1) market beta, 2) unsystematic risk, 3)
earnings variability, 4) leverage, 5) firm size, 6) long-term growth in expected earnings, and 7) bookto-market ratio. ese are the typical risk indicators adopted in prior studies (e.g., Gebhardt et al.
2001; Claus and omas 2001; Gode and Mohanram 2003; Easton 2004; Botosan and Plumlee2005).
3.2.1 Market Beta
Prior studies use market beta as a risk factor. eir argument is based on CAPM, which predicts
a positive association between a firm’s market beta and the risk premium. In addition, several studies
show that there is statistically significant association between market beta and the risk premium (e.g.,
Gordon and Gordon 1997; Harris and Marston 1992; Marston and Harris 1993; Harris et al. 2002).
According to preceding studies, we estimate market beta (hereinafter referred to as Beta), using dataon daily stock returns over the past year from the announcement date of analysts’ forecasts by IBES.
3.2.2 Unsystematic Risk
Although some studies find no statistical relationship between unsystematic risk and expected
return (see, e.g., Pratt and Grabowski 2008, p. 169), many prior studies show a positive association
between unsystematic risk and future stock returns (e.g., Malkiel and Xu 1997). We extract
unsystematic risk by estimating the regression model in which daily stock returns in the previous year
are a dependent variable and the stock returns of market portfolios are an independent variable. We
then use the variance of the residuals obtained from the regression as a proxy for unsystematic risk(hereinafter referred to as Unsyst).
3.2.3 Earnings Variability
Graham et al. (2005) provide survey evidence that corporate executives prefer smooth earnings,
in part because they believe that higher earnings volatility increases the cost of capital. Francis etal. (2004) show a positive relation between earnings volatility and expected returns. We also predicta positive association between earnings variability and risk premiums. In prior studies, Gebhardt
et al. (2001) and Gode and Mohanram (2003) measured earnings variability using the following
procedures. First, they computed the following variables expressing earnings variability: 1) the mean
absolute error of analyst forecasts over the past five years; 2) the coefficient of variation in EPS; and 3)
the dispersion of analysts’ forecasts. en, using factor analysis, they identified a single variable fromthese three variables, and used it as a criterion in expressing earnings variability. In this study, wemeasure earnings variability using the standard deviation of ROA (net income divided by total assets)over the past five years (hereinafter referred to as Earnvar).

Kitagawa and Gotoh: Implied Cost of Capital over the Last 20 Years79

3.2.4 Leverage
Modigliani and Miller (1958) demonstrate that the risk premium can be expressed as anincreasing function of leverage. Fama and French (1992) show a positive association between leverage
and realized stock returns. Dhaliwal et al. (2006) also find evidence that the equity risk premium ispositively related to leverage. According to preceding studies, we use leverage measured as the ratio of
the book value long-term debt to the market value of equity (hereinafter referred to as Leverage) as arisk factor. We predict a positive association between the risk premium and leverage.
3.2.5 Firm Size
Numerous studies have shown the negative association between market capitalization andrealized returns (e.g., Fama and French 1992; Berk 1995). In addition, market capitalization can bea risk factor as a proxy for the information environment, which is affected by many factors, including
trading volume, firm size, bid-ask spreads, and institutional factor; and these factors are highly
correlated with each other. Prior studies show that firms that are better connected with informationintermediaries, such as analysts and institutional investors, have lower risk premiums because the easy
availability of information lowers the information asymmetry between a firm and its investors, andlowers the information risk for investors (e.g., Demsetz 1968; Copeland and Galai 1983; Glosten
and Milgrom 1985; Amihud and Mendelson 1986; Diamond and Verrecchia 1991; Brennan andSwaminathan 1993; Handa and Linn 1993; Coles et al. 1995; Clarkson et al. 1996; Botosan 1997;
Healy and Palepu 1999).10 erefore, we use the firm size measured by the log of the market valueof equity (hereinafter referred to as Size) as a risk factor. According to preceding studies, we expect anegative association between the size and the risk premium.
3.2.6 Long-Term Growth in Expected Earnings
Gebhardt et al. (2001) and Gode and Mohanram (2003) use the long-term growth in expected
earnings from IBES as a proxy for market mispricing, and predict a negative correlation between
the risk premium and long-term growth. eir argument is based on two reasons. First, based on
La Porta (1996), they argue that analysts are overoptimistic for high-growth firms and that theirstock prices are too high, which results in a low risk premium. Gebhardt et al. (2001) explain thesecond reason for a negative association between long-term growth and the risk premium as follows.
Residual income models assume that ROE reverts to the industry median ROE. If the industry
median ROE is lower than the analysts’ estimate of a firm’s long-run ROE, then these firms willappear to have a higher price and a lower risk premium. erefore, a negative association between
the risk premium and long-term growth is expected. In this study, we use the forecasted long-term
growth reported by IBES to define variables regarding the long-term growth in expected earnings(hereinafter referred to as LTG).
3.2.7 Book-to-Market (BM) ratio
Gebhardt et al. (2001) and Gode and Mohanram (2003) control for the book-to-market ratio
as measured by the log of the ratio of shareholders’ equity to the market value of equity. is isconsistent with Fama and French (1992) and Berk et al. (1999). A high book-to-market (BM) ratio
could reflect lower growth opportunities and lower accounting conservatism. As argued by Godeand Mohanram (2003), it is difficult to conclude how the combination of these factors will influence10

Based on these arguments, Botosan and Plumlee (2005) use both information risk and firm size as a risk factor. Information risk ismeasured as the width of the range between Value Line’s minimum and maximum price forecasts scaled by the midpoint of range,
and firm size is measured as the market value of equity.

80

e Japanese Accounting Review, 1 (2011), 71-104

the risk premium. According to preceding studies, however, we expect a positive correlation between
the BM ratio and the risk premium. In this study, we estimate a variable of book-to-market ratio(hereinafter referred to as BM) as the log of the ratio of shareholders’ equity to the market value ofequity.

4. Sample and Descriptive Statistics
e sample of this study includes listed firms (excluding financial institutions) that had forecasts
both one and two years ahead and a long-term growth forecast, all of which were announced
simultaneously by IBES, during the period from 1987 to 2007.11 us, 4,465 firm-years are extracted
as a sample.12 Earnings forecasts from IBES cover one-third of the Japanese listed firms. Earnings
forecasts for different firms are announced every month. e earnings forecast seems to be irregularly
announced, only when certain information is disclosed. In our analysis, we use forecast data
announced in August. In a case where the earnings forecast in August is not available, we use forecast
data announced in the nearest accounting month before August as a substitute.
We use consolidated financial statement data from Nikkei Media Marketing, Inc., Nikkei
Financial Data, available on CD-ROM. If the data required for an estimation of the cost of capitaland risk factors are unavailable, the firms are excluded from the sample. In particular, as earnings
data over the past five years are required to compute the earnings variability, the sample for a forecast
announced in 1987 requires ROA data since 1983. e industry median of the Gebhardt et al. (2001)
model is computed by using the ROE of the same data from Nikkei Media Marketing and Nikkei
industry code. We also obtain the daily stock price data from Nikkei Media Marketing, Inc., whichis called the “daily Japanese stock return data.” Since daily returns over the past year are required forthe calculation of Beta and Unsyst, firms with a shorter period of listings than required are excluded
from the sample. Given all of these requirements, the number of sample firms decreased to 3,976.
Furthermore, a firm for which the cost of capital cannot be estimated is excluded from thesample. In the Gebhardt et al. (2001) model, when the solution is negative or multiple solutions are
obtained, such a firm is eliminated from the sample. In addition, when a solution cannot be specified
or obtained, such a firm is also eliminated from the sample. Meanwhile, in both the Ohlson andJuettner-Nauroth (2005) and Easton (2004) models, it is required that an earnings forecast for two
years ahead be higher than that for one year. A firm that does not fulfill the requirement is excluded
from the sample. In the Ohlson and Juettner-Nauroth (2005) model with γ = 1.03, the costs ofcapital for some firms cannot be estimated.13 As a result of considering the above-mentioned matters,
the final sample consists of 3,517 firm-year observations.14
Industries are classified by Nikkei industry code.
During the analysis period, 46,292 firm-years announce consolidated financial data. Among them, one-year-ahead forecasts of
21,005 firms and two-year-ahead forecasts of 27,873 firms are unavailable. Although some preceding studies use a three-yearahead earnings forecast, we use instead the long-term growth forecast for computation in this study. Since the databases ofcompanies other than IBES seldom announce long-term growth, we have to use the IBES data. However, as many precedingstudies in the U.S. use forecasts from IBES, it seems safe to assume that there is no problem.
13
We think that this is a significant problem. If the cost of capital cannot be computed just because a value to be assigned to theexpression is limited, it may be argued that only preferable sample firms are selected. Also in this study, about 20% of firms are
excluded from the sample due to the impossibility of calculation.
14
e final sample varies, depending on the model adopted for estimating the cost of capital. As this study focuses on a comparisonof the costs of capital as estimated by each model, we conduct analyses with the Ohlson and Juettner-Nauroth (2005) model inwhich the final number of samples is the least.
11
12

Kitagawa and Gotoh: Implied Cost of Capital over the Last 20 Years

mean
s.d.
p10
p25
p50
p75
p90

GLS
0.043
0.033
0.018
0.027
0.036
0.048
0.066

OJ
EP
0.170 0.032
0.359 0.059
0.057 -0.002
0.075 0.021
0.099 0.038
0.139 0.055
0.219 0.076

T 1: D S

PEG MPEG Beta Unsyst Earnvar Leverage
0.088 0.080 0.883 0.048
0.022
0.568
0.050 0.058 0.362 0.035
0.059
0.876
0.041 0.027 0.422 0.015
0.002
0.025
0.057 0.047 0.618 0.024
0.003
0.084
0.078 0.069 0.870 0.038
0.006
0.256
0.105 0.096 1.124 0.061
0.015
0.645
0.143 0.139 1.367 0.093
0.041
1.420

81

Size
26.1071.402
24.27125.13326.05527.10827.973

LTG
0.136
0.165
0.001
0.050
0.100
0.176
0.306

BM
0.726
0.437
0.298
0.430
0.633
0.897
1.262

Note: GLS: the cost of capital inferred using Gebhardt et al.(2001) model.
OJ: the cost of capital inferred using Ohlson and Juettner-Nauroth(2005) model
EP: expected earnings to price ratio
PEG: PEG ratio proposed by Easton (2004)
MPEG: modified PEG ratio proposed by Easton (2004)
Beta: market beta using daily stock returns over the past 1 year from the announcement date of analysts’
forecasts by IBES
Unsyst: unsystematic risk as measured by the residual from the regression over the previous year of a firm’s
daily return on the daily market return
Earnvar: earning variability using the standard deviation of ROA (net income divided by total assets) overthe past five years
Leverage: leverage as the ratio of the book value long-term debt to the market value of equity
Size: the natural log of the market value of equity
LTG: forecasted long-term growth reported by IBES to define variables regarding the long-term growthin expected earnings
BM: book-to-market ratio as the ratio of shareholders’ equity to the market value of equity

F 1: T S M   C  C
0.14
0.12
0.1
0.08
0.06

GLS
OJ
EP
PEG
MPEG

0.04

19
87
19
88
19
89
19
90
19
91
19
92
19
93
19
94
19
95
19
96
19
97
19
98
19
9
20 9
00
20
01
20
02
20
03
20
04
20
05
20
06
20
07

0.02

�

82

e Japanese Accounting Review, 1 (2011), 71-104

T 2: D S   C  C  Y   I

Panel A: Descriptive Statistics for the Cost of Capital by Year
GLS
OJ
EP
year
mean median mean median mean median1987 0.062 0.062 0.064 0.062 0.030 0.031
1988 0.065 0.059 0.073 0.070 0.041 0.033
1989 0.054 0.041 0.070 0.064 0.027 0.023
1990 0.075 0.051 0.080 0.068 0.032 0.032
1991 0.085 0.055 0.094 0.069 0.052 0.041
1992 0.072 0.050 0.080 0.076 0.040 0.036
1993 0.063 0.041 0.093 0.073 0.019 0.020
1994 0.063 0.040 0.106 0.073 0.027 0.019
1995 0.063 0.044 0.114 0.073 0.026 0.028
1996 0.058 0.037 0.089 0.076 0.029 0.029
1997 0.049 0.034 0.080 0.062 0.029 0.027
1998 0.057 0.042 0.098 0.076 0.010 0.030
1999 0.045 0.031 0.106 0.081 0.012 0.019
2000 0.030 0.029 0.113 0.092 0.016 0.023
2001 0.039 0.036 0.148 0.106 0.026 0.036
2002 0.039 0.035 0.164 0.118 0.013 0.031
2003 0.035 0.032 0.209 0.107 0.027 0.036
2004 0.034 0.034 0.205 0.101 0.042 0.045
2005 0.036 0.035 0.201 0.104 0.046 0.048
2006 0.038 0.034 0.209 0.098 0.046 0.045
2007 0.044 0.039 0.203 0.100 0.046 0.050
total
0.043 0.036 0.170 0.099 0.032 0.038

PEG
mean median
0.052 0.051
0.063 0.058
0.057 0.050
0.044 0.053
0.071 0.054
0.062 0.062
0.068 0.060
0.063 0.055
0.076 0.061
0.074 0.064
0.065 0.053
0.079 0.063
0.087 0.066
0.091 0.078
0.093 0.081
0.104 0.089
0.092 0.083
0.080 0.077
0.092 0.081
0.085 0.081
0.085 0.081
0.088 0.078

MPEGmean median
0.051 0.051
0.060 0.057
0.055 0.048
0.043 0.052
0.069 0.053
0.058 0.060
0.066 0.055
0.064 0.052
0.075 0.058
0.068 0.060
0.063 0.048
0.077 0.058
0.083 0.063
0.094 0.074
0.085 0.073
0.096 0.078
0.081 0.070
0.070 0.068
0.083 0.072
0.073 0.070
0.075 0.069
0.080 0.069

N
7
12
35
13
27
49
47
47
38
56
69
54
72
136
534
522
404
340
366
335
354
3517

(Continued)

Table 1 provides the descriptive statistics of the sample.15 As for the cost of capital estimated in
the Gebhardt et al. (2001) model (hereinafter referred to as GLS), the mean and the median are 4.3%
and 3.6%, respectively. ese points are lower than those of the Ohlson and Juettner-Nauroth (2005)
model (hereinafter referred to as OJ), which shows 17.0% and 9.9%, respectively. is is because, in
estimating the cost of capital, Ohlson and Juettner-Nauroth (2005) take into account the abnormal
earnings growth. In the PEG and modified PEG ratios in Easton (2004) (hereinafter referred to as
PEG and MPEG, respectively) which ignore abnormal earnings growth and dividends, the meanvalues are 8.0% and 6.9%, respectively, and the medians are 8.8% and 7.8%, respectively, which are
lower than those of the OJ model. However, they are still higher than those of the GLS model.16
Table 2 shows a change in each cost of capital by year and by industry. Focusing on a change inthe cost of capital by year in Panel A, we find that the level of OJ is high over the entire period. In
particular, OJ has increased since 1997, and the difference from GLS and EP has become larger. e
PEG and MPEG have also increased, but not as remarkably as OJ. e GLS and EP are relatively
Table 1 provides values after considering the effect of outliers. In this study, a value which is lower than 1 percentile (or higher than
the 99th percentile) of each variable is regarded as an outlier, and it is replaced by 1 percentile (99th percentile).
16
Preceding studies also observe such a tendency. In Gode and Mohanram (2003), the mean value of GLS is 3.2%, in comparison
with the 5.1% of OJ. In Botosan and Plumlee (2005), while GLS is 1.0% and PEG is 5.0%, OJ is 6.6%. In Easton and Monahan(2005), GLS is 10.9%, PEG is 11.0%, and MPEG is 12.2%. In Guay et al. (2006), GLS is 9.9%, PEG is 13.2%, and OJ is 13.4%.
15

Kitagawa and Gotoh: Implied Cost of Capital over the Last 20 Years

83(–Continued)

Panel B: Descriptive Statistics for the Cost of Capital by Industry
GLS
OJ
EP
Industry mean median mean median mean mediancode
10.041 0.036 0.102 0.075 0.028 0.032
3
0.023 0.019 0.103 0.094 0.026 0.034
5
0.046 0.028 0.421 0.160 0.035 0.033
7
0.037 0.035 0.100 0.092 0.032 0.040
90.047 0.041 0.092 0.082 0.046 0.040
11
0.051 0.050 0.125 0.114 0.055 0.049
13
0.043 0.042 0.110 0.103 0.052 0.061
15
0.031 0.027 0.105 0.100 0.039 0.034
17
0.032 0.020 0.125 0.110 0.027 0.046
19
0.035 0.031 0.122 0.104 0.031 0.045
21
0.035 0.028 0.121 0.106 0.027 0.039
23
0.048 0.036 0.132 0.094 0.021 0.032
25
0.063 0.065 0.130 0.124 0.022 0.036
27
0.058 0.050 0.115 0.093 0.043 0.056
29
0.020 0.016 0.073 0.072 0.046 0.044
31
0.036 0.034 0.111 0.096 0.025 0.034
33
0.037 0.033 0.110 0.101 0.038 0.043
35
0.042 0.045 0.086 0.069 0.025 0.022
37
0.030 0.029 0.177 0.165 0.046 0.046
41
0.049 0.043 0.125 0.100 0.013 0.033
43
0.043 0.039 0.249 0.122 0.037 0.046
45
0.043 0.035 0.161 0.097 0.033 0.037
53
0.046 0.040 0.260 0.110 0.039 0.036
55
0.020 0.014 0.242 0.202 0.034 0.040
57
0.060 0.056 0.132 0.097 0.020 0.040
59
0.059 0.058 0.117 0.112 0.064 0.056
61
0.040 0.006 0.117 0.103 0.005 0.020
63
0.051 0.048 0.097 0.075 0.048 0.049
65
0.043 0.040 0.398 0.187 0.017 0.031
67
0.059 0.057 0.090 0.082 0.059 0.055
69
0.060 0.060 0.097 0.096 0.054 0.057
71
0.037 0.033 0.395 0.119 0.031 0.036
total
0.043 0.036 0.170 0.099 0.032 0.038

PEG

MPEG

mean median mean median

N

0.067
0.087
0.131
0.086
0.073
0.088
0.101
0.088
0.105
0.099
0.092
0.090
0.100
0.097
0.051
0.091
0.081
0.069
0.052
0.102
0.095
0.087
0.099
0.069
0.087
0.095
0.104
0.070
0.089
0.075
0.078
0.086
0.088

197
61
28
244
159
11
29
50
55
92
260
575
5
167
4
87
74
8
4
102
201
270
86
43
55
16
10
29
73
50
15
378
3517

0.057
0.082
0.125
0.079
0.066
0.080
0.095
0.086
0.096
0.089
0.085
0.080
0.107
0.082
0.053
0.084
0.077
0.054
0.046
0.081
0.085
0.075
0.077
0.072
0.070
0.078
0.093
0.061
0.069
0.069
0.083
0.077
0.078

0.061
0.085
0.100
0.081
0.071
0.085
0.096
0.085
0.104
0.099
0.086
0.086
0.099
0.093
0.047
0.084
0.068
0.065
0.031
0.099
0.078
0.077
0.094
0.042
0.077
0.094
0.104
0.064
0.073
0.071
0.076
0.067
0.080

0.048
0.075
0.097
0.074
0.062
0.076
0.082
0.084
0.096
0.088
0.079
0.075
0.107
0.077
0.049
0.075
0.061
0.054
0.034
0.073
0.067
0.064
0.073
0.026
0.058
0.077
0.093
0.055
0.034
0.063
0.080
0.056
0.069

Note: is table shows a descriptive statistics for each cost of capital by year and by industry. Panel A
shows descriptive statistics for the cost of capital by year, and Panel B shows by industry.
N: the number of firms
GLS: the cost of capital inferred using Gebhardt et al.(2001) model.
OJ: the cost of capital inferred using Ohlson and Juettner-Nauroth(2005) model
EP: expected earnings to price ratio
PEG: PEG ratio proposed by Easton (2004)
MPEG: modified PEG ratio proposed by Easton (2004)
e category of Industry is based on Nikkei industry code. Banks, securities firms, insurance firms, andother financial institutions are eliminated from the sample.

84

e Japanese Accounting Review, 1 (2011), 71-104

T 3: C M   C  C  R F

Panel A: Correlations among the Cost of Capitals
GLS
OJ
EP
PEG
GLS
1.000
0.118
0.162
0.178
OJ
0.053
1.000
-0.057
0.834
EP
0.050
-0.0341.000-0.073
PEG
0.200
0.164
-0.274
1.000
MPEG
0.153
0.003
-0.330
0.900

MPEG
0.173
0.585
-0.1350.874
1.000

Panel B: Correlations among the Risk Factors
Beta
Unsyst Earnvar Leverage
Size
Beta
1.000
0.118
0.262
0.018
0.241
Unsyst
0.161
1.000
0.172
-0.095-0.373
Earnvar
0.076
0.045
1.000
0.284
-0.114
Leverage-0.008
0.008
0.101
1.000
0.050
Size
0.236
-0.349-0.047-0.028
1.000
LTG
0.135
0.136
0.041
-0.087-0.066BM-0.197-0.0280.078
0.336-0.405

LTG
0.088
0.137
0.112
-0.125-0.0651.000-0.109BM-0.205-0.0440.066
0.389-0.363-0.2161.000

Note: is table shows the correlations matrix. Numbers to the left below the diagonal are Pearson
correlation coefficients, while numbers to the right above the diagonal are Spearman rank-order correlation
coefficients. Panel A represents correlation coefficients among costs of capital. On the other hand, Panel B
represents correlation coefficients among risk factors.
GLS: the cost of capital inferred using Gebhardt et al.(2001) model.
OJ: the cost of capital inferred using Ohlson and Juettner-Nauroth(2005) model
EP: expected earnings to price ratio
PEG: PEG ratio proposed by Easton (2004)
MPEG: modified PEG ratio proposed by Easton (2004)
Beta: market beta using daily stock returns over the past 1 year from the announcement date of analysts’
forecasts by IBES
Unsyst: unsystematic risk as measured by the residual from the regression over the previous year of a firm’s
daily return on the daily market return
Earnvar: earning variability using the standard deviation of ROA (net income divided by total assets) overthe past five years
Leverage: leverage as the ratio of the book value long-term debt to the market value of equity
Size: the natural log of the market value of equity
LTG: forecasted long-term growth reported by IBES to define variables regarding the long-term growthin expected earnings
BM: book-to-market ratio as the ratio of shareholders’ equity to the market value of equity

stable at a low level. On the other hand, Panel B provides the cost of capital by industry.17 ere is notas large a difference in magnitude relationally among the costs of capital in any industries. However,
the industry that has a high (or low) cost of capital varies, depending on which cost of capital is thefocus.
Table 3 provides correlation coefficients. Numbers to the left below the diagonal are Pearson
correlation coefficients, while numbers to the right above the diagonal are Spearman rank-ordercorrelation coefficients. Panel A represents correlation coefficients among costs of capital. Although
the costs of capital have a positive correlation with each other in general, some costs of capital havea negative correlation only with EP. While a correlation between PEG and MPEG is as high as
17

Classification of industries is based on the Nikkei industry code.

Kitagawa and Gotoh: Implied Cost of Capital over the Last 20 Years

85

T 4: C M  C  C  R F
Expected sign
GLS
OJ
EP
PEG
MPEG

Beta
(+)
-0.056***(0.001)
0.023(0.180)-0.113***(0.000)0.093***(0.000)0.058***(0.001)

Unsyst(+)-0.105***(0.000)0.218***(0.000)-0.229***(0.000)0.152***(0.000)0.192***(0.000)

EarnvarLeverage(+)(+)-0.0040.273***(0.800)(0.000)0.001
0.008(0.951)(0.640)-0.148*** -0.114***(0.000)(0.000)0.139***
0.276***(0.000)(0.000)0.126***
0.279***(0.000)(0.000)Size(–)-0.007(0.663)-0.198***(0.000)0.014(0.362)-0.109***(0.000)-0.238***(0.000)LTG(–)-0.022(0.163)0.109***(0.000)-0.039**(0.013)0.060***(0.000)0.095***(0.000)BM(+)
0.372***(0.000)-0.035**(0.038)-0.015(0.332)0.245***(0.000)0.276***(0.000)Note: is table shows the correlations matrix between each cost of capital and risk factors. ere are 3,517
observations in the sample from 1987-2007. P-values are in parentheses.
*** Statistically significant at the 0.01 level of significance using a two-tailed t-test.
** Statistically significant at the 0.05 level of significance using a two-tailed t-test.
GLS: the cost of capital inferred using Gebhardt et al.(2001) model.
OJ: the cost of capital inferred using Ohlson and Juettner-Nauroth(2005) model
EP: expected earnings to price ratio
PEG: PEG ratio proposed by Easton (2004)
MPEG: modified PEG ratio proposed by Easton (2004)
Beta: market beta using daily stock returns over the past 1 year from the announcement date of analysts’
forecasts by IBES
Unsyst: unsystematic risk as measured by the residual from the regression over the previous year of a firm’s
daily return on the daily market return
Earnvar: earning variability using the standard deviation of ROA (net income divided by total assets) overthe past five years
Leverage: leverage as the ratio of the book value long-term debt to the market value of equity
Size: the natural log of the market value of equity
LTG: forecasted long-term growth reported by IBES to define variables regarding the long-term growthin expected earnings
BM: book-to-market ratio as the ratio of shareholders’ equity to the market value of equity

90%, OJ has a slightly lower correlation with them. e correlation between OJ and GLS is just
5.3%.18 Panel B represents correlation coefficients among risk factors. While the coefficients have theexpected signs in general, the correlation with LTG tends to be different from the expectation. Since
the maximum coefficient is -0.405 for SIZE and BM, the problem of multicollinearity seems to betrivial.19

In preceding studies, the correlation between GLS and OJ is quite high. For example, Gode and Mohanram (2003) and Botosan
and Plumlee (2005) observed the correlation to be as high as 36%. In the analysis of this study, the correlation between GLS andOJ is almost 40% in the first half of the sampling period. For this reason, it has been found that the correlation is significantly
dependent on the adopted sampling period.
19
To test the possible multi-correlation problem statistically, we calculated the VIF (variance inflation factor) statistics, and we findthat the VIF values of the multi-regression model in the next section are all less than 10 for the multicollinearity detection point.
erefore, we believe that our result is robust under multi-correlation problems.
18

86

e Japanese Accounting Review, 1 (2011), 71-104

T 5: C M D  T P

Panel A: e First Half of Ten Years (1987-1996)
Beta
UnsystEarnvar
Expected sign
(+)
(+)
(+)
GLS
0.009
-0.103**-0.007(0.867)(0.047)(0.886)OJ
0.031-0.032
0.093*(0.571)(0.567)(0.090)EP-0.245***-0.025-0.290***(0.000)(0.630)(0.000)PEG
0.004-0.0800.185***(0.944)(0.136)(0.001)MPEG
0.019-0.0800.184***(0.732)(0.138)(0.001)

Leverage(+)
0.414***(0.000)0.460***(0.000)0.347***(0.000)0.562***(0.000)0.525***(0.000)

Size
(–)
0.035
(0.501)-0.244***(0.000)-0.287***(0.000)-0.264***(0.000)-0.214***(0.000)LTG(–)-0.086*(0.095)0.027(0.620)0.182***(0.000)0.026(0.633)0.012(0.822)

BM(+)
0.548***(0.000)0.419***(0.000)0.628***(0.000)0.602***(0.000)0.522***(0.000)Panel B: e Latter Half of Eleven Years (1997-2007)
Beta
UnsystEarnvar
Expected sign
(+)
(+)
(+)
GLS
-0.079***-0.075***0.012(0.000)(0.000)(0.478)OJ
0.025
0.212***-0.005(0.171)(0.000)(0.795)EP-0.107***-0.240***-0.143***(0.000)(0.000)(0.000)PEG
0.067***
0.184***
0.116***(0.000)(0.000)(0.000)MPEG
0.101***
0.147***
0.132***(0.000)(0.000)(0.000)

Leverage(+)
0.257***(0.000)-0.005(0.796)-0.149***(0.000)0.252***(0.000)0.255***(0.000)Size(–)-0.059***(0.000)-0.192***(0.000)0.033**(0.049)-0.216***(0.000)-0.086***(0.000)

LTG
(–)
0.013
(0.425)0.103***(0.000)-0.047***(0.005)0.081***(0.000)0.050***(0.004)BM(+)
0.368***(0.000)-0.053***(0.003)-0.064***(0.000)0.236***(0.000)0.215***(0.000)Note: is table shows the result of correlations matrix dividing into two periods. Panel A shows theresult of first half of ten years, and Panel B shows the result of last half of eleven years. P-values are inparentheses.
*** Statistically significant at the 0.01 level of significance using a two-tailed t-test.
** Statistically significant at the 0.05 level of significance using a two-tailed t-test.
* Statistically significant at the 0.10 level of significance using a two-tailed t-test.
GLS: the cost of capital inferred using Gebhardt et al.(2001) model.
OJ: the cost of capital inferred using Ohlson and Juettner-Nauroth(2005) model
EP: expected earnings to price ratio
PEG: PEG ratio proposed by Easton (2004)
MPEG: modified PEG ratio proposed by Easton (2004)
Beta: market beta using daily stock returns over the past 1 year from the announcement date of analysts’
forecasts by IBES
Unsyst: unsystematic risk as measured by the residual from the regression over the previous year of a firm’s
daily return on the daily market return
Earnvar: earning variability using the standard deviation of ROA (net income divided by total assets) overthe past five years
Leverage: leverage as the ratio of the book value long-term debt to the market value of equity
Size: the natural log of the market value of equity
LTG: forecasted long-term growth reported by IBES to define variables regarding the long-term growthin expected earnings
BM: book-to-market ratio as the ratio of shareholders’ equity to the market value of equity

Kitagawa and Gotoh: Implied Cost of Capital over the Last 20 Years87

5. Results
5.1 Univariate Analysis
Table 4 indicates a correlation matrix between each cost of capital and risk factor. Both GLS andOJ have two variables that are statistically significant and have expected signs. Leverage and BM in
GLS, as well as Unsyst and Size in OJ, have the expected signs.20 In EP, only LTG has the expected
sign.21 Meanwhile, PEG and MPEG have the most consistent correlation because six risk factors
other than LTG are statistically significant and have the expected signs. erefore, PEG and MPEG
are considered to have the most preferable correlation with risk factors in the entire sample.
Next, we compare the sample, dividing the period into the first half of 10 years and the latter
half of 11 years in order to observe the tendencies in each period.22 e result is presented in Table 5.
In the first half, OJ, PEG, and MPEG have a more consistent correlation with risk factors than withGLS and EP. In other words, four risk factors—including Earnvar, Leverage, Size, and BM—havethe expected signs. In the latter half, however, while the number of variables with the expected signs
increases in PEG and MPEG, only Unsyst and Size have a consistent correlation with OJ. Moreover,in EP, the number of such variables decreases, but in GLS, three variables have expected signs, asmany as in the first half. Consequently, it is suggested that the abnormal earnings growth valuation
model has a lower correlation with risks in the latter half of the analysis period.
Furthermore, Table 6 summarizes the results by year of correlation between the cost of capitaland risk factors.23 Leverage and BM in GLS have the expected sign and a significant correlation
over almost the entire period. e correlation with Earnvar and Size is significant in more years in
the latter half. On the other hand, in OJ, Unsyst, Leverage, Size, and BM have the expected signs inmany years. However, as with Earnvar, the correlation with leverage has tended to be insignificant
since 2000. In contrast to expectations, the correlation with BM since 2003 has tended to besignificantly negative in the latter half. Meanwhile, in PEG and MPEG, several variables are foundto have the expected signs and significant correlations over the entire year. ese tendencies imply
that the results of Tables 5 and 6 are not caused by effects in specific years.
As a summary of the results above, we can argue as follows. According to the result of the entire
sample, the correlation of PEG and MPEG with risk factors is the most consistent with the expected
signs. Only in the first half of the analysis period, OJ is comparable to PEG and MPEG. However, inthe latter half, the number of risk factors with expected signs decreases. While GLS is stable withouta significant variation over the entire period, fewer risk factors show expected correlations in general,compared with PEG and MPEG. Consequently, in the correlation analysis, the PEG and modified
PEG ratios are considered advantageous.

Beta and Unsyst in GLS, as well as BM in OJ, show a significant correlation with an unexpected sign. In EP, Beta, Unsyst,
Earnvars, and Leverage have unexpected signs. As an additional analysis, we estimate Beta and Unsyst using different time period.
We adopted an estimation period of both 180 days and three months prior to forecast data announcement by IBES. However, theremarkable differences in the main results are not found.
21
LTG in EP is contrary to the expectation that LTG and the cost of capital mostly have a significant and positive correlation.
Although the LTG sign forecast is based on Gode and Mohanram(2003), even in their analysis, the same tendency is observed.
erefore, our result is consistent with preceding studies.
22
In dividing the sample, it is possible to examine a structural change. However, as confirmed in Table 2, the increasing variationin levels of cost of capital was observed around 1997, and so the way to divide the sample adopted here is deemed valid to someextent. We conducted a similar verification after dividing the sample into two around 2000. While the difference in adjusted
R-squares among subsamples became smaller slightly, there were not the remarkable difference in analysis results.
23
Although we conducted an analysis of correlation by industry, notable tendencies could not be found.
20e Japanese Accounting Review, 1 (2011), 71-104

88

Panel A: GLS Model
Expected sign
1987
1988
1989
1990
1991
1992
1993
1994
1995
1996
1997
1998
1999
2000
2001
2002
2003
2004
2005
2006
2007

Beta
(+)
-0.356(0.433)0.299(0.321)
0.218(0.176)-0.053(0.833)-0.262(0.178)-0.196(0.134)0.218(0.117)0.029(0.838)-0.010(0.952)0.016(0.900)0.040(0.735)-0.059(0.630)-0.048(0.662)-0.522***(0.000)-0.216***(0.000)-0.088**(0.038)-0.072(0.139)0.001(0.982)0.058(0.239)-0.096*(0.071)-0.021(0.684)T 6: C M  Y
Unsyst(+)
0.667(0.102)0.404(0.171)-0.114(0.486)-0.324(0.189)-0.233(0.233)-0.332***(0.010)-0.156(0.264)-0.191(0.179)-0.100(0.535)-0.058(0.649)-0.111(0.346)-0.092(0.450)0.001(0.993)-0.251***(0.002)-0.112***(0.005)-0.017(0.683)-0.131***(0.007)-0.119**(0.016)-0.083*(0.089)-0.047(0.377)0.026(0.606)

Earnvar(+)-0.395(0.381)0.225(0.461)0.260(0.105)-0.127(0.616)-0.120(0.542)-0.100(0.448)0.441***(0.001)-0.103(0.472)-0.137(0.394)0.048(0.704)-0.155(0.187)-0.102(0.403)-0.082(0.452)0.036(0.672)0.031(0.446)0.016(0.696)0.085*(0.076)0.102**(0.038)-0.008(0.867)-0.043(0.411)0.004(0.934)

Leverage(+)
0.408(0.364)0.288(0.341)0.435***(0.005)0.059(0.817)0.443**(0.018)0.544***(0.000)0.333**(0.015)0.586***(0.000)0.528***(0.000)0.331***(0.007)0.397***(0.001)0.110(0.368)0.520***(0.000)0.437***(0.000)0.195***(0.000)0.219***(0.000)0.321***(0.000)0.336***(0.000)0.352***(0.000)0.305***(0.000)0.169***(0.001)Size(–)-0.287(0.532)-0.325(0.279)-0.003(0.987)0.387(0.112)0.042(0.831)
0.234*(0.072)
0.234*(0.092)-0.131(0.359)-0.051(0.754)-0.138(0.275)0.054(0.649)-0.046(0.709)-0.264**(0.014)-0.347***(0.000)-0.246***(0.000)-0.167***(0.000)0.005(0.917)0.136***(0.006)0.140***(0.004)0.141***(0.007)-0.080(0.109)LTG(–)
0.721*(0.067)0.085(0.782)0.284*(0.076)-0.073(0.774)-0.158(0.423)-0.149(0.256)-0.016(0.911)-0.020(0.887)-0.034(0.835)-0.270**(0.028)-0.206*(0.078)-0.214*(0.078)-0.041(0.708)-0.104(0.214)-0.037(0.359)0.020(0.637)-0.103**(0.031)
0.057(0.247)0.074(0.125)0.149***(0.004)0.149***(0.003)

BM
(+)
0.284
(0.537)0.869***(0.000)0.611***(0.000)0.357(0.146)0.512***(0.005)0.623***(0.000)0.436***(0.001)0.520***(0.000)0.515***(0.001)0.722***(0.000)0.502***(0.000)0.526***(0.000)0.671***(0.000)0.702***(0.000)0.462***(0.000)0.403***(0.000)0.364***(0.000)0.240***(0.000)0.264***(0.000)0.235***(0.000)0.209***(0.000)(Continued)

Kitagawa and Gotoh: Implied Cost of Capital over the Last 20 Years

89(–Continued)

Panel B: OJ Model
Expected sign
1987
1988
1989
1990
1991
1992
1993
1994
1995
1996
1997
1998
1999
2000
2001
2002
2003
2004
2005
2006
2007

Beta
(+)
-0.182(0.696)0.048(0.881)0.206(0.235)0.025(0.935)-0.185(0.356)-0.221(0.127)0.245(0.101)-0.160(0.288)0.082(0.623)0.035(0.799)-0.046(0.710)0.103(0.461)0.278**(0.018)-0.293***(0.001)
0.044(0.315)-0.016(0.721)-0.068(0.182)0.165***(0.003)0.038(0.474)0.057(0.305)-0.076(0.161)

Unsyst(+)
0.731*(0.062)0.488(0.108)0.000(1.000)-0.507*(0.077)-0.132(0.513)-0.274*(0.057)0.033(0.829)0.046(0.761)
0.159(0.341)0.210(0.125)0.518***(0.000)0.170(0.218)0.481***(0.000)-0.009(0.917)0.226***(0.000)0.215***(0.000)0.304***(0.000)0.448***(0.000)0.298***(0.000)0.345***(0.000)0.331***(0.000)

Earnvar(+)-0.484(0.271)0.120(0.710)0.627***(0.000)-0.274(0.365)0.149(0.459)-0.149(0.307)0.415***(0.004)-0.005(0.971)-0.033(0.844)
0.416***(0.001)0.213*(0.079)0.024(0.864)0.024(0.839)0.025(0.774)0.009(0.830)0.003(0.945)-0.009(0.855)0.010(0.853)-0.040(0.447)-0.033(0.543)0.011(0.832)

Leverage(+)
0.357(0.431)
0.432(0.161)0.516***(0.002)0.010(0.975)0.135(0.502)0.608***(0.000)0.379***(0.009)0.860***(0.000)0.627***(0.000)0.644***(0.000)0.116(0.344)0.447***(0.001)0.539***(0.000)0.347***(0.000)0.044(0.309)0.036(0.416)-0.047(0.349)-0.048(0.373)-0.001(0.982)-0.008(0.885)0.021(0.697)Size(–)-0.299(0.514)-0.660**(0.020)-0.365**(0.031)0.218(0.475)-0.136(0.498)-0.187(0.197)0.035(0.816)-0.377***(0.009)-0.346**(0.033)-0.319**(0.016)-0.295**(0.014)-0.354***(0.009)-0.248**(0.035)-0.219***(0.010)-0.141***(0.001)-0.138***(0.002)-0.223***(0.000)-0.196***(0.000)-0.184***(0.000)-0.284***(0.000)-0.280***(0.000)LTG(–)
0.805**(0.029)0.272(0.393)0.651***(0.000)0.035(0.911)0.024(0.905)-0.076(0.606)-0.017(0.909)0.155(0.299)0.025(0.882)-0.085(0.532)-0.019(0.875)-0.034(0.809)-0.120(0.315)-0.006(0.944)0.209***(0.000)0.113***(0.010)0.035(0.488)0.072(0.184)
0.108**(0.040)0.108**(0.048)0.127**(0.017)

BM
(+)
0.268
(0.561)0.869***(0.000)0.551***(0.001)-0.164(0.593)0.323(0.100)0.632***(0.000)0.245*(0.097)0.474***(0.001)0.428***(0.007)0.657***(0.000)0.354***(0.003)0.610***(0.000)0.341***(0.003)0.392***(0.000)0.028(0.519)0.019(0.664)-0.132***(0.008)-0.164***(0.002)-0.108**(0.039)-0.105*(0.056)-0.024(0.658)(Continued)e Japanese Accounting Review, 1 (2011), 71-104

90(–Continued)

Panel C: EP Ratio
Expected sign
1987
1988
1989
1990
1991
1992
1993
1994
1995
1996
1997
1998
1999
2000
2001
2002
2003
2004
2005
2006
2007

Beta
(+)
-0.447(0.314)0.013(0.965)0.088(0.588)-0.128(0.612)-0.364*(0.057)-0.373***(0.003)-0.468***(0.000)-0.513***(0.000)-0.303*(0.054)-0.248**(0.049)-0.139(0.237)-0.299**(0.013)-0.265**(0.013)-0.030(0.717)0.020(0.629)-0.340***(0.000)-0.395***(0.000)-0.234***(0.000)-0.059(0.225)0.056(0.289)0.142***(0.005)

Unsyst(+)
0.335(0.463)0.284(0.346)-0.011(0.949)-0.398(0.102)-0.238(0.224)-0.148(0.259)-0.142(0.312)-0.228(0.108)-0.018(0.910)0.095(0.455)-0.233**(0.046)-0.349***(0.003)-0.437***(0.000)-0.054(0.520)-0.101**(0.012)-0.217***(0.000)-0.275***(0.000)-0.142***(0.004)-0.226***(0.000)-0.113**(0.032)-0.337***(0.000)

EarnvarLeverage(+)(+)-0.659-0.581(0.108)(0.171)-0.0100.292(0.974)(0.333)-0.1620.780***(0.317)(0.000)0.002
0.266(0.995)(0.286)-0.2720.667***(0.161)(0.000)-0.186
0.771***(0.154)(0.000)-0.541*** -0.440***(0.000)(0.001)-0.2190.549***(0.119)(0.000)-0.547*** 0.509***(0.000)(0.001)-0.300**-0.309**(0.015)(0.012)-0.318*** 0.195*(0.006)(0.095)-0.133-0.556***(0.277)(0.000)-0.173-0.103(0.109)(0.343)-0.268*** -0.074(0.001)(0.374)-0.104*** -0.170***(0.010)(0.000)-0.212*** -0.129***(0.000)(0.002)-0.209*** 0.021(0.000)(0.655)-0.112**-0.049(0.022)(0.315)-0.034-0.017(0.476)(0.722)-0.0550.131**(0.290)(0.012)-0.159*** -0.194***(0.001)(0.000)Size(–)-0.339(0.458)-0.665**(0.013)-0.399**(0.011)0.348(0.158)-0.276(0.156)-0.386***(0.002)-0.206(0.136)-0.572***(0.000)-0.279*(0.077)-0.083(0.512)-0.040(0.735)0.071(0.563)-0.083(0.445)-0.081(0.326)0.060(0.133)-0.042(0.309)0.008(0.868)-0.037(0.455)0.046(0.333)-0.031(0.557)0.047(0.344)

LTG
(–)
0.358
(0.431)
0.113(0.714)0.075(0.647)0.473**(0.047)-0.122(0.535)0.310**(0.016)0.325**(0.017)0.346**(0.012)0.171(0.286)0.200(0.111)-0.086(0.468)0.051(0.675)-0.008(0.940)-0.095(0.249)-0.055(0.170)-0.068(0.102)-0.139***(0.003)-0.160***(0.001)-0.122**(0.011)-0.053(0.313)0.032(0.525)BM(+)
0.785**(0.037)0.971***(0.000)0.904***(0.000)0.664***(0.003)0.925***(0.000)0.864***(0.000)0.254*(0.064)0.847***(0.000)0.557***(0.000)0.233*(0.062)0.390***(0.001)
0.193(0.113)0.239**(0.026)0.144*(0.081)-0.092**(0.022)-0.076*(0.066)-0.051(0.284)0.102**(0.036)0.164***(0.001)0.140***(0.007)-0.077(0.123)(Continued)

Kitagawa and Gotoh: Implied Cost of Capital over the Last 20 Years

91(–Continued)

Panel D: PEG Ratio
Expected sign
1987
1988
1989
1990
1991
1992
1993
1994
1995
1996
1997
1998
1999
2000
2001
2002
2003
2004
2005
2006
2007

Beta
(+)
-0.231(0.618)0.071(0.828)0.231(0.175)-0.785***(0.000)-0.234(0.241)-0.235*(0.084)0.299**(0.035)-0.155(0.288)-0.114(0.495)0.007(0.960)-0.096(0.417)0.119(0.376)
0.278**(0.014)-0.307***(0.000)0.066(0.124)0.264***(0.000)0.166***(0.001)
0.043(0.425)0.036(0.486)0.142***(0.009)-0.043(0.417)

Unsyst(+)
0.739*(0.058)0.465(0.128)0.016(0.927)-0.331(0.194)-0.150(0.456)-0.376***(0.005)0.086(0.551)0.132(0.364)0.206(0.215)0.097(0.476)
0.339***(0.003)0.179(0.178)0.445***(0.000)-0.065(0.447)0.125***(0.003)0.245***(0.000)0.165***(0.001)-0.041(0.450)0.134***(0.010)0.471***(0.000)0.395***(0.000)

Earnvar(+)-0.548(0.203)0.107(0.741)0.610***(0.000)0.392(0.120)-0.059(0.770)-0.096(0.484)
0.536***(0.000)0.052(0.718)0.019(0.911)0.433***(0.001)0.309***(0.008)0.028(0.837)0.028(0.811)
0.043(0.607)0.081*(0.057)0.175***(0.000)0.158***(0.001)0.109**(0.038)0.045(0.374)0.190***(0.000)0.170***(0.001)

Leverage(+)
0.261(0.572)0.436(0.156)
0.508***(0.002)-0.216(0.406)0.485***(0.010)0.445***(0.001)0.504***(0.000)0.884***(0.000)0.875***(0.000)0.616***(0.000)0.245**(0.037)0.453***(0.000)0.620***(0.000)0.216***(0.010)0.219***(0.000)0.312***(0.000)0.177***(0.000)0.183***(0.001)0.105**(0.040)0.126**(0.019)0.207***(0.000)Size(–)-0.346(0.448)-0.640**(0.025)-0.281*(0.098)0.616***(0.009)-0.371*(0.057)-0.119(0.388)-0.013(0.928)-0.364***(0.009)-0.561***(0.000)-0.234*(0.081)-0.225*(0.056)-0.372***(0.004)-0.261**(0.022)-0.215***(0.010)-0.160***(0.000)-0.184***(0.000)-0.121**(0.014)-0.054(0.304)-0.189***(0.000)-0.316***(0.000)-0.358***(0.000)LTG(–)
0.844**(0.017)0.265(0.405)0.676***(0.000)0.465*(0.060)0.100(0.620)-0.058(0.677)-0.226(0.111)0.013(0.930)0.059(0.724)-0.067(0.621)0.010(0.935)-0.063(0.637)-0.134(0.244)-0.050(0.550)0.056(0.192)0.133***(0.002)
0.093*(0.058)0.174***(0.001)0.125**(0.014)0.106**(0.050)0.103**(0.049)

BM
(+)
0.348
(0.444)0.901***(0.000)0.529***(0.001)0.008(0.976)
0.841***(0.000)0.531***(0.000)0.345**(0.013)0.588***(0.000)0.848***(0.000)0.620***(0.000)0.325***(0.005)0.572***(0.000)0.390***(0.001)0.321***(0.000)0.170***(0.000)0.297***(0.000)0.147**(0.003)0.070(0.183)0.142***(0.005)-0.044(0.414)0.272***(0.000)(Continued)e Japanese Accounting Review, 1 (2011), 71-104

92(–Continued)

Panel E: Modified PEG Ratio
Beta
Expected sign(+)
1987
-0.184(0.694)1988
0.097(0.765)1989
0.252(0.139)1990-0.766***(0.000)1991-0.221(0.268)1992-0.220(0.106)1993
0.326**(0.021)1994-0.107(0.466)
1995-0.097(0.564)1996
0.037(0.785)1997-0.058(0.627)1998
0.106(0.427)
1999
0.327***(0.004)2000-0.250***(0.003)2001
0.106**(0.013)
2002
0.294***(0.000)2003
0.220***(0.000)2004
0.052(0.333)2005
0.070(0.174)2006
0.165***(0.002)
2007
0.088*(0.095)

Unsyst(+)
0.746*(0.054)0.463(0.130)0.007(0.968)-0.342(0.180)-0.173(0.389)-0.406***(0.002)0.079(0.587)0.209(0.150)0.222(0.181)0.029(0.832)
0.396***(0.001)0.162(0.225)0.468***(0.000)-0.044(0.608)0.075*(0.081)0.248***(0.000)0.063(0.210)-0.146***(0.006)0.067(0.192)0.253***(0.000)0.292***(0.000)

Earnvar(+)-0.550(0.201)0.123(0.705)0.664***(0.000)0.387(0.125)-0.047(0.817)-0.087(0.527)0.528***(0.000)0.028(0.848)0.015(0.927)0.507***(0.000)0.293**(0.012)0.040(0.767)0.025(0.827)0.259***(0.002)0.083*(0.052)0.183***(0.000)0.177***(0.000)0.101*(0.055)0.051(0.315)0.210***(0.000)0.160***(0.002)

Leverage(+)
0.325(0.477)0.403(0.194)0.457***(0.005)-0.203(0.435)0.394**(0.042)0.390***(0.003)0.488***(0.000)0.843***(0.000)0.916***(0.000)0.545***(0.000)0.173(0.144)0.474***(0.000)0.534***(0.000)0.204**(0.014)0.246***(0.000)0.302***(0.000)0.190***(0.000)0.211***(0.000)0.116**(0.023)0.128**(0.017)0.235***(0.000)Size(–)-0.262(0.571)-0.599**(0.040)-0.252(0.138)0.631***(0.007)-0.311(0.115)-0.053(0.700)0.046(0.750)-0.396***(0.004)-0.528***(0.001)-0.062(0.647)-0.188(0.111)-0.308**(0.019)-0.171(0.137)-0.219***(0.009)-0.066(0.124)-0.093**(0.031)
0.051(0.299)0.172***(0.001)-0.081(0.113)-0.045(0.406)-0.157***(0.003)LTG(–)
0.808**(0.028)0.273(0.391)0.702***(0.000)0.463*(0.061)0.086(0.669)-0.096(0.486)-0.230(0.105)0.027(0.854)0.052(0.758)-0.087(0.520)0.004(0.974)-0.064(0.635)-0.134(0.244)-0.097(0.248)0.039(0.364)0.084*(0.052)0.047(0.343)0.130**(0.013)0.087*(0.088)0.036(0.500)0.134***(0.010)

BM
(+)
0.291
(0.527)0.886***(0.000)0.470***(0.004)0.001(0.997)0.783***(0.000)0.486***(0.000)0.299**(0.033)0.512***(0.000)0.826***(0.000)0.392***(0.003)0.249**(0.034)0.520***(0.000)0.237**(0.038)0.306***(0.000)0.158***(0.000)0.280***(0.000)0.142***(0.004)0.070(0.188)0.144***(0.005)-0.047(0.380)0.203***(0.000)Note: is table shows the correlations matrix by year. Panel A shows the correlation between GLS andKitagawa and Gotoh: Implied Cost of Capital over the Last 20 Years

93

risk factors. From Panel B to E shows the result of OJ, EP, PEG, and MPEG, respectively. P-values are inparentheses.
*** Statistically significant at the 0.01 level of significance using a two-tailed t-test.
** Statistically significant at the 0.05 level of significance using a two-tailed t-test.
* Statistically significant at the 0.10 level of significance using a two-tailed t-test.
Beta: market beta using daily stock returns over the past 1 year from the announcement date of analysts’
forecasts by IBES
Unsyst: unsystematic risk as measured by the residual from the regression over the previous year of a firm’s
daily return on the daily market return
Earnvar: earning variability using the standard deviation of ROA (net income divided by total assets) overthe past five years
Leverage: leverage as the ratio of the book value long-term debt to the market value of equity
Size: the natural log of the market value of equity
LTG: forecasted long-term growth reported by IBES to define variables regarding the long-term growthin expected earnings
BM: book-to-market ratio as the ratio of shareholders’ equity to the market value of equity

Intercept
Expected sign(?)
GLS
-0.064***(0.000)OJ
1.110***(0.000)EP
0.157***(0.000)PEG
0.142***(0.000)MPEG
0.009(0.708)T 7: T R  P R

Beta
(+)
-0.004***(0.005)-0.030(0.142)-0.005(0.110)0.001(0.602)0.005*(0.095)

Unsyst(+)
0.050(0.483)2.224***(0.000)-0.405***(0.000)0.250***(0.000)0.276***(0.000)

Earnvar(+)
0.011(0.152)-0.095(0.336)-0.111***(0.000)0.051***(0.000)0.077***(0.000)

Leverage(+)
0.007***(0.000)0.024***(0.005)-0.011***(0.000)0.017***(0.000)0.019***(0.000)Size(–)
0.003***(0.000)-0.032***(0.000)-0.003***(0.000)-0.004***(0.000)0.001(0.454)LTG(–)
0.000***(0.000)0.100***(0.001)0.000(0.181)0.000***(0.000)0.000***(0.003)BM(+)
0.032***(0.000)-0.029(0.102)0.003(0.205)0.019***(0.000)0.023***(0.000)

adj.R2
0.319
0.124
0.133
0.227
0.188

Note: is table shows the result of pooled regression. ere are 3,517 observations in the sample
from 1987-2007. Indicator for the year and the industry are included but not reported. P-values are inparentheses.
*** Statistically significant at the 0.01 level of significance using a two-tailed t-test.
* Statistically significant at the 0.10 level of significance using a two-tailed t-test.
GLS: the cost of capital inferred using Gebhardt et al. (2001) model.
OJ: the cost of capital inferred using Ohlson and Juettner-Nauroth (2005) model
EP: expected earnings to price ratio
PEG: PEG ratio proposed by Easton (2004)
MPEG: modified PEG ratio proposed by Easton (2004)
Beta: market beta using daily stock returns over the past 1 year from the announcement date of analysts’
forecasts by IBES
Unsyst: unsystematic risk as measured by the residual from the regression over the previous year of a firm’s
daily return on the daily market return
Earnvar: earning variability using the standard deviation of ROA (net income divided by total assets) overthe past five years
Leverage: leverage as the ratio of the book value long-term debt to the market value of equity
Size: the natural log of the market value of equity
LTG: forecasted long-term growth reported by IBES to define variables regarding the long-term growthin expected earnings
BM: book-to-market ratio as the ratio of shareholders’ equity to the market value of equity

e Japanese Accounting Review, 1 (2011), 71-104

94

T 8: T R  R D  T P

Panel A: e First Half of Ten Years (1987-1996)
Intercept
Expected sign(?)
GLS
-0.516***(0.000)OJ
0.136(0.258)EP-0.019(0.632)PEG
0.001(0.984)MPEG-0.012(0.832)

Beta
(+)
0.008
(0.331)0.024(0.134)-0.016***(0.002)0.012*(0.089)0.012*(0.087)

Unsyst(+)
0.189(0.189)-0.368(0.229)-0.002(0.979)-0.223*(0.072)-0.217(0.103)

Earnvar(+)-0.077(0.176)
0.199*(0.061)-0.213***(0.000)0.231***(0.000)0.225***(0.000)Panel B: e Latter Half of Eeleven Years (1997-2007)
Intercept
Expected sign(?)
GLS
-0.033***(0.002)OJ
1.468***(0.000)EP
0.165***(0.000)PEG
0.170***(0.000)MPEG
0.019(0.404)Beta(+)-0.001(0.265)0.016(0.380)-0.008***(0.005)0.013***(0.000)0.016***(0.000)Unsyst(+)-0.034***(0.010)1.353***(0.000)-0.417***(0.000)0.153***(0.000)0.194***(0.000)

Earnvar(+)-0.012*(0.090)-0.100(0.350)-0.112***(0.000)0.053***(0.000)0.083***(0.000)

Leverage(+)
0.009***(0.002)0.027***(0.000)-0.005**(0.019)0.012***(0.000)0.013***(0.000)Size(–)
0.019***(0.000)-0.004(0.377)0.001(0.448)0.001(0.654)0.001(0.504)

LTG
(–)
0.000
(0.239)0.000(0.403)0.001***(0.000)0.000(0.173)0.000(0.397)BM(+)
0.070***(0.000)0.036***(0.003)0.056***(0.000)0.041***(0.000)0.036***(0.000)

Leverage(+)
0.005***(0.000)0.018**(0.026)-0.007***(0.000)0.012***(0.000)0.012***(0.000)Size(–)
0.002***(0.000)-0.051***(0.000)-0.003***(0.000)-0.005***(0.000)0.000(0.714)LTG(–)
0.000***(0.000)0.001***(0.000)0.000**(0.021)0.000***(0.000)0.000***(0.001)BM(+)
0.025***(0.000)-0.104***(0.000)-0.012***(0.000)0.018***(0.000)0.026***(0.000)

adj.R2
0.420
0.241
0.519
0.447
0.387

adj.R2
0.191
0.076
0.099
0.146
0.122

Note: is table shows the result of regression dividing into two periods. Panel A shows the result of firsthalf of ten years, and Panel B shows the result of last half of eleven years. Indicator for the year and theindustry are included but not reported. P-values are in parentheses.
*** Statistically significant at the 0.01 level of significance using a two-tailed t-test.
* Statistically significant at the 0.10 level of significance using a two-tailed t-test.
GLS: the cost of capital inferred using Gebhardt et al. (2001) model.
OJ: the cost of capital inferred using Ohlson and Juettner-Nauroth (2005) model
EP: expected earnings to price ratio
PEG: PEG ratio proposed by Easton (2004)
MPEG: modified PEG ratio proposed by Easton (2004)
Beta: market beta using daily stock returns over the past 1 year from the announcement date of analysts’
forecasts by IBES
Unsyst: unsystematic risk as measured by the residual from the regression over the previous year of a firm’s
daily return on the daily market return
Earnvar: earning variability using the standard deviation of ROA (net income divided by total assets) overthe past five years
Leverage: leverage as the ratio of the book value long-term debt to the market value of equity
Size: the natural log of the market value of equity
LTG: forecasted long-term growth reported by IBES to define variables regarding the long-term growthin expected earnings
BM: book-to-market ratio as the ratio of shareholders’ equity to the market value of equity

Kitagawa and Gotoh: Implied Cost of Capital over the Last 20 Years

Panel A: GLS Model

Intercept
Expected sign(?)
1988
-0.339*(0.082)1989-0.786***(0.000)1990-0.666(0.431)1991-0.908**(0.050)1992-0.609***(0.001)1993-0.619***(0.002)1994-0.303(0.109)1995-0.471(0.121)1996-0.270*(0.054)1997-0.370***(0.001)
1998-0.348**(0.035)1999-0.383***(0.003)2000-0.019(0.546)2001
0.027(0.299)2002-0.019(0.557)2003-0.010(0.722)
2004-0.056**(0.029)2005-0.077***(0.002)
2006-0.096***(0.001)2007-0.053(0.191)

95

T 9: T R  R  Y
Beta(+)
-0.024(0.522)0.016(0.397)-0.028(0.878)-0.097(0.239)-0.008(0.748)0.050(0.125)0.065**(0.044)0.047(0.164)0.017(0.246)0.009(0.485)-0.004(0.848)-0.018(0.198)-0.010***(0.001)-0.008***(0.006)-0.009**(0.014)-0.003(0.284)-0.001(0.684)0.001(0.763)-0.009**(0.027)0.001(0.786)

Unsyst(+)-0.274(0.437)0.897(0.136)-0.449(0.823)0.766(0.462)-0.094(0.822)0.043(0.938)-0.693(0.360)-0.471(0.625)-0.776(0.252)-0.337(0.267)0.007(0.979)-0.024(0.881)-0.006(0.854)-0.021(0.509)0.065(0.145)0.017(0.678)0.031(0.453)0.138**(0.024)0.126**(0.012)0.128(0.169)Earnvar(+)
3.675*(0.095)2.469***(0.006)-5.310(0.555)6.462(0.265)-0.005(0.991)1.655(0.140)-0.008(0.978)-0.168(0.132)0.022(0.738)-0.102*(0.081)-0.047(0.685)-0.013(0.868)-0.009(0.567)-0.011(0.446)-0.003(0.862)0.016(0.291)
0.013(0.294)-0.017(0.290)-0.003(0.889)-0.073(0.111)

Leverage(+)
0.006*(0.087)0.002(0.737)0.004(0.895)0.030*(0.082)0.019*(0.073)-0.001(0.921)0.035***(0.001)0.031*(0.058)-0.012*(0.035)0.009**(0.049)0.002(0.633)0.009**(0.045)0.002**(0.027)0.003***(0.005)0.004***(0.001)0.008***(0.000)0.008***(0.000)0.011***(0.000)0.010***(0.000)0.007**(0.027)Size(–)
0.014*(0.072)0.028***(0.000)0.029(0.286)
0.037**(0.020)0.024***(0.001)
0.022***(0.004)0.010(0.118)0.017(0.102)0.010**(0.048)0.014***(0.001)0.013**(0.021)0.014***(0.002)0.002(0.141)0.000(0.920)0.001(0.227)0.001(0.277)0.003***(0.002)0.003***(0.000)0.004***(0.000)0.002*(0.092)LTG(–)-0.023(0.882)-0.011(0.896)-0.555(0.357)-0.195(0.347)-0.003(0.970)0.137(0.197)0.037(0.763)-0.033(0.826)-0.108***(0.004)-0.022(0.584)-0.023(0.467)0.010(0.594)0.010(0.143)0.015**(0.041)0.016*(0.066)-0.006(0.327)0.016***(0.002)0.012**(0.015)0.030***(0.000)0.031***(0.000)BM(+)
0.064***(0.002)0.109***(0.000)0.118(0.418)0.053(0.126)0.045*(0.071)0.075***(0.000)0.040**(0.021)
0.047(0.120)0.107***(0.000)0.077***(0.000)0.065***(0.000)0.078***(0.000)0.021***(0.000)0.023***(0.000)0.024***(0.000)0.021***(0.000)0.019***(0.000)0.023***(0.000)0.023***(0.000)0.035***(0.000)

adj.R20.871
0.656-0.111
0.352
0.532
0.377
0.429
0.330
0.577
0.455
0.329
0.515
0.545
0.233
0.195
0.216
0.167
0.205
0.190
0.126
(Continued)e Japanese Accounting Review, 1 (2011), 71-104

96(–Continued)

Panel B: OJ Model

Intercept
Expected sign(?)
1988
-0.002(0.994)1989-0.047(0.698)1990
0.348(0.860)1991
0.778(0.331)
1992
0.363**(0.041)1993-0.205(0.444)1994
0.359(0.259)1995
0.467(0.512)1996
0.066(0.654)1997-0.158(0.472)
1998-0.148(0.590)1999
0.038(0.877)2000-0.150(0.414)2001
1.851*(0.072)2002
2.058*(0.094)2003
6.932**(0.015)2004
0.925(0.384)2005
2.938*(0.067)2006
6.346**(0.012)2007
5.390(0.154)

Beta(+)-0.022(0.741)-0.005(0.681)-0.137(0.566)-0.074(0.611)0.006(0.816)0.067(0.170)0.130**(0.036)0.078(0.303)0.028*(0.074)-0.066*(0.025)-0.011(0.757)0.027(0.326)-0.034*(0.037)-0.135(0.257)-0.065(0.645)-0.362(0.226)-0.050(0.702)-0.062(0.794)-0.254(0.452)-0.771*(0.087)

Unsyst(+)
0.186(0.738)0.274(0.548)-4.585(0.274)-3.579*(0.064)-0.923*(0.065)-0.012(0.989)-0.965(0.472)-1.405(0.519)-0.239(0.741)2.894***(0.000)-0.233(0.603)0.700**(0.031)0.403**(0.036)1.052(0.425)1.386(0.423)6.567*(0.092)8.645***(0.000)9.519**(0.017)7.355*(0.085)21.322**(0.014)

Earnvar Leverage
(+)
(+)
0.731
0.003
(0.821)(0.545)
3.177*** 0.007*(0.000)(0.094)-4.1040.075(0.758)(0.802)21.182** -0.019(0.037)(0.494)-0.1580.009(0.682)(0.398)3.755**
0.012(0.017)(0.418)-0.2710.182***(0.585)(0.000)-0.1470.108***(0.540)(0.004)0.454*** 0.012**(0.000)(0.041)0.294**
0.011(0.015)(0.298)0.106
0.027***(0.577)(0.000)-0.1760.018*(0.354)(0.052-0.0490.018**(0.672)(0.018)0.156
0.008(0.801)(0.867)-0.0490.015(0.950)(0.736)0.495
0.046(0.731)(0.749)-0.1720.073(0.735)(0.259)-0.8620.114(0.425)(0.353)-1.818-0.013(0.422)(0.947)-0.379-0.026(0.935)(0.938)

Size
(–)
0.002
(0.891)
0.002(0.619)0.005(0.946)-0.023(0.380)-0.011(0.105)0.007(0.469)-0.016(0.156)-0.016(0.518)-0.003(0.598)0.006(0.415)0.006(0.552)-0.001(0.922)0.007(0.247)-0.061(0.109)-0.070(0.129)-0.237*(0.025)-0.037(0.340)-0.106*(0.075)-0.218*(0.015)-0.174(0.190)

LTG
(–)
0.207
(0.580)0.144**(0.025)-0.558(0.634)0.216(0.536)-0.086(0.272)0.125(0.382)0.421**(0.048)0.057(0.879)0.014(0.740-0.019(0.821)
0.098(0.116)-0.019(0.598)0.056(0.179)0.433(0.165)0.278(0.394)0.091(0.876)-0.190(0.401)0.079(0.808)-0.074(0.891)0.594(0.430)

BM
(+)
0.033
(0.147)0.044***(0.001)-0.194(0.329)0.040(0.503)0.030(0.228)0.030(0.221)-0.051*(0.090)-0.038(0.573)0.083***(0.000)0.044(0.133)0.103***(0.000)0.021(0.483)0.050***(0.009)-0.173*(0.091)-0.178(0.102)-0.711*(0.024)-0.063(0.716)-0.200(0.376)-0.463(0.278)-0.819(0.159)adj.R20.545
0.821-0.223
0.113
0.404
0.200
0.785
0.302
0.745
0.341
0.480
0.311
0.187
0.007
0.004
0.054
0.129
0.037
0.047
0.047
(Continued)

Kitagawa and Gotoh: Implied Cost of Capital over the Last 20 Years

97(–Continued)

Panel C: EP Ratio

Intercept
Expected sign(?)
1988
-0.087(0.621)1989-0.141*(0.056)1990-0.008(0.947)
1991-0.270**(0.021)1992
0.116*(0.088)1993
0.111(0.125)1994
0.221**(0.012)
1995-0.016(0.932)1996-0.105(0.422)
1997-0.094(0.302)
1998-0.259(0.436)1999
0.112(0.589)2000
0.061(0.631)2001
0.146*(0.052)
2002
0.196**(0.022)2003
0.190***(0.006)
2004
0.094**(0.047)2005
0.054(0.323)2006
0.135**(0.025)2007
0.286***(0.000)Beta(+)-0.045(0.273)0.017**(0.037)-0.001(0.976)-0.033(0.114)-0.006(0.509)-0.022*(0.065)-0.028*(0.057)-0.013(0.518)-0.021(0.137)0.002(0.829)0.014(0.710)0.000(0.998)0.010(0.383)0.016*(0.074)-0.060***(0.000)-0.046***(0.000)-0.016***(0.005)-0.002(0.846)
0.026***(0.001)0.033***(0.000)Unsyst(+)-0.535(0.179)-0.041(0.868)-0.284(0.334)0.658**(0.017)-0.156(0.319)-0.236(0.251)-0.799**(0.023)-0.421(0.475)0.379(0.554)-0.651**(0.014)-0.463(0.402)-0.903***(0.001)-0.034(0.800)-0.311***(0.001)-0.419***(0.001)-0.306***(0.002)-0.069(0.368)-0.474***(0.001)-0.290***(0.004)-1.117***(0.000)

Earnvar(+)
1.395(0.492)-0.353(0.311)0.971(0.452)-1.342(0.346)-0.341**(0.041)-1.378***(0.001)-0.200(0.142)-0.325***(0.000)-0.079(0.208)-0.154***(0.003)0.002(0.992)-0.116(0.351)-0.230***(0.001)-0.099**(0.018)-0.222***(0.000)-0.133***(0.000)-0.040*(0.090)-0.011(0.757)-0.054(0.257)-0.133**(0.037)

Leverage(+)
0.002(0.511)0.006***(0.010)0.000(0.940)0.001(0.842)-0.005(0.176)-0.032***(0.000)0.000(0.977)0.024**(0.019)-0.032***(0.000)0.002(0.598)-0.041***(0.000)-0.008(0.262)-0.006(0.161)-0.011***(0.000)-0.006*(0.062)0.006*(0.070)-0.003(0.357)-0.006(0.132)0.010**(0.034)-0.011***(0.010)

Size
(–)
0.005
(0.448)0.005*(0.054)0.000(0.996)0.011***(0.007)-0.004*(0.079)-0.003(0.300)-0.007**(0.022)0.001(0.831)
0.005(0.334)0.004(0.206)0.010(0.408)-0.002(0.735)-0.002(0.672)-0.003(0.245)-0.003(0.339)-0.003(0.226)-0.001(0.503)0.000(0.985)-0.004**(0.045)-0.008***(0.000)LTG(–)-0.014(0.931)0.001(0.967)0.199**(0.036)-0.107**(0.045)0.150***(0.000)0.037(0.342)0.112**(0.049)0.147(0.118)0.021(0.541)0.021(0.541)0.027(0.670)-0.005(0.859)-0.035(0.200)-0.046**(0.033)-0.036(0.116)-0.037**(0.012)-0.018*(0.063)-0.012(0.288)-0.005(0.710)0.006(0.592)BM(+)
0.080***(0.001)0.055***(0.000)0.063***(0.010)0.074***(0.000)0.073***(0.000)0.042***(0.000)0.046***(0.000)0.017(0.365)0.070***(0.000)0.044***(0.000)0.076***(0.003)0.046**(0.038)0.023*(0.071)-0.014**(0.039)-0.017*(0.018)-0.028***(0.000)0.001(0.927)0.016**(0.045)0.018*(0.083)-0.013(0.135)

adj.R2
0.927
0.854
0.564
0.904
0.851
0.745
0.812
0.579
0.488
0.308
0.369
0.247
0.086
0.055
0.175
0.235
0.059
0.056
0.054
0.217
(Continued)e Japanese Accounting Review, 1 (2011), 71-104

98(–Continued)

Panel D: PEG Ratio

Intercept
Expected sign(?)
1988
-0.105(0.650)1989-0.197*(0.093)1990-0.079(0.686)1991
0.064(0.735)
1992
0.381**(0.036)1993-0.100(0.507)
1994-0.116(0.225)1995
0.125(0.387)1996
0.008(0.953)1997-0.139(0.330)1998
0.037(0.861)1999-0.014(0.945)2000
0.065(0.667)2001
0.133**(0.029)2002
0.156**(0.011)2003
0.143**(0.021)2004
0.148***(0.003)2005
0.190***(0.006)2006
0.143***(0.001)2007
0.128***(0.007)

Beta(+)-0.037(0.508)-0.002(0.847)-0.082*(0.092)0.041(0.239)0.046*(0.084)0.038(0.144)0.012(0.455)0.014(0.349)0.017(0.243)-0.044**(0.014)-0.002(0.951)
0.022(0.311)-0.028**(0.042)0.010(0.149)0.040***(0.000)0.018***(0.006)0.004(0.499)0.012(0.260)-0.006(0.283)-0.001(0.830)Unsyst(+)
0.040(0.929)0.523(0.245)-0.375(0.426)-0.513(0.250)-1.401***(0.002)0.263(0.589)0.768*(0.059)0.088(0.843)-0.681(0.321)
1.469***(0.000)-0.215(0.555)0.503*(0.054)0.080(0.613)0.157**(0.040)0.268***(0.002)0.106(0.216)-0.115(0.133)0.374**(0.030)0.522***(0.000)0.645***(0.000)

Earnvar(+)
0.575(0.827)2.916***(0.000)3.806(0.133)2.153(0.347)-0.126(0.769)2.911***(0.001)0.008(0.959)0.037(0.452)0.420***(0.000)0.254***(0.001)0.083(0.595)-0.122(0.429)0.014(0.886)0.036(0.309)0.112***(0.004)0.075**(0.019)0.027(0.252)0.008(0.873)0.203***(0.000)0.107*(0.074)

Leverage(+)
0.004(0.344)0.008**(0.047)-0.016(0.730)-0.021***(0.004)-0.005(0.624)0.010(0.225)0.049***(0.000)0.029***(0.000)0.011*(0.056)0.009(0.136)0.020***(0.001)0.020***(0.004)0.004(0.369)0.010***(0.000)0.014***(0.000)0.007**(0.019)0.009***(0.002)0.015***(0.006)0.012***(0.001)0.015***(0.000)

Size
(–)
0.005
(0.564)0.007*(0.096)0.007(0.255)-0.003(0.581)-0.013*(0.056)0.003(0.530)0.004(0.183)-0.005(0.354)0.000(0.965)0.006(0.216)-0.001(0.921)0.001(0.898)0.001(0.904)-0.003(0.170)-0.005**(0.016)-0.004(0.113)-0.003*(0.082)-0.006**(0.031)-0.003**(0.045)-0.003**(0.038)

LTG
(–)
0.248
(0.426)0.184***(0.003)0.103(0.444)0.116(0.170)-0.009(0.923)-0.053(0.517)-0.006(0.920)0.066(0.388)0.021(0.595)0.001(0.989)0.053(0.288)-0.020(0.485)0.016(0.633)0.023(0.222)0.057***(0.001)
0.019(0.138)0.037***(0.000)0.024*(0.097)0.001(0.916)0.019*(0.054)BM(+)
0.039*(0.056)0.045***(0.001)-0.021(0.549)0.086***(0.000)0.052**(0.041)0.029**(0.041)
0.014(0.122)0.050***(0.001)0.075***(0.000)0.030*(0.084)0.059***(0.000)0.018(0.412)0.023(0.118)0.011*(0.078)0.021***(0.000)0.017**(0.012)0.004(0.604)0.029***(0.005)0.002(0.814)0.033***(0.000)

adj.R2
0.684
0.820
0.626
0.774
0.355
0.429
0.781
0.835
0.706
0.299
0.409
0.390
0.092
0.067
0.276
0.104
0.068
0.078
0.285
0.291
(Continued)

Kitagawa and Gotoh: Implied Cost of Capital over the Last 20 Years

99(–Continued)

Panel E: Modified PEG Ratio
Intercept
Expected sign(?)
1988
-0.113(0.613)1989-0.159(0.117)
1990-0.116(0.575)1991
0.058(0.765)1992
0.333*(0.062)1993-0.145(0.348)1994-0.053(0.691)
1995
0.042(0.773)1996-0.040(0.758)1997-0.174(0.273)
1998-0.053(0.830)1999
0.005(0.982)2000
0.107(0.555)2001
0.013(0.848)2002-0.004(0.959)2003-0.041(0.555)2004-0.044(0.448)2005
0.095(0.250)2006-0.010(0.858)2007-0.009(0.901)

Beta(+)-0.035(0.517)-0.001(0.897)-0.078(0.121)
0.047(0.194)0.049*(0.064)0.040(0.140)0.025(0.274)0.016(0.305)0.014(0.314)-0.046**(0.019)-0.009(0.794)0.027(0.233)-0.018(0.268)0.017**(0.031)
0.044***(0.000)0.023***(0.002)0.005(0.475)0.018(0.133)0.003(0.684)0.015*(0.088)

Unsyst(+)
0.053(0.902)0.437(0.261)-0.397(0.425)-0.625(0.179)-1.432***(0.001)
0.273(0.584)
1.184**(0.038)0.201(0.656)-0.670(0.290)1.872***(0.000)-0.187(0.661)0.580**(0.032)-0.002(0.993)0.121(0.149)0.430***(0.000)0.093(0.334)-0.161*(0.075)0.335(0.101)0.394***(0.000)0.710***(0.000)

Earnvar(+)
0.475(0.850)2.754***(0.000)3.944(0.139)2.818(0.238)-0.081(0.848)2.894***(0.002)-0.139(0.510)0.015(0.755)0.400***(0.000)0.268***(0.002)0.102(0.577)-0.131(0.410)0.261***(0.007)0.046(0.236)0.137***(0.003)0.103***(0.004)0.031(0.256)0.028(0.631)0.245***(0.000)0.152*(0.091)

Leverage(+)
0.003(0.418)0.007*(0.055)-0.013(0.790)-0.024***(0.002)-0.006(0.551)
0.012(0.186)
0.061***(0.000)0.044***(0.000)0.013**(0.016)0.007(0.252)0.025***(0.000)0.019***(0.010)0.003(0.585)0.012***(0.000)0.014***(0.000)0.005(0.113)0.009**(0.015)0.015**(0.020)0.010**(0.018)0.021***(0.001)

Size
(–)
0.006
(0.527)0.006(0.109)0.008(0.209)-0.003(0.594)-0.011*(0.092)0.005(0.368)0.001(0.776)-0.002(0.732)0.002(0.670)0.007(0.190)0.002(0.776)0.000(0.963)-0.001(0.874)0.001(0.689)0.000(0.868)0.003(0.289)0.004*(0.072)-0.003(0.407)
0.002(0.290)0.000(0.922)

LTG
(–)
0.231
(0.438)0.163***(0.002)0.106(0.452)0.125(0.154)-0.013(0.879)-0.050(0.547)0.038(0.664)0.052(0.501)0.008(0.816)-0.010(0.873)0.059(0.315)-0.022(0.455)0.004(0.913)0.018(0.371)
0.043**(0.023)0.011(0.442)0.042***(0.001)0.017(0.316)-0.009(0.479)0.037***(0.009)BM(+)
0.035*(0.068)0.035***(0.002)-0.026(0.480)0.085***(0.000)0.050**(0.046)
0.026*(0.078)0.004(0.780)0.043***(0.004)0.058***(0.000)0.022(0.237)0.065***(0.001)-0.003(0.901)
0.028(0.114)0.015**(0.020)0.032***(0.000)0.025***(0.001)
0.011(0.231)0.033***(0.006)0.002(0.837)0.043***(0.000)

adj.R2
0.608
0.825
0.611
0.737
0.330
0.414
0.719
0.866
0.686
0.278
0.375
0.326
0.113
0.064
0.269
0.100
0.086
0.042
0.116
0.186

Note: is table shows the result of the regression by year. Panel A shows the result of the regression on
GLS. From Panel B to E shows the result of OJ, EP, PEG, and MPEG, respectively. P-values are inparentheses.
*** Statistically significant at the 0.01 level of significance using a two-tailed t-test.
** Statistically significant at the 0.05 level of significance using a two-tailed t-test.
* Statistically significant at the 0.10 level of significance using a two-tailed t-test.
Beta: market beta using daily stock returns over the past 1 year from the announcement date of analysts’(Continued)e Japanese Accounting Review, 1 (2011), 71-104

100(–Continued)

forecasts by IBES
Unsyst: unsystematic risk as measured by the residual from the regression over the previous year of a firm’s
daily return on the daily market return
Earnvar: earning variability using the standard deviation of ROA (net income divided by total assets) overthe past five years
Leverage: leverage as the ratio of the book value long-term debt to the market value of equity
Size: the natural log of the market value of equity
LTG: forecasted long-term growth reported by IBES to define variables regarding the long-term growthin expected earnings
BM: book-to-market ratio as the ratio of shareholders’ equity to the market value of equity

5.2 Multivariate Analysis
Table 7 shows the estimation result of a multiple regression model in which costs of capital
estimated by each model are dependent variables and seven risk factors are independent variables.
In order to control the effects of year and industry, we regress the model including year dummies
and industry dummies. According to the result of Table 7, the adjusted R-square of GLS is thehighest, 31.9%. However, among risk factors included in independent variables, only the coefficientsof Leverage and BM have the expected signs, and this result should be interpreted carefully. On theother hand, as for OJ, three risk factors—including Unsyst, Leverage, and Size—have the expected
signs and significant values, but the adjusted R-square is about 12%, lower than that of other models.
According to the results of PEG and MPEG, five risk factors, including Unsysts, Earnvar, Leverage,
Size, and BM, have the expected signs and significant values. e R-squares are, respectively, 22.7%
and 18.8%, higher than the one for the OJ model. As with the result of the correlation matrix, fromthe viewpoint of the correlation with individual risk factors, the PEG and modified PEG ratios
appear to be advantageous.
Gode and Mohanram (2003) compared GLS and OJ, obtaining a result that showed hardly any
differences between them. However, our result is different from theirs, in terms of the considerable
variation in the signs of estimated coefficients and their levels of significance.
In order to analyze this tendency in detail, as with the correlation analysis, we regress the modelby dividing the period into 10 years in the first half and 11 years in the latter half. e result is shownin Table 8. As for any costs of capital, the adjusted R-square in the first half is higher than in thelatter half. It is also found that the values of the cost of capital reflect more risks in the first half. In
particular, the R-squares of EP and PEG are, respectively, 51.9% and 44.7%, higher than 42.0% of
GLS. Briefly, the reason why the R-square of GLS is high in the analysis with the entire sample is arelatively higher power of explanation for the model in the latter half.
Table 9 shows the result of a year-by-year regression.24 In the comparison of R-squares, wefound that OJ, PEG, and MPEG are high in the first half, and GLS is high in the second half.
e result in Table 8 is not affected by a specific year. Focusing on signs of coefficients and levelsof significance, the following tendency can be pointed out. Specifically, as GLS has a positive andsignificant correlation with leverage in 15 years out of 20, and with BM in 17 years, its result is stable.
On the other hand, OJ has a positive and significant correlation with Unsyst in 8 years, relatively
more years than in other models. In PEG and MPEG, more variables have the expected signs andsignificant values over the entire period, whereas in EP, few variables have the expected signs andsignificant values over the entire period. ese results are consistent with the correlation analysis.
24

For 1987, because the low number of samples made a reliable estimation impossible, the result of 1987 is not presented.
Although we conducted the regression analysis by industry, we could not find notable tendencies, like the correlation analysis. epresentation of said analysis is omitted, due in part to limitations of space.

Kitagawa and Gotoh: Implied Cost of Capital over the Last 20 Years101

e results in this section are summarized as follows. We find that GLS is the indicator that has
the highest R-square and reflects risks the best in the entire sample. is tendency shows especiallyin the latter half. However, in the first half, the R-squares of EP and PEG are higher. Furthermore,in GLS analysis using entire sample, the fact that several coefficients have unexpected signs isstill controversial. Costs of capital that show preferable results in terms of R-square, the sign, andsignificance over the entire period are PEG and MPEG. For this reason, the PEG and modified
PEG ratios appear to be advantageous.

6. Conclusion
In this study, we estimate an alternative implied cost of capital as inferred from a valuation
model, and attempt to compare its validity.
Many valuation models have been proposed to estimate the implied cost of capital, and theirresults vary, depending on assumptions for earnings growth, dividends, and the forecast period.
Among them, we compare the following models: 1) the model proposed by Gebhardt et al. (2001),
2) the model proposed by Ohlson and Juettner-Nauroth (2005), 3) the EP ratio，4) the PEG ratio,
and 5) the modified PEG ratio, both PEG ratios being proposed by Easton (2004). As criteria toevaluate their validity, we focus on the following two points. One is a significant correlation withrisk factors in consistency with the expected sign. Another is that variables have the expected signs,
and the adjusted R-square is high in the multiple regression model, in which the cost of capital isa dependent variable and the risk factors are independent variables. We use seven risk factors as follows:
1) Beta, 2) Unsystematic risk, 3) Earnings variability, 4) Leverage, 5) Size, 6) Long-term growth in
expected earnings, and 7) Book-to-market ratio.
As the result of the univariate analysis, we found the PEG and modified PEG ratios to show
a significant correlation in consistency with the expected sign. Although the cost of capital inferredby the Ohlson and Juettner-Nauroth (2005) model also shows a preferable correlation in just thefirst half of the analysis period, the one in the latter half is not as correlative as expected. e cost ofcapital estimated by the Gebhardt et al. (2001) model has the expected correlations with just a few
risk factors over the entire period.
In the multiple regression analysis, the Gebhardt et al. (2001) model shows the highest
R-square. However, in this model, few of the coefficients of independent variables are consistent withthe expected sign. In the first half of the analysis period, the R-squares in the EP and PEG ratios
are rather higher. Furthermore, in the PEG and modified PEG ratios, the most coefficients have theexpected signs.
We conclude that the PEG and modified PEG ratios reflect the risk factors most appropriately
and that they are superior to other models. e estimated value of the cost of capital can be used forthe valuation and forecast of risks associated with capital investment. e result suggests that more
appropriate risk valuation and forecast will be enabled if the PEG and modified PEG ratios are used
as a form of the abnormal earnings growth valuation model.
However, some problems remain in this study. e result obtained here implies that the costof capital can be appropriately estimated in Japan by assuming that the abnormal earnings growthis zero in the abnormal earnings growth valuation model. In preceding studies, however, it has
been argued that the PEG and modified PEG ratios cause a downward bias in general due to theassumption that the abnormal earnings growth and dividends are zero. is argument is inconsistent102

e Japanese Accounting Review, 1 (2011), 71-104

with our results; therefore, we must examine this inconsistent result in detail. Furthermore, somerecent studies have argued that the correlation with risk factors should be analyzed not at the firmlevel, but at the portfolio level. ough we analyze at the firm level in order to ensure comparability
with many preceding studies, analysis must occur at the portfolio level in the future.

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