Corporate Life Cycle and Cost of Equity Capital
Abstract
This paper investigates the impact of the corporate life cycle on the cost of equity capital.
Using a sample of Australian firms during the years 1990–2012, we find that the proxies for
the cost of equity capital vary across the life cycle of the firm. In particular, we find that the
cost of equity declines as the earned/contributed capital mix (a proxy for the firm life cycle)
increases, after controlling for other relevant firm characteristics and unobserved
heterogeneity. Moreover, when different stages of the firm life cycle are taken into account,
we find that the cost of equity is higher in the introduction and decline stages and lower in the
growth and mature stages, resembling a ‘U’ shaped pattern. These findings are robust when
subjected to a series of sensitivity tests. Collectively, the results are consistent with the notion
that firms in the introduction (or decline) stages are more risky in the sense that their resource
base, competitive advantages and capabilities are limited (concentrated), while those in the
growth and mature stages are relatively less risky due to the richness and diversity of their
resource base, competitive advantages and capability. Hence, the market demands a higher
risk premium for the former than for the latter.
JEL classifications: D21, G12, G30, L22
Keywords: Cost of equity; Firm life cycle; Earned equity; Contributed capital
1
Corporate Life Cycle and Cost of Equity Capital
I.
Introduction
This paper investigates whether and how the firm life cycle1 affects the cost of equity capital.
In particular, we test whether the cost of equity capital of the firm implied in stock prices and
forecasts of analysts’ earnings corresponds to different stages in the firm life cycle. In this
study, we integrate two strands of research, viz., corporate life cycle and cost of equity
capital. The first stream of research, corporate life cycle theory, suggests that firms, like
living organisms, pass through a series of predictable patterns of development and that the
resources, capabilities, strategies, structures and functioning of the firm vary significantly
with the corresponding stages of development (Miller and Friesen 1980, 1984; Quinn and
Cameron 1983). Studies in the field of organisational science and strategic management have
long recognised the existence and importance of the firm life cycle. Life cycle theory
provides management with some parameters, guidelines and diagnostic tools to assess the
transition of the firm from one stage to the next: hence, understanding the essence of the life
cycle can help firms to utilise valuable resources in the optimal way to outperform their peers
(Adizes 2004; Solomon et al. 2003) and to achieve and retain the prime life stage. Recent
research in financial economics and accounting (e.g., DeAngelo et al. 2006, 2010; Dickinson
2011) also recognises that firm life cycle stages have important implications for
understanding the financial performance of firms.
The second stream of research, cost of equity capital, is of paramount importance in
accounting and finance research. This is frequently used in settings such as estimation of
equity risk premiums, firm valuation and capital budgeting, and investment management
1
We use the terms ‘firm life cycle’, ‘corporate life cycle’ and ‘organisational life cycle’ interchangeably
throughout this paper. Anthony and Ramesh (1992), DeAngelo et al. (2006), Coulton and Ruddock (2011) and
Dickinson (2011) use ‘firm life cycle’; DeAngelo et al. (2010) use ‘corporate life cycle’; and Adizes (1979) and
Smith et al. (1985) use ‘organisation life cycle’ to refer to the same concept.
2
practices such as portfolio allocation, performance evaluation, active risk management and
attribution analysis (Hou et al. 2012; Câmara et al. 2009). The cost of equity depends on
firms’ economic fundamentals, industry dynamics and overall national economic conditions
(Banz 1981; Fama and French 1989; Gebhardt et al. 2001). Previous research indicates that
firm-specific determinants of the cost of equity include size, leverage, financial strength,
level of disclosure and overall riskiness of the firm. Since the resource base and
corresponding competitive advantages of the firm vary across the life cycle, the investors’
demand for a risk premium could potentially vary accordingly. Therefore, these two streams
of research together suggest that the firm life cycle should have important implications for the
ability of a firm to attract investors, which eventually increases the liquidity of shares and
lowers the cost of equity capital. However, there has been little research on their
interrelationship. Hence, in this study, we make an important contribution to the literature by
investigating the association between the corporate life cycle and cost of equity so as to
reveal whether and how the cost of equity capital of the firm varies with the corresponding
change in the stage of the firm’s life cycle.
This study is primarily motivated by the ‘dynamic resource-based view’ of the firm
which articulates that the general patterns and paths in the evolution of organisational
capabilities change over time. This resource-based view analyses firms from the resource side
rather than from the product side, and posits that the existence and application of the bundle
of valuable, interchangeable, immobile and imitable resources2 generate the basis of the
competitive advantage of a firm and that this resource base is the basis of heterogeneity in
organisational capabilities (Wernerfelt 1984; Rumelt 1984; Penrose 1959). Dynamic
2
‘Resource’ refers to any assets or input (tangible and intangible) to the production which are tied semipermanently to the firm (Caves 1980) and which help the firm to implement strategies to improve efficiency and
effectiveness. Examples of resources include brand names, in-house knowledge of technology, employment of
skilled personnel, trade contacts, machinery, efficient procedures, capital, etc. (Wernerfelt 1984).
3
resource-based theory incorporates the founding, development and maturity of capabilities
and thereby suggests that the competitive advantages and disadvantages in terms of resources
and capabilities evolve over time in important ways (Helfat and Peteraf 2003). This dynamic
resource-based theory is mainly based on The Theory of the Growth of the Firm (Penrose
1959) which proposes that the growth of the firm depends on the efficient and effective
interaction of the firm’s resources and management (human beings). Thus, the evolution of
the firm’s competitiveness, in terms of its resource base and capabilities, is the foundation of
the firm’s life cycle.
The essence of firm life cycle theory suggests that the investment and financing
decision and the operating performance of the firm are greatly influenced by the change in
the firm’s organisational capabilities (life cycle stages). Recent research in finance and
accounting that confirms the unique role of the firm life cycle stage in the functioning of a
firm also instigates the quest for our study. Management accounting literature (Rappaport
1981; Richardson and Gordon 1980) provides evidence that performance measures differ
across life cycle stages. In a recent paper, DeAngelo et al. (2010) demonstrate that the
corporate life cycle has a significant influence on the probability that a firm will engage in
secondary equity offerings. Other studies (e.g., Fama and French 2001; DeAngelo et al. 2006;
Coulton and Ruddock 2011; Bulan et al. 2007) acknowledge the role of the firm life cycle in
determining the dividend payout policy. Berger and Udell (1998), in a related study, view
the firm through a financial growth cycle paradigm in which different capital structures are
optimal at different points in the cycle. Evidence in the accounting literature also suggests
that investors’ valuation of firms is a function of the life cycle stage of the firm (Anthony and
Ramesh 1992). Based on the above theoretical framework in strategic management and
subsequent application of life cycle theory in accounting and finance, we also posit that the
4
life cycle has significant influences on the firm’s ability to attract investors, which eventually
affects the ex-ante cost of equity capital of the firm.
Using a sample of Australian listed companies, we find that the cost of equity
decreases as the retained earnings as a proportion of total assets (RE/TA) and total equity
(RE/TE) increase. Moreover, compared to the shake-out stage of the firm life cycle, the cost
of equity is significantly higher in the introduction and decline stages of the firm life cycle,
while it is lower in the growth and mature stages of the firm. Our results conform to the
findings of Bender and Ward (1993) that financing strategy and structures of firms evolve
over the firms’ life cycles. Furthermore, we conduct an additional test to ascertain that our
results are robust to alternative measures of cost of equity and firm life cycle. Endogeneity
issues may affect the sign, magnitude or statistical significance of the results. To mitigate this
concern, we use instrumental-variables techniques together with fixed effects estimation that
can control for unobserved heterogeneity. The instrumental-variables results are very similar
to the baseline firm fixed effect results and indicate that endogeneity cannot explain away the
negative relationship between cost of equity and firm life cycle.
Our study contributes to the literature in several ways. First, in this paper, we extend
life cycle literature to cover a key input in the firm’s financial decision making by directly
examining the role of the firm life cycle in influencing the cost of equity. While prior
research investigates the role of the firm life cycle in dividend and capital structure decisions,
little attention has been paid to the role of the firm life cycle in determining the cost of equity
capital. Even though Easley and O'Hara's (2004) model predicts that the “life cycle of a firm
may also influence its cost of capital. In particular, it seems reasonable that a firm with a long
operating history will be better known by investors … the greater the prior precision, the
5
lower the cost of capital”, they have not examined the validity of this prediction empirically.
This paper attempts to fill that gap in the literature. Second, the cost of equity represents the
return that the investors require on their investment in the firm and thus it is a key factor in
firms’ long-term investment decisions. Examining the link between the firm life cycle and the
cost of equity, therefore, should help managers understand the effect of the life cycle on
firms’ financing costs, and hence this study has important implications for strategic planning.
Indeed, the cost of equity capital could be the channel through which capital markets
encourage firms to reach and maintain maturity, the prime stage, in their life cycle. Third,
given the importance of the firm life cycle and the cost of equity capital in the literature, and
the longstanding interest in trying to understand their determinants, an empirical study on the
association between corporate life cycle and cost of equity is timely.
The remainder of the paper is organised as follows: in section two, we review studies
on the cost of equity and life cycle theory and develop testable hypotheses. Section three
focuses on the research design, data sources and sample selection. Section four documents
the results of the study, while section five concludes the paper.
II. Literature Review and Hypotheses Development
In this section, we review prior studies related to the firm life cycle and cost of equity
separately and then show the interrelationship between them for hypotheses development.
Substantial research in industrial organisation, strategic management and accounting and
finance has investigated the firm life cycle and cost of equity in isolation. However, no
studies have yet shed light on how these issues may relate to one another.
6
2.1 Corporate Life Cycle: Theory
Corporate life cycle theory derives its roots from organisational science literature. The
corporate life cycle model suggests that firms, like the organic body, tend to progress in a
linear fashion through predictable stages of development sequentially from birth to decline
and that their strategies, structures and activities correspond to their stages of development
(Gray and Ariss 1985; Miller and Friesen 1984, 1980; Quinn and Cameron 1983). Strategy
and management researchers have adopted the firm life cycle model from the biological
sciences (Van De Ven and Poole 1995) and have incorporated it into business research since
the 1960s. Penrose (1959) provides a general theory of growth of the firm and argues that
firm growth depends on the firm’s resources and productive opportunities. She identifies
managerial limitations as the main source of constraint to a firm’s growth rate. Chandler
(1962), one of the pioneers in life cycle theory, argues that organisational structure follows
the growth strategy of the firm to avail itself of external opportunities. Subsequent studies in
organisational science reveal the grounds behind the existence of the firm life cycle. For
example, the resource-based theory of Wernerfelt (1984) suggests that resources are the
ultimate source of establishing and maintaining competitive advantage. He argues that firms
possess resources, a subset of which allows them to achieve competitive advantage over
others, and a subset of those helps them to attain superior long-term performance and thus to
earn above average profits (Grant 1991). In a more recent study, Helfat and Peteraf (2003)
argue that the resource-based view must incorporate the emergence, development and
progression of organisational resources and capabilities over time and hence they introduce a
more comprehensive and vibrant view: ‘the dynamic resource-based theory’. This view
suggests that the resource base that forms the foundation of competitive advantage and
disadvantage comes about over a period of time and also may shift over time. They document
7
that firms’ portfolios of resources and capacities and their characteristics change over time,
and this variation results in different stages in the firm life cycle.
There are several multi-stage life cycle models which differ in terms of the number of
stages involved and the features that correspond to each stage. For example, Greiner (1972)
proposes that firms move through five stages of life cycle in their movement from growth
through creativity: direction, delegation, coordination, monitoring and collaboration. Adizes
(1979) proposes that firms evolve through ten stages in their life cycle ranging from courtship
(where the firm exists only as an idea) to death. Kazanjian and Drazin (1990) propose four
stages in the firm life cycle which are conception and development, commercialisation,
growth and stability. Gort and Klepper (1982) suggest five stages in the firm life cycle, viz.,
introduction, growth, maturity, shake-out and decline. Summarising the prior literature on life
cycle models, Miller and Friesen (1984) propose a similar classification that separates the
firm life cycle into five common phases: birth, growth, maturity, revival and decline. Based
on this, Dickinson (2011) provides empirical methodology to classify firms into different life
cycles.
The firm life cycle has important implications in management and business strategy.
Each stage in the firm life cycle enforces unique characteristics and demands which entail
organisational structures, personnel, leadership styles and decision-making processes
appropriate to meet the requirements (Kazanjian 1988). The stages in the life cycle are a key
determinant of organisational competitiveness. Koberg et al. (1996) document that
organisational and environmental attributes’ impact on innovation is moderated by the firm’s
life cycle stage. However, much of the work in the field of management, entrepreneurship
and strategy is conceptual rather than empirical.
8
There are some recent empirical studies in accounting and finance that investigate the
impact of the firm life cycle on corporate financial decisions.Bender and Ward (1993) report
that the financial structure of firms changes over the firms’ life cycles. Berger and Udell
(1998) argue that small and young firms generally resort to private equity and debt markets,
whereas larger and mature firms mainly rely on public markets. Richardson (2006) suggests
that a firm is more likely to undertake relatively larger, growth-oriented investments in the
initial stage while, in the mature stage, its investments are more likely to be geared towards
maintenance of assets-in place. Fama and French (2001), Grullon et al. (2002) and DeAngelo
et al. (2006) find that the life cycle of the firm can influence payout policies. More recently,
in an Australian study, Coulton and Ruddock (2011) document that mature and profitable
firms are more likely to pay dividends and young firms with higher growth options are less
likely to do so. These archival studies suggest that the firm life cycle should have important
implications for corporate financing decisions, especially in the area of the cost of equity
capital.
2.2 Cost of Equity: Theory
Cost of equity is the return that shareholders require on their investment in the firm.. Cost of
equity is extensively used in the valuation of investment projects and estimation of equity risk
premiums (Câmara et al. 2009). This is also important in optimum capital structure
determination, portfolio formation and performance evaluation, risk management and
attribution analysis (Hou et al. 2012). Therefore, estimating and validating the cost of equity
has become a considerable research interest in the literature.
Firm-specific factors such as firm size, age, riskiness, liquidity of stock, financial
leverage and quality of disclosure determine the cost of equity. Moreover, non-firm-specific
9
factors such as the industry and the economy also influence the cost of equity. Transparency
and availability of information about management and potential earnings of large firms
reduce uncertainty level. Hence, investors of larger firms require less return on their
investment, which effectively reduces the cost of equity (Witmer and Zorn 2007; Banz 1981;
Berk 1995). Firm age or maturity affects equity price and thereby the cost of equity (Pástor et
al. 2008). Transaction cost (e.g., commission, fees and other charges incurred in buying or
selling a security) is higher for less liquid stock and hence investors require more return for
these securities. Shareholders are the residual claimers and hence an increase in the financial
leverage also increases the risk to the shareholders. This effectively increases the cost of
equity (Witmer and Zorn 2007). Firms in different industries have different costs of equity
depending on the nature of their business. For example, Gebhardt et al. (2001) find that the
implied risk premium is higher for firms in recreational products, tobacco products, banks,
computers and automotive industries, while this is consistently lower for firms in real estate,
agriculture, trading (financial) and medical equipment industries. Moreover, the cost of
equity is higher under weak economic conditions, while it is lower under strong economic
conditions (Fama and French 1989).
2.3 Association between Corporate Life Cycle and Cost of Equity Capital
Firms in different life cycle stages differ in their ability to raise funds from the market
(Berger and Udell 1998). Firms at the earlier stage of the life cycle are relatively small and
unknown, and are less closely followed by analysts and investors. Hence, these firms suffer
from substantial information asymmetry. This information asymmetry may cause equity
mispricing (Myers and Majluf 1984) which has a positive relation with riskiness and
consequently increases the cost of capital (Armstrong et al. 2011). On the other hand, mature
firms have a long existence in the market and they are more closely followed by analysts and
10
investors. Hence, these firms suffer from less information asymmetry. Therefore, these firms
are less risky. Easley and O'Hara (2004) also note that firms with a long operating history are
better known by investors, which improves the precision of information about the firm and
lowers the cost of capital. Investors generally prefer securities with low estimation risk, low
transaction costs and/or less information asymmetry (Botosan 2006). Greater demand for
securities with these characteristics enhances the liquidity of the stocks (Diamond and
Verrecchia 1991) which influences the cost of equity (O'Hara 2003). Prior studies (e.g.,
Gebhardt et al. 2001) overwhelmingly show that firm maturity is associated with a decline in
systematic risk.
In addition, resource-based theory assumes that firms differ in terms of their bundle of
resources (e.g., financial, physical, human capital, technological, reputation and
organisational resources) and capabilities (Barney 1991; Dierickx and Cool 1989; Grant
1991), and that these firm-specific resources and capabilities are crucial in explaining the
firm’s growth and performance (Penrose 1959). According to this view, the resource base and
capabilities of mature firms are large, diverse and rich, while those of young and declining
firms are small, concentrated and limited. This resource base and its accompanying superior
competitive advantages and capacities help mature firms to benefit from cheaper and easier
sources of finance. More specifically, since the life cycle affects the perceived riskiness of the
firm, firms in the mature stage of their life cycle should be in a better position to raise
adequate capital at a lower cost. Therefore, we hypothesise that:
H1: Compared to the shake-out stage of the firm life cycle3, the cost of equity is negatively
associated with the mature stage of the firm life cycle.
3
As Dickinson (2011) remarks, the literature clearly spells out the role of different stages of the firm life cycle
except for the shake-out stage. As a result, the expected signs of this stage are unclear. Thus, in developing
hypothesis H1, we use the shake-out stage as a basis of comparison with other stages of the firm life cycle.
11
Although firms in the growth stage of the life cycle have an insufficient resource base,
these firms are promising and have good potential. Growth firms invest more in research and
development and seek innovation and rapid development. Organisational theory suggests that
growth firms maintain greater information asymmetry to benefit from product development
and market movement (Aboody and Lev 2000; Barth et al. 2001; Smith and Watts 1992).
However, prior studies also suggest that characteristics of growth firms attract greater analyst
coverage to attain potential benefits from private information acquisition (Barth et al. 2001;
Lehavy et al. 2011). Greater analyst coverage in turn reduces mispricing and information
asymmetry (Barth et al. 2001; Brennan and Subrahmanyam 1995). Furthermore, growth firms
are more likely to receive coverage in the business press (Bentley et al. 2012). Firms with
greater press coverage are associated with lower levels of information asymmetry (Bushee et
al. 2010). Moreover, growth firms have greater strategic incentives to reduce information
asymmetry via voluntary disclosure to attract potential providers of capital. ‘Growth
investors4’ are willing to invest in these firms to realise benefit from the above-average
earnings. Moreover, ‘strategic investors5’ are attracted to invest in growth firms to gain
benefits from the future success of the business enterprise. In summary, greater analyst
following, press coverage and voluntary disclosures reduce the information asymmetry of
growth firms eventually reducing the cost of capital. Hence, we hypothesise that:
H2: Compared to the shake-out stage of the firm life cycle, the cost of equity is negatively
associated with the growth stage of the firm life cycle.
4
Growth investors invest in companies that exhibit signs of above average growth potential. They bet on more
structural changes in the firm and expect a run-up in price (Bourguignon and de Jong 2003).
5
Strategic investors invest in young companies that have the potential to bring something of value to investors
or to create synergy with the existing business of the investor. An independent venture capitalist only cares
about financial gain, while the strategic investor also cares about the new venture’s strategic impact (Hellmann
2002).
12
On the other hand, firms in the introduction (and decline) stages have limited
(downgraded) resources and resource combination. Dickinson (2011) provides empirical
evidence that both introduction and decline stages of the firm life cycle are associated with
negative earnings per share, return on net operating assets and profit margin. Since
investments in these firms are relatively less attractive, analysts are reluctant to cover firms in
these stages. Therefore, these firms cannot raise capital unless investors are properly
compensated (Nickel and Rodriguez 2002), which effectively increases the cost of equity for
these firms. Based on this argument, we hypothesise that:
H3: Compared to the shake-out stage of the firm life cycle, the cost of equity is positively
associated with the introduction (decline) stages of the firm life cycle.
III. Research Method
3.1 Sample and Data
We draw the sample from the population of companies listed on the Australian Securities
Exchange (ASX) and covered by the I/B/E/S International database for the period 1990–
2012. This yields an initial sample of 8020 firm-year observations. Data for the control
variables, except beta, are extracted from the Aspect Financial Analysis databases and
Connect 4. Data for beta (systematic risk) and fiscal year end stock price are collected from
DataStream and DatAnalysis Morningstar, respectively. Moreover, the risk-free rate (10-year
Treasury note rates) required to calculate the cost of equity has been collected from statistics
available on the Reserve Bank of Australia website.6 To avoid the undesirable influence of
outliers we winsorize continuous variables at the 1st and 99th percentiles. We exclude the
6
http://www.rba.gov.au/statistics/tables/index.html
13
financial sector7 from our sample for two reasons. First, the risk and complexity
characteristics of financial institutions are substantially different from those of other firms.
Second, financial sector firms differ significantly from other sectors in terms of accounting
practice. We also exclude observations with missing values in the computation of cost of
equity and control variables and lose 545, 189 and 196 firm years for price/earnings to
growth ratio (PEG), modified PEG ratio (MPEG) and Ohlson and Juettner-Nauroth (2005)
(OJ) models, respectively. This produces a final sample size of 3888, 3563 and 3482 firmyear observations for the PEG (Easton 2004) model, MPEG (Easton 2004) model and
(Ohlson and Juettner-Nauroth 2005) OJ model, respectively. Table 1 presents sample
distribution by cost of equity models (Panel A), yearly distribution of observations during the
sample period from 1990–2012 (Panel B) and sample distribution by industry sector
(Panel C).
Insert Table 1 about Here
Table 1 shows that sample size increases over the sample period (with the largest
sample of 292 and 289 in the years 2008 and 2011, respectively) and the sample is unevenly
distributed across industries (with the largest sample being in industrial (24.72%) and
consumer discretionary (21.04%) sectors). This study suffers from a relatively limited sample
size for two reasons: (i) the implied approach to estimating the cost of equity capital requires
expected future cash flows, which can be derived from analyst forecasts. As analysts
generally cover larger and established firms, the sample size is thus reduced. The second
reason is that: (ii) sample restrictions also occur with the implied valuation models which
require positive earnings and positive growth in earnings to generate meaningful cost of
7
Exclusion of the financial sector and delisted firms reduces the sample size by 1337, 1311 and 1297 for the
PEG (Easton 2004) model, MPEG (Easton 2004) model and OJ (Ohlson and Juettner-Nauroth 2005) model.
14
equity estimates. A smaller sample size may make it difficult to draw inferences using the
implied method. Moreover, the limited sample size may introduce a possible sample selection
bias. However, we control for these effects in our regression analysis by including several
control variables, such as firm size and leverage. Moreover, we also examine the robustness
of our analysis using alternative estimates of the cost of equity and corporate life cycle to deal
with the potential bias that may be induced by these data constraints.
3.2 Empirical Model
We test the relation between the ex-ante cost of equity and the firm life cycle by four
measures of cost of equity and three measures of firm life cycle proxies. To control for
individual firm heterogeneity, we employ the following fixed effect model:
(1)
Where,
R
= ex-ante cost of equity;
CLC
= a vector of dummy variables that capture firms’ different stages in the life
cycle;
SIZE
= firm size measured by the natural logarithm of total assets of the firm at the
end of the fiscal year;
BM
= book-to-market ratio at the end of the fiscal year;
BETA
= stock beta (systematic risk);
LOSSt-1
= dummy variable equal to 1 if earnings before extraordinary income in year t1 is negative, otherwise 0;
15
LEV
= leverage measured by the ratio of total debt to total equity at the end of the
fiscal year;
ZSCORE
= probability of bankruptcy estimated using Altman’s equation (1968);
= year dummy variable, which is used to control for year fixed effects;
= firm-specific unobserved fixed effects.
Our main variable of interest is CLC. Based on the dynamic resource-based view and the life
cycle theory, we predict
to be negative for H1 and H2 but positive for H3.
3.2 Measurement of Variables
3.2.1 Estimation of Corporate Life Cycle
Assessing the life cycle stage at the firm level is difficult because the individual firm is
composed of many overlapping, but distinct, product life cycle stages. Moreover, firms can
compete in multiple industries and their product offerings are fairly diverse (Dickinson
2011). To overcome this estimation problem, we follow the methodologies of DeAngelo et al.
(2006) and Dickinson (2011) to develop proxies for the firms’ stage in the life cycle.8
Following DeAngelo et al. (2006), we use retained earnings as a proportion of total assets
(RE/TA) and total equity (RE/TE) as the proxy for corporate life cycle. These proxies
measure the extent to which a firm is self-financing or reliant on external capital. A high
RE/TA and RE/TE imply that the firm is more mature or old with declining investment, while
the firm with a low RE/TA and RE/TE tends to be young and growing (DeAngelo et al.
2006).
8
Anthony and Ramesh (1992) provide one of the first empirical procedures for classifying firms in different life
cycle stages. However, we do not use their method for several reasons. These include (1) this classification
scheme requires at least six years of data availability for each firm, which reduces our sample size significantly;
(2) the life cycle proxy in this procedure is ‘ad hoc’ and relies on portfolio sorts to classify the firm in different
life cycle stages; and (3) Dickinson (2011) has shown that life cycle classification based on Anthony and
Ramesh’s (1992) procedure leads to an erronous classification of the stage of firms in the life cycle.
16
An alternative parsimonious measure offered by Dickinson (2011) deploys data from
the firm’s cash flow statement. She argues that cash flows capture differences in a firm’s
profitability, growth and risk and, hence, that one may use the cash flow from operating
(CFO), investing (CFI) and financing (CFF) to group firms in life cycle stages such as:
‘introduction’, ‘growth’, ‘mature’, ‘shake-out’ and ‘decline’.9 The methodology is:
introduction: if CFO ≤ 0, CFI ≤ 0 and CFF ˃ 0; growth: if CFO ˃ 0, CFI ≤ 0 and CFF ˃ 0;
mature: if CFO ˃ 0, CFI ≤ 0 and CFF ≤ 0; decline: if CFO ≤ 0, CFI ˃ 0 and CFF ≤ or ≥ 0; and
the remaining firm years will be classified under the shake-out stage. Identification of life
cycle stages based on Dickinson (2011) combines the implications from diverse research
areas such as production behaviour, learning/experience, investment, market share and
entry/exit patterns. As a result, this process can capture the performance and allocation of
resources of the firm.
3.2.2 Estimation of Cost of Equity
Cost of equity can be measured using both the implied approach and the realised approach.
Estimation of implied cost of equity involves calculating the internal rate of return that
equates the stock prices to the present value of forecasted cash flows (Hou et al. 2012). On
the other hand, the realised approach uses ex-post stock returns to estimate the cost of equity.
However, estimates based on ex-post realised stock returns suffer from measurement errors
such as imprecise estimates of factor risk premium and risk loading (Fama and French 1997).
Furthermore, Elton (2002) argues that information surprises cause realised returns to be a
biased and noisy measure of expected returns. Pástor et al. (2008) document that estimation
of the cost of equity that uses forward estimates of earnings outperforms measures based on
realised returns. Hence, researchers are increasingly relying on the implied cost of equity
9
For detailed justification used to classify firms into different life cycle stages based on cash flow statement
data, please refer to Dickinson (2011).
17
capital.10 In line with previous studies, we use implied approach to estimate the cost of
equity. Particularly we use Easton (2004)11 and Ohlson and Juettner-Nauroth (2005) as
modified by Gode and Mohanram (2003) models to estimate the cost of equity. We choose
these measures because Botosan and Plumlee (2005) document that t Easton’s (2004) PEG
ratio model and the target price (or dividend discount) method, introduced by Botosan and
Plumlee (2002), are preferable measures of the cost of equity as both dominate the other
alternatives in the sense that they are consistently and predictably related to various risk
measures.12 In addition, we use the Ohlson and Juettner-Nauroth (2005) (OJ) model modified
by Gode and Mohanram (2003) because this model is theoretically rigorous yet
parsimonious, and provides a simple closed form solution for the implied cost of capital
(Gode and Mohanram 2008). Furthermore, prior studies document that while the Ohlson and
Juettner-Nauroth (2005) model provides cost of capital estimates that are highly correlated
with ex-ante risk factors (Gode and Mohanram 2003), they are weakly correlated with
realised returns (Easton and Monahan 2005). Consistent with prior studies (e.g., Hail and
Leuz 2006; Chen et al. 2009; Hou et al. 2012), we use a simple average of three models due
to the lack of consensus on precision of the estimation of implied e cost of capital .
3.3 Control Variables
Prior research has revealed several risk factors and firm characteristics that affect the cost of
equity. Accordingly, we control for these risk factors and firm characteristics. .
10
Most Australian studies on the cost of equity adopt the realised approach to estimate the cost of equity. For
example, Gray et al. (2009) use industry-adjusted earnings-to-price ratio and Monkhouse (1993) uses the capital
asset pricing model (CAPM) to estimate the cost of equity. However, Azizkhani et al. (2010) use the PEG
approach to estimate the cost of equity. Moreover, some cross-country studies (e.g., Gray et al. 2009; Hail and
Leuz 2006; Khurana and Raman 2004) use the implied approach to estimate the cost of equity with a limited
sample size.
11
We use both PEG and MPEG approaches.
12
The necessary forecasted data for the target price (or dividend discount) method are not available for
Australian companies. Using forecasted eps4 and eps5 for Australian companies to calculate the cost of equity
would significantly reduce our sample size.
18
Firm Size (SIZE)
Firm size affects the cost of equity capital because a large firm has a lower probability of
default (Berger and Udell 1995). Fama and French (1992) also find that stock returns are
negatively correlated with firm size. Moreover, large firms are more followed by analysts and
these firms have more liquidity in the capital market which effectively reduce the cost of
equity to firms (Witmer and Zorn 2007). Consistent with Francis et al. (2005) and Owen and
Yawson (2010), we use the natural log of total assets to measure firm size.
Beta (BETA)
The capital asset pricing model (CAPM) suggests that systematic risk (beta) is positively
associated with the cost of equity capital (Sharpe 1964; Lintner 1965; Mossin 1966; Harris
and Marston 1992; Botosan and Plumlee 2005). Hence, we control for systematic risk using
the firm’s market beta. We collect beta from Datastream which is calculated over a five-year
period by regressing the share price against the respective Datastream total market index
using log changes of the closing price on the first day of each month.
Book-to-Market Ratio (BM)
Book-to-market ratio, a measure of growth opportunity, increases the uncertainty and risk
and, therefore, is expected to be positively associated with the cost of equity capital. Prior
studies (Chan et al. 1991; Fama and French 1992; Davis 1994; Boone et al. 2008; Khurana
and Raman 2004) also consistently document a positive relation between book-to-market
ratio and cost of equity capital.
Loss (LOSSt-1)
A continuous negative earnings stream for a firm could influence investors to consider a
higher probability that the firm will abandon its resources (Collins et al. 1999). This is how
19
negative earnings relate to business risk. Therefore, we include a negative earnings indicator
variable (LOSSt-1) equal to 1 if the firm has loss in the previous year, 0 otherwise. We expect
the coefficient on the variable LOSSt-1 to be positive to the degree that it proxies for a firm’s
business risk.
Leverage (LEV)
Leverage is related to the riskiness of the firm. The higher the level of leverage, the greater
the perceived risk associated with the firm and, consequently, the higher the cost of equity
capital (Modigliani and Miller 1958; Fama and French 1992; Petersen and Rajan 1994;
Gebhardt et al. 2001). We measure financial leverage as (short-term debt + long-term
debt)/shareholders’ equity.
Probability of Bankruptcy (ZSCORE)
In order to control for the bankruptcy risk, we use Altman’s (1968) Z score to develop a
proxy for the inverse likelihood of bankruptcy (i.e., a higher score indicates better financial
health and the lower possibility of financial distress).13 Altman’s Z score is an unsystematic
risk factor and Dichev (1998) suggests that it is separate from the size and book-to-market
factors. However, we acknowledge the inherent limitation of Altman’s model that uses
historical information to predict current bankruptcy.
IV. Empirical Results and Discussion
4.1 Descriptive Statistics
Table 2 reports the summary statistics for the key variables included in the regression model.
Panel A contains the descriptive statistics for the pooled model (average of the three cost of
13
Altman’s Z score = 1.2(Working Capital/Total Assets) + 1.4(Retained Earnings/Total Assets) + 3.3(Earnings
Before Interest & Tax/Total Assets) + 0.6(Market Value of Equity/Total Liabilities) + 0.999(Sales/Total
Assets).
20
equity estimates). The mean (median) cost of equity (simple average of the three cost of
equity estimates) for the sample is 17.79% (13.96%) with a standard deviation of 12.92%.
Owing to limited study on Australian listed firms using the same models for calculating the
cost of equity capital, a reliable comparison to this estimate is difficult. The closest possible
comparison is with Khurana and Raman (2004) and Azizkhani et al. (2010). Using a sample
of 508 Australian firms audited by the Big Auditors (71 firms audited by non-Big Auditors)
from 1990–1999, Khurana and Raman (2004) find that the mean cost of equity, estimated by
the PEG (Easton 2004) model, is 10.3% (and 10.7%) and that the median cost is 9.1% (and
9.7%). Furthermore, using a sample of 1925 Australian firms audited by Big Auditors and
245 firms audited by non-Big Auditors during the period 1995–2005, Azizkhani et al. (2010)
find that the mean cost of equity, estimated by the same model, is 10.8% and 14.3% for the
firms audited by Big and non-Big Auditors, respectively.14 The reported mean (median) cost
of equity for this paper estimated by the PEG (Easton 2004) model with a sample of 3888
firm years from 1990–2012 is 15.63% (11.81%).15 Botosan (1997) uses a US sample to
estimate the cost of equity based on Ohlson (1995) and shows that the cost of equity is
20.1%. Therefore, an average cost of equity of 17.61% for this study is consistent with prior
studies. Table 2 shows that there is a large dispersion among the sample firms in terms of
control variables, and this dispersion indicates a considerable diversity in the sample.
Insert Table 2 about here
14
Moreover, using median analyst forecasts as inputs, Truong and Partington (2007) estimate the cost of equity
for Australian firms and find that the average estimates produced by different valuation models are in the range
of from 10% to 17%.
15
Our results differ from those of Azizkhani et al. (2010) for several reasons. (a) Our sample size and sample
period differ from that of their study. More specifically, our sample covers the global financial crisis period
which is associated with increased risk and cost of equity. (b) We winsorize the cost of equity estimates at the
1% level (both sides), while they exclude the extreme values. (c) Azizkhani et al. (2010) use the square root of
the numerator only, while we use the square root of both numerator and denominator, which is consistent with
Easton’s (2004) original model.
21
Panel A of Table 2 presents descriptive statistics for the dependent, independent and
control variables. The mean (median) RE/TA and RE/TE are .0383 (.0887) and .0662
(.1894), respectively. The mean values of SIZE (19.9026), ZSCORE (3.8928) and Losst-1
(.1052) suggest the presence of large and financially sound firms in the sample. Moreover,
the mean (.8047) and median (.5657) of the book-to-market ratio suggest that the sample
firms have valuable growth opportunities. The mean BETA (.9538) is slightly lower than that
of Azizkhani et al. (2010) (1.02) and higher than that of Chen et al. (2004) (.75). The mean
LEV (.5439) is similar to that of Cassar and Holmes (2003) (.57).
Panel B of Table 2 exhibits the life cycle-wise (Dickinson 2011) cost of equity under
different models. All the models show that the cost of equity is lowest in the mature stage,
while it is comparatively higher in the introduction and decline stages. The lowest cost of
equity for mature stage firms indicates that mature firms are, on average, the least risky
among firms in other stages. Panel C of Table 3 shows the graphical expression of the cost of
equity under different models and different life cycle stages. The cost of equity under all
models shows a “U” shaped pattern across the life cycle.
Panel D of Table 2 reports life cycle-wise descriptive statistics for the sample firms.
Firms in the mature stage are characterised by stability, while firms in the decline stage are in
a transition phase (Dickinson 2011). Consistent with the findings of Dickinson (2011), we
find that highest (lowest) observations belong to the mature (decline) stage with 47.07%
(1.52%) of observations. The overall results of Panel D of Table 2 show that mature firms,
consistent with their lower riskiness, have the lowest BETA, lowest rate of LOSSt-1, and
highest ZSCORE. Moreover, the descriptive statistics show that firms in the introduction and
decline stages are relatively more risky (with BETA of 1.15 and 1.42 as opposed to .97 and
.89 in the growth and mature stages) and hence investors demand a relatively higher risk
22
premium (average cost of equity of .29 and .36) for firms in these stages (compared to .17
and .15 in growth and mature stages). Further analysis reveals that SIZE, RE/TA and RE/TE
progressively increase as firms move from introduction to mature stage and that these
estimates then decline as firms move from mature to decline stage: the opposite pattern is
observed for the average cost of equity, BETA and LOSSt-1. The estimates in Panel D of
Table 2 are also consistent with life cycle theory and the pattern of the statistics across the
life cycle is in line with Dickinson (2011), signifying the reliability of the estimates.
4.2 Correlation Analysis
Table 3 reports the Pearson pairwise correlations among different estimates of the cost of
equity, life cycle proxies and control variables. As expected, the cost of equity, estimated by
all the models, is positively correlated (significant at 0.000 level) with introduction, shake-out
and decline stages of the firm and significantly negatively correlated (significant at 0.000
level) with the mature stage of the firm. Interestingly, all the cost of equity estimates are
negatively correlated (although insignificant) with the growth stage of the firm. This is
possibly because growth firms can attract strategic investors who, in turn, allow these firms to
use the capital with less cost. Moreover, consistent with expectations, the cost of equity
estimates are also significantly negatively correlated (significant at 0.000 level) with RE/TA
and RE/TE. Finally, the correlations among cost of equity estimates and BM, BETA and
LOSSt-1 are positive and significant (at p = 0.000), while the correlation of cost of equity with
SIZE and ZSCORE is negative and significant (at p = 0.000). Overall, the correlations among
cost of equity estimates, life cycle proxies and the control variables are all in the expected
direction.
Insert Table 3 about Here
23
4.3 Univariate t-Test
Table 4 reports the mean cost of equity capital for different stages of the firm life cycle.
Panel A shows that the mean ex-ante cost of equity capital for each stage significantly differs
from that of other stages. For all models of cost of equity estimates, the average cost of equity
significantly decreases (significant at < 0.01 level) from introduction to growth stage, from
growth to mature stage, from introduction to mature stage and from introduction to shake-out
stage of the firm life cycle. However, the mean cost of equity increases significantly
(significant at 0.000 level) from mature to shake-out stage, from shake-out to decline stage,
from introduction to decline stage, from growth to shake-out stage and finally from growth to
decline stage.
Insert Table 4 about Here
4.4 Association between Cost of Equity and Firm Life Cycle
4.4.1 Firm Fixed Effect Estimation
In examining the association between the firm life cycle and the cost of equity, we
statistically test which empirical model – pooling, random effect or fixed effect regression –
is most suitable for estimating the relationship. Specifically, following Aivazian et al. (2005),
we conduct two statistical tests: the first is the Lagrangian Multiplier (LM) test of the random
effect model (Breusch and Pagan 1980). The null hypothesis is that the individual effect,
,
is 0 for all i. The chi-square statistics for the four models of cost of equity in Panel A of
Table 5 are 543.90, 564.46, 566.05, and 589.57 respectively. Thus, the null hypothesis is
rejected at the 1% significance level, which suggests that the cohort effect is not zero and that
the pooling regression is not suitable in this case. For the second test, we perform the
Hausman specification test (Hausman 1978) to compare between fixed effect and random
24
effect models. The null hypothesis is that unique errors
are not correlated with the
regressors. If the model specification is correct and if individual effects are uncorrelated with
the independent variables, the fixed effect and random effect estimators should not be
statistically different. For all models in Panel A of Table 5, null hypotheses are rejected at the
1% significance level. The results suggest that the fixed effect model is most appropriate in
estimating the impact of the firm life cycle on the cost of equity. We repeat these tests for all
the estimates in Panel B and Panel C of Table 5 and find that the fixed effect model is best for
investigating the intended relationship. Hence, we report only fixed effect estimates results in
our study.
Table 5 reports the fixed effect estimates of the relationship between the cost of equity
and the corporate life cycle. As firm fixed effects and year dummies are specified in the
regressions, their estimates are constant at firm level and year level respectively. All other
control variables (such as SIZE, B/M, BETA, LOSSt-1, LEV, and ZSCORE) are measured at
firm-year level. The regression coefficients on these control variables remain constant in the
sample. Panel A shows the results for different measures of the cost of equity and RE/TA, a
life cycle proxy proposed by DeAngelo et al. (2006). The coefficient on RE/TA is negative
and statistically significant for all of the cost of equity measures, suggesting that investors’
demand for the cost of equity decreases as RE/TA increases. The results also reveal that
investors demand less risk premium for large and financially sound firms (the coefficients on
SIZE and ZSCORE are both negative and statistically significant). On the other hand,
demand for risk premium is higher for growth and risky firms (with positive and statistically
significant coefficients on BM, BETA, LOSSt–1 and LEV).
Insert Table 5 about Here
25
Panel B of Table 5 presents the association between cost of equity and RE/TE,
another measure of corporate life cycle proxy proposed by DeAngelo et al. (2006).
Obviously, a firm cannot have a high RE/TE ratio without substantial prior earnings
(DeAngelo et al. 2006): hence, it is justified to use RE/TE as a proxy for the firm life cycle.
All these specifications show a highly significant negative relation between RE/TE and the
cost of equity estimates. The coefficients on the control variables, for example, SIZE, BM,
BETA, LOSSt–1, LEV and ZSCORE have the predicted signs and significance. These
findings are consistent with the resource-based view and corporate life cycle theory.
The results for Dickinson’s (2011) life cycle measures are shown in Panel C of
Table 5. The life cycles of firms are categorised by Dickinson (2011) into five stages:
introduction, growth, maturity, shake-out and decline. Five dummy variables are thus created
for each of the five stages. However, to avoid the multicollinearity problem in the regression
model, one of the stages should be dropped. Since the shake-out stage of the life cycle is
ambiguous in theory (Dickinson 2011), we drop this stage in the regression model. The
regression results suggest that, compared to the shake-out stage, the introduction and decline
stages of the firm life cycle are significantly positively associated with the cost of equity,
while the growth and mature stages of the life cycle are negatively associated with all
estimates of the cost of equity (at p < .01 level). Finally, the coefficients on all of the control
variables have the predicted signs and are statistically significant, suggesting that the model
specification is reasonable.
Overall, our evidence is consistent with the resource-based theory and life cycle
explanation for the cost of equity of the firm. Controlling for known determinants of the cost
of equity (SIZE, BM, BETA, LOSSt–1, LEV, and ZSCORE) and individual firm
26
heterogeneity, we find that the cost of equity is significantly negatively associated with both
life cycle proxies – RE/TA and RE/TE. Moreover, when the stages in the firm life cycle are
taken into account, compared to the shake-out stage, the cost of equity is negative and
significant in the growth and mature stages, while it is positive and significant in the
introduction and decline stages. These results support the notion that, in the early stages of
the life cycle, firms have a limited resources base. These firms do not have a long-term
relationship with the financial market and consequently do not enjoy the opportunity to raise
capital at the same cost as firms in the growth and mature stages. Growth firms have good
potential, disclose more information to reduce information asymmetry and hence can attract
growth and strategic investors and thereby can raise capital at a lower cost. Moreover, mature
firms have positive goodwill and good credit history: thus, these firms have access to less
expensive money. The cost of equity is higher in the decline stage because potential investors
do not want to invest money into a crisis firm unless they are properly compensated for their
risk. The important bottom line of the analysis is that all the life cycle proxies and cost of
equity estimates uniformly and strongly support the view that firms’ cost of equity varies
significantly with the stages in the firms’ life cycle.
4.5 Two Stage Least Squares (2SLS) Regression
Even though fixed effect estimation suggests a negative association between firm maturity
and cost of equity that is both statistically and economically significant, the sign, magnitude
or statistical significance of these estimates may be biased due to endogeneity, that is, that the
life cycle proxy and the error term in Equation (1) are correlated. Three factors may
potentially contribute to this effect: reverse causality, omitted unobserved characteristics and
measurement error (Aivazian et al. 2005). To formally address the concern that the proxy for
the corporate life cycle is endogenous, we adopt a two-stage instrumental variable approach
27
to re-examine the fixed effect panel’s data-based findings reported in Table 5. The first stage
of this procedure involves regressing endogenous variables (proxies for the firm life cycle) on
selected instruments and the exogenous variables from the main analyses in Table 5. In the
second stage, we estimate analyses in Table 5 by replacing the endogenous variables (proxies
for the firm life cycle) with fitted values from the first-stage regressions.
Contemporary studies in finance and accounting extensively adopt the two-stage
instrumental variable approach to address endogeneity concerns.16 However, this approach is
appropriate only if the instrumental variables are correlated with the endogenous regressor
but uncorrelated with the error term of the second-stage regression. In this context, good
instruments are exogenous variables that are economically related to the life cycle proxy but
are uncorrelated with the error term of the second-stage regression relating the cost of equity
to the life cycle. Hence, we use the average cost of equity (simple average of all non-missing
observations), industry average earnings per share (EPS), industry average ZSCORE and
firm-level operating performance (proxied by dummy variable for firm loss) as instruments
for firm life cycle proxies (RE/TA and RE/TE). We use average cost of equity because it is
expected to exhibit lower measurement error than any of the individual measures. Use of
industry average EPS and Z score as instruments can be justified on the basis that industrylevel operating performance and financial strength of the firms reflect the growth and
maturity of the industry to which a particular firm belongs and, therefore, it should be highly
correlated with the life cycle of the firm. Lumpkin and Dess (2001) suggest that the industry
life cycle affects firms’ strategy on proactiveness or competitive aggressiveness. When
demand grows in an industry, firms can realise initial success without the intense competitive
threat that firms face in mature industries. Therefore, it is expected that industry-level growth,
16
Please refer to Larcker and Rusticus (2010) for discussion on the use of instrumental variables in
contemporary accounting research.
28
performance and financial solvency of the firm have direct impact on the overall performance
of the firm, which eventually shapes the stages of the life cycle of the firm. Firm-level
operating performance is one of the key indicators of the firm’s stage in the life cycle
(Dickinson 2011). Firms in the introduction and decline stages generally have negative
operating performance, while firms in the growth and mature stages have strong operating
performance. Hence, we use a dummy variable for loss of the firm which reflects different
stages of the firm life cycle.
Panel A of Table 6 reports the first-stage regression results in which the endogenous
variables, RE/TA and RE/TE, are regressed on the selected instruments and the exogenous
variables from our analyses in Table 5. Consistent with expectations, coefficients on the
instrumental variables are significant (at the 1% level), suggesting that firm maturity (RE/TA
and RE/TE) is positively associated with profitability (EPS) and negatively related to loss.
Panel B of Table 6 shows the results from the instrumental variable approach and suggests
that the negative relationship between life cycle proxies (RE/TA and RE/TE) and the cost of
equity remain robust after accounting for the endogenous relationship between the life cycle
proxy and the implied cost of equity capital. The estimated coefficients of RE/TA and RE/TE
are -.519 and -.276, respectively (both are significant at < .001) in the fixed effect two stage
least squares (2SLS) regression, suggesting that endogeneity cannot explain away the
negative relationship between the life cycle and the cost of equity capital.17
Insert Table 6 about Here
In support of the instruments, we also conduct underidentification, weak
identification, Hansen’s overidentifying restrictions and Hausman’s endogeneity tests. In
17
We perform Hausman’s specification test (Hausman 1978) to test whether the fixed effect and random effect
instrumental variable approaches are suitable. Test results suggest that the data support the fixed effect model in
estimating the relationship.
29
Table 6, underidentification test results (LM statistic) reveal that the excluded instruments are
"relevant". The weak instrument test is performed to test whether the excluded instruments
are sufficiently correlated with the included endogenous regressors—the goodness-of-fit of
the “first stage”. Test results show that the excluded instruments are correlated with the
endogenous regressors because the Cragg-Donald Wald F statistic is greater than Stock and
Yogo’s (2002) critical value.18 Results from Hansen’s overidentifying restrictions test do not
reject the null hypothesis (p-value > .10), suggesting that instruments are uncorrelated with
the error term and are correctly excluded from the second-stage regression, which reflects the
validity of the instruments used for the 2SLS regression. Finally, we perform Hausman’s
(1978) test to ascertain whether the endogeneity problem is really a concern for the estimates.
For our analysis, Hausman’s test strongly rejects (p-value = 0.000) the exogeneity of the firm
life cycle (RE/TA and RE/TE) which justifies the use of the 2SLS regression estimates.
We also employ a two-stage instrumental variable approach to address the
endogeneity concern with Dickinson’s (2011) life cycle measure. The untabulated19 results of
the weak instrument test, overidentification test, underidentification test and Hausman’s test
indicate the validity of the instruments used and confirm that the 2SLS regression estimate is
preferable for estimating the association between the cost of equity and the firm life cycle.
Moreover, the second-stage results continue to provide strong evidence of a statistically
significant and positive relationship between the cost of equity and the introduction and
decline stages, while a statistically significant negative relationship exists between the cost of
equity and the growth and decline stages of the firm life cycle.
18
When the instrument is only weakly correlated with the regressor, IV methods provide highly biased
estimates (Larcker and Rusticus 2010). We also test whether 2SLS regression estimates suffer from the
heteroskedasticity problem and the results reveal that our estimates do not suffer from this problem. Hence, we
report the Cragg-Donald Wald F statistic for the weak identification test in Panel B of Table 6.
19
For brevity, results are not tabulated: they may be requested from the authors.
30
4.6 Additional Analysis and Robustness Check
In this section, we examine the robustness of the results to alternative measurements and
specifications.
4.6.1 Alternative Measure of Firm Life Cycle
To mitigate the concerns as to whether the main results are sensitive to how the life cycle is
measured, we use firm age as an alternative measure.20 Firm age is a simple and natural
choice for measuring the life cycle stage of a firm because life cycle stages are naturally
linked to firm age. We define AGE as the difference between the current year and the year of
incorporation of the firm.21 Panel A of Table 7 reports the results of the sensitivity tests
where the dependent variable is cost of equity (for the four models used in the main analysis)
and the key independent variable is AGE. In Panel A, Models 1 to 4 show that the association
between all the estimates of the cost of equity and AGE are negative and statistically
significant. However, considering that firm age can be a proxy for various time-varying
arguments, we also use a dummy variable to distinguish between firms in old and young
groups. We use AGE equals 1 if the firm age is greater than the median in any given year, 0
otherwise. The untabulated results remain qualitatively the same. Overall, the results using
AGE as an alternative measure of the firm life cycle are similar to those obtained in our main
analysis and this helps to justify that the results are not sensitive to the choice of the life cycle
proxy.
4.6.2 Alternative Measure of Cost of Equity
To mitigate the concerns that our results are driven by the choice of dependent variable
(estimation of the cost of equity), we use an alternative approach to measure the cost of
20
Pástor and Pietro (2003) also use firm age as a “natural proxy” for investors’ uncertainty about the
profitability of the firm.
21
We have collected data on the firm’s year of incorporation from company history and listing details of
DatAnalysis Morningstar.
31
equity. For this purpose, we follow Easton and Monahan (2005) and use the following model
to calculate the ex-ante cost of equity:
(
( )
)
Panel B of Table 7 reports the results of the sensitivity analysis with RPE as the
dependent variable and four alternative measures of firm life cycle proxies (RE/TA, RE/TE,
Dickinson’s (2011) measure and AGE) as the key independent variables along with control
variables. As reported in the table, our inferences on the role of the firm life cycle on the cost
of equity remain unaltered when the new empirical proxy for the cost of equity is used as the
dependent variable. For example, in Panel B of Table 7, Model 1 and Model 2 show that the
cost of equity is significantly negatively associated with RE/TA and RE/TE. In Model 3, in
considering Dickinson’s (2011) life cycle stages, the cost of equity is positively associated
with the decline stages, and negatively associated with the growth and mature stages.
Moreover, Model 4 shows that the relationship between the cost of equity and AGE (the life
cycle proxy) is negative and significant.
In conclusion, regression results using the alternative measures of life cycle and cost
of equity suggest that our results are not sensitive to the choice of estimation of the life cycle
and the cost of equity.
4.6.3 Estimates Excluding Regulated Industries
We repeat estimations in the main analysis by excluding utilities, telecommunications and
energy industries from the sample. The rationale for excluding these industries is that the
investment behaviour of these firms is more likely to be affected by regulations and by the
nature of their activities (Aivazian et al. 2005). In untabulated results, estimates of this
32
restricted sample are very similar to the estimates with the main analysis. None of the
significant coefficients changes its sign.
V. Concluding Remarks
Our study provides evidence on the cost of equity for Australian listed firms and tests
whether the dynamic resource-based view and life cycle theory can explain the variation in
the cost of equity across different phases of the firm life cycle. In this study, we posit that
firms in different life cycle stages have different levels of resource base, competitive
advantages, information asymmetry and riskiness and, hence, the cost of equity of the firm
should vary systematically across the firm’s life cycle. Using a sample of Australian listed
firms from 1990–2012, our results show that the cost of equity of the firm significantly
differs across the life cycle stages. In particular, the study reveals that the cost of equity is
higher in the introduction and decline stages of the firm, while it is lower in the mature stage.
Moreover, the mean difference test also suggests that there is a large difference in the cost of
equity for various stages of the firm life cycle. Specifically, the results are unaffected by
different estimations of the cost of equity and the firm life cycle.
Overall, our empirical evidence contributes to the growing body of literature that
focuses on the financial implications of the firm life cycle. Our primary contribution is in
extending this body of research to document the role of the life cycle as a key determinant of
the cost of equity capital.
Our findings strongly support the resource-based view of competitive advantage and
firm life cycle theory. The resource-based view (RBV) suggests that a firm’s resources are
the ultimate determinants of competitive advantage and performance. According to the
33
resource-based view, the financial capital, physical resources, human resources, intangible
know-how, and skills and capabilities of large and mature firms are rich, diverse and strong,
while those of small and young firms are small, concentrated and limited. These resource
bases and expertise help mature firms to achieve competitive advantage, to reduce the risk
and information asymmetry problem, and to gain easy access to finance which contribute to a
reduction in the cost of equity capital. The findings are also consistent with the life cycle
theory of the firm in that different stages of the life cycle exhibit different levels of
disclosure, analyst and investors’ following, liquidity of stock, existence, credibility and
reputation in the market. Hence, as a consequence of transition from one stage to another, the
cost of equity changes accordingly. Finally, from a practitioner’s perspective, our results have
direct implications for the financial management and strategic direction of the firm. Our
results provide evidence suggesting that firms should reach and maintain maturity, the prime
stage of the firm life cycle, to benefit from the lower cost of equity.
34
Appendix A: Variable Definition and Measurement
Variables
=
Definition and Measurement
Dependent Variable
RPEG
Implied cost of equity, estimated by the PEG model of Easton (2004)
RMPEG
Implied cost of equity, estimated by the MPEG model of Easton (2004)
ROJ
Implied cost of equity, estimated by the modified Ohlson and Juettner-Nauroth (2005) model
(modified by Gode and Mohanram (2003))
RAverage
Implied cost of equity, estimated as the average of the above three models
Firm Life Cycle Proxies
RE/TA
Retained earnings as a proportion of total assets. Measured as: retained earnings/total assets
RE/TE
Retained earnings as a proportion of total equity. Measured as: retained earnings/total equity
CLC
A vector of dummy variables that capture firms’ different stages in the life cycle
AGE
The difference between the current year and the year of incorporation of the firm
Control Variables
SIZE
Natural log of total assets of the firm at the end of the fiscal year
BM
Ratio of book value of equity to market value of equity at the end of the fiscal year
BETA
A measure of systematic risk, extracted from Datastream. Datastream uses a five-year period
and regresses the share price against the respective Datastream total market index using log
changes of the closing price on the first day of each month
LOSSt-1
An indicator variable that equals 1 if net income before abnormal is negative in the previous
years, 0 otherwise
LEV
(Short term debt + long term debt)/Shareholders’ equity
ZSCORE
A model, developed by Edward I. Altman in 1968, used to predict publicly traded
manufacturing companies’ likelihood of bankruptcy. Altman’s Z score = 1.2(Working
Capital/Total Assets) + 1.4(Retained Earnings/Total Assets) + 3.3(Earnings Before Interest &
Tax/Total Assets) + 0.6(Market Value of Equity/Total Liabilities) + 0.999(Sales/Total Assets)
Year
Dummy variables to control for fiscal year
Firm-specific unobserved fixed effects
35
Table 1: Sample Selection and Distribution of the Sample
Panel A: Sample Selection by Models
Description
I/B/E/S forecasted EPS (fiscal year
1990-2012)
Less: Firm years dropped due to:
Model’s specific requirement22
Absence of forecasted DPS1
Financial sector and delisted firms
Missing values on control valuables
Final Sample
Pooled
Easton
PEG
(2004)
Easton
MPEG
(2004)
8020
8020
8020
Ohlson and
JuettnerNauroth
(2005)
8020
2250
N/A
1337
545
3888
2250
N/A
1337
545
3888
2250
707
1311
189
3563
2342
703
1297
196
3482
Panel B: Distribution by Year (Pooled)
Year
1990
1991
1992
1993
1994
1995
1996
1997
N
Year
35
1998
46
1999
46
2000
43
2001
46
2002
87
2003
120
2004
118
2005
N
Year
127
2006
145
2007
162
2008
230
2009
223
2010
188
2011
191
2012
231
Total
N
252
275
292
216
262
289
264
3888
Panel C: Distribution by Sectors and Cost of Equity Models
Name of the Sector
Consumer Discretionary
Consumer Staples
Energy
Health Care
Industrials
Information Technology
Materials
Telecommunication Services
Utilities
Total
22
Pooled
Easton
PEG
(2004)
Easton
MPEG
(2004)
Ohlson and
JuettnerNauroth (2005)
818
362
283
266
961
273
776
79
70
3888
818
362
283
266
961
273
776
79
70
3888
770
322
246
250
918
263
656
69
69
3563
765
320
231
243
912
258
621
65
67
3482
For estimating the cost of equity, we exclude cases where eps2 > eps1 > 0 are not met.
36
Table 2: Descriptive Statistics This table presents descriptive statistics for the major variables
used in the study. All the variables are defined in Appendix A.
Panel A: Pooled Descriptive Statistics
Variables
N
RAverage
RE/TA
RE/TE
SIZE
BM
BETA
LOSSt-1
LEV
ZSCORE
3888
3888
3888
3888
3888
3888
3888
3888
3888
Mean
.1779
.0383
.0662
19.9026
.8047
.9538
.1052
.5439
3.8928
Standard
Deviation
.1292
.3380
.7375
1.6795
.9047
.7791
.3068
.5881
4.0709
25%
.1048
.0084
.0206
18.706
.3114
.4735
0.0000
.1500
1.8991
Panel B: Life Cycle-wise Cost of Equity Using Different Models
Statistics Pooled Introducti Growth Maturity
Model
on
RPEG
Mean
.1563
.2670
.1536
.1317
(Easton
Median
.1181
.2041
.1194
.1075
2004)
Std. Dev. .1226
.1980
.1099
.0911
RMPEG
(Easton
2004)
R(Ohlson
and JuettnerNauroth
Median
.1396
.0887
.1894
19.7753
.5657
.8570
0.0000
.4200
2.8350
75%
.2018
.1844
.3771
21.0821
.9419
1.3045
0.0000
.7200
4.4014
Shakeout
.1779
.1329
.1364
Decline
.3385
.2679
.2218
Mean
Median
Std. Dev.
. 1846
. 1465
.1330
.3099
.2289
.2295
.1785
.1444
.1204
.1615
.1365
.0954
.2042
.1606
.1421
.3693
.2774
.2564
Mean
Median
Std. Dev.
.1873
.1535
.1193
.2951
.2271
.1997
.1852
.1537
.1129
.1670
.1442
.0893
.2037
.1636
.1244
.3594
.2589
.2286
Mean
Median
Std. Dev.
.1779
.1396
.1293
.2908
.2165
.2113
.1741
.1396
.1174
.1535
.1286
.0951
.1990
.1542
.1429
.3677
.2931
.2355
2005)
RAverage
Panel C: Life Cycle-wise Mean Cost of Equity Using Different Models
0.4
0.35
0.3
0.25
0.2
0.15
0.1
0.05
0
PEG (Easton 2004)
MPEG (Easton 2004)
Ohlson and JuettnerNauroth (2005)
Average
Introduction
Growth
Maturity
Shake-out
37
Decline
Panel D: Life Cycle-wise Descriptive Statistics
Variables
RE/TA
RE/TE
SIZE
BM
BETA
LOSSt -1
LEV
ZSCORE
Statistics
Mean
Median
Standard Deviation
Mean
Median
Standard Deviation
Mean
Median
Standard Deviation
Mean
Median
Standard Deviation
Mean
Median
Standard Deviation
Mean
Median
Standard Deviation
Mean
Median
Standard Deviation
Mean
Median
Standard Deviation
N
Introduction Growth
-.2798
.0485
-.0716
.0769
.5514
.2363
-.5702
.0921
-.1079
.1654
1.3414
.5527
18.8836 20.0333
18.8311 19.9263
1.4782 1.5733
.7749
.7799
.5705
.5600
.9309
.8495
1.1538
.9782
1.0630
.8875
1.0116
.7665
.4096
.0973
0.0000 0.0000
.4927
.2965
.6897
.6355
.4700
.5200
.7965
.5816
3.4767 3.3226
1.9590 2.5789
5.6652 3.2954
271
1356
38
Maturity
.1031
. 1198
.2918
.1954
.2477
.5649
19.9791
19.8747
1.7123
.7816
.5383
.9053
.8954
.8080
.7103
.0459
0.0000
.2093
.4798
.3500
.5310
4.3926
3.2308
4.0190
1830
ShakeDecline
out
-.0032
-.4824
.0811
-.2996
.3597
.7275
-.0069 -1.1516
.1605
-.5401
.6898 1.9636
19.9356 18.9995
19.8323 19.0704
1.7220 1.8281
1.0026
.9791
.7250
.7037
.9897 1.2384
.9315 1.4249
.8250 1.2550
.8608 1.0039
.1559
.4068
0.0000 0.0000
.3633
.4954
.4717
.5589
.3400
.2300
.5748
.8663
3.8353 3.7729
2.6565 1.6107
4.4890 7.2754
372
59
Table 3: Correlation Matrix
Correlation among the Different Estimates of Cost of Equity, Life Cycle Proxies and
Control Variables
Models
Introduction
RPEG
RMPEG
ROJ
RAverage
0.247***
0.258***
0.232***
0.239***
Growth
-0.016
-0.034**
-0.013
-0.021
Mature
-0.189***
-0.165***
-0.164***
-0.178***
Shake-out
0.057***
0.045***
0.042**
0.053***
Decline
0.184***
0.171***
0.174***
0.182***
RE/TA
-0.436***
-0.416***
-0.389***
-0.416***
RE/TE
-0.393***
-0.383***
-0.366***
-0.382***
SIZE
-0.325***
-0.315***
-0.306***
-0.319***
BM
0.254***
0.286***
0.292***
0.271***
BETA
0.204***
0.230***
0.218***
0.196***
LOSSt-1
0.367***
0.285***
0.285***
0.328***
LEV
-0.023
0.012
0.028
0.005
ZSCORE
-0.130***
-0.163***
-0.163***
-0.145***
This table presents the correlation among different estimates of the cost of equity, life cycle proxies
and control variables. The values in the matrix are Pearson correlation coefficients and ***, **, and *
denote significance at 1%, 5% and 10% levels respectively (two-tailed tests). All the variables are as
defined in Appendix A.
39
Table 4: Mean Difference Test of Cost of Equity (assuming unequal variance)
Mean Difference Test of Cost of Equity Using Dickinson (2011)
Cost of Equity
Cost of Equity
t statistics for
Estimates
p-values
(Stage 1)
(Stage 2)
differences
Introduction
Growth
RPEG
.267
.154
-9.153
0.000
RMPEG
.309
.178
-8.783
0.000
ROJ
.295
.185
-7.855
0.000
RAverage
.291
.174
-8.822
0.000
Growth
Maturity
RPEG
.154
.132
-5.969
0.000
RMPEG
.178
.162
-4.137
0.000
ROJ
.185
.167
-4.694
0.000
RAverage
.174
.154
-5.309
0.000
Maturity
Shake-out
RPEG
.132
.178
6.253
0.000
RMPEG
.162
.204
5.033
0.000
ROJ
.167
.204
4.847
0.000
RAverage
.154
.199
5.884
0.000
Shake-out
Decline
RPEG
.178
.338
5.404
0.000
RMPEG
.204
.369
4.567
0.000
ROJ
.204
.359
4.698
0.000
RAverage
.199
.368
5.347
0.000
Introduction
Maturity
RPEG
.267
.132
-11.078
0.000
RMPEG
.309
.162
-10.057
0.000
ROJ
.295
.167
-9.284
0.000
RAverage
.291
.154
-10.540
0.000
Introduction
Shake-out
RPEG
.267
.178
-6.387
0.000
RMPEG
.309
.204
-6.326
0.000
ROJ
.295
.204
-5.919
0.000
RAverage
.291
.199
-6.194
0.000
Introduction
Decline
RPEG
.267
.338
2.286
0.025
RMPEG
.309
.369
1.559
0.123
ROJ
.295
.359
1.833
0.071
RAverage
.291
.368
2.312
0.023
Growth
Shake-out
RPEG
.154
.178
3.165
0.001
RMPEG
.178
.204
2.911
0.004
ROJ
.185
.204
2.341
0.019
RAverage
.174
.199
3.085
0.002
Growth
Decline
RPEG
.154
.334
6.371
0.000
RMPEG
.178
.358
5.394
0.000
ROJ
.185
.350
5.363
0.000
RAverage
.174
.361
6.279
0.000
40
Table 5: Association between Cost of Equity and Firm Life Cycle
Panel A: Association between Cost of Equity and RE/TA (Life Cycle Proxy of DeAngelo
(2006))
Model 1
Easton 2004
RPEG
Model 2
Easton 2004
RMPEG
Model 3
OJ 2005
ROJ
Model 4
?
0.415***
(5.47)
0.364***
(4.95)
0.377***
(5.50)
0.392***
(5.09)
RE/TA
-
-0.058***
(-4.14)
-0.051***
(-3.10)
-0.034**
(-2.41)
-0.056***
(-3.81)
SIZE
-
-0.012***
(-3.31)
-0.011***
(-2.88)
-0.011***
(-3.09)
-0.011***
(-2.94)
BM
+
0.032***
(6.86)
0.041***
(7.52)
0.040***
(7.88)
0.037***
(7.19)
BETA
+
0.004
(1.23)
0.010***
(2.61)
0.010***
(2.68)
0.005
(1.43)
LOSSt-1
+
0.027***
(3.14)
0.011
(1.29)
0.011
(1.35)
0.020**
(2.34)
LEV
+
0.013***
(2.84)
0.017***
(2.87)
0.015***
(3.29)
0.017***
(3.24)
ZSCORE
-
-0.003***
(-4.85)
-0.004***
(-4.75)
-0.003***
(-4.68)
-0.004***
(-5.23)
Year Dummy
Yes
Yes
Yes
Yes
Firm Fixed Effect
Yes
Yes
Yes
Yes
Adj. R-squared
0.759
0.781
0.767
0.755
Observations (N)
3,888
3,563
3,482
3,888
Number of Firms
704
679
656
704
Variables
Pred.
Sign
Intercept
Robust t-statistics in brackets
*** p < 0.01, ** p < 0.05, * p < 0.10
41
RAverage
Panel B: Association between Cost of Equity and RE/TE (Life Cycle Proxy of
(DeAngelo 2006))
Model 1
Easton 2004
RPEG
Model 2
Easton 2004
RMPEG
Model 3
OJ 2005
ROJ
Model 4
Variables
Pred.
Sign
Intercept
?
0.452***
(5.75)
0.379***
(4.92)
0.374***
(5.23)
0.422***
(5.25)
RE/TE
-
-0.017***
(-3.15)
-0.019***
(-3.43)
-0.015***
(-2.97)
-0.017***
(-3.16)
SIZE
-
-0.014***
(-3.69)
-0.012***
(-2.90)
-0.011***
(-2.87)
-0.012***
(-3.19)
BM
+
0.033***
(7.23)
0.042***
(7.71)
0.040***
(7.95)
0.038***
(7.46)
BETA
+
0.005
(1.38)
0.010***
(2.59)
0.010***
(2.62)
0.006
(1.54)
LOSSt-1
+
0.031***
(3.67)
0.014
(1.64)
0.012
(1.45)
0.024***
(2.79)
LEV
+
0.010**
(2.13)
0.013**
(1.99)
0.011**
(2.30)
0.014**
(2.45)
ZSCORE
-
-0.004***
(-5.62)
-0.004***
(-5.26)
-0.004***
(-5.05)
-0.004***
(-5.89)
Year Dummy
Yes
Yes
Yes
Yes
Firm Fixed Effect
Yes
Yes
Yes
Yes
Adj. R-squared
0.757
0.780
0.767
0.754
Observations (N)
3,888
3,563
3,482
3,888
Number of Firms
704
679
656
704
Robust t-statistics in brackets
*** p < 0.01, ** p < 0.05, * p < 0.10
42
RAverage
Panel C: Association between Cost of Equity and Life Cycle Proxies of Dickinson (2011)
Model 1
Easton 2004
RPEG
Model 2
Easton 2004
RMPEG
Model 3
OJ 2005
ROJ
Model 4
?
0.503***
(6.72)
0.458***
(5.75)
0.438***
(5.86)
0.475***
(6.11)
Introduction
+
0.017
(1.57)
0.032***
(2.65)
0.024**
(2.32)
0.019*
(1.68)
Growth
-
-0.015***
(-2.84)
-0.014***
(-2.89)
-0.012***
(-2.68)
-0.017***
(-3.08)
Maturity
-
-0.015***
(-3.13)
-0.014***
(-2.89)
-0.014***
(-3.00)
-0.016***
(-3.28)
Decline
+
0.076***
(2.96)
0.061**
(2.12)
0.055**
(1.99)
0.069***
(2.62)
SIZE
-
-0.017***
(-4.76)
-0.016***
(-3.78)
-0.014***
(-3.57)
-0.015***
(-4.13)
BM
+
0.033***
(7.46)
0.042***
(7.89)
0.040***
(8.14)
0.038***
(7.63)
BETA
+
0.006*
(1.75)
0.012***
(3.06)
0.011***
(3.04)
0.007*
(1.93)
LOSSt-1
+
0.031***
(3.44)
0.014*
(1.66)
0.012
(1.46)
0.025***
(2.77)
LEV
+
0.016***
(3.36)
0.019***
(3.16)
0.016***
(3.47)
0.020***
(3.70)
ZSCORE
-
-0.004***
(-6.25)
-0.004***
(-5.76)
-0.004***
(-5.40)
-0.005***
(-6.40)
Year Dummy
Yes
Yes
Yes
Yes
Firm Fixed Effect
Yes
Yes
Yes
Yes
Adj. R-squared
0.761
0.783
0.770
0.757
Observations (N)
3,888
3,564
3,483
3,888
Number of Firms
704
679
656
704
Variables
Pred.
Sign
Intercept
Robust t-statistics in brackets
*** p < 0.01, ** p < 0.05, * p < 0.10
43
RAverage
Table 6: Two Stage Least Squares (2SLS) Regression
Panel A: First-Stage Regressions of Life Cycle Proxy (RE/TA and RE/TE) and Validity
of Instruments
Explanatory Variable
Model 1
Model 2
(RE/TA)
(RE/TE)
Instruments
Industry Mean EPS
0.005***
.011***
(4.72)
(4.41)
Industry Mean Z score
-0.019*
-.032
(-1.75)
(-1.23)
Loss
-0.143*** -0.251***
(-6.96)
(-5.13)
Unreported Control Variables Included in Regression
All Predetermined Variables in Main Specification
Year Fixed Effects
Firm Fixed Effect
Observation (N)
Adjusted R2
Yes
Yes
Yes
3735
0.607
Yes
Yes
Yes
3735
0.281
Underidentification Test
Kleibergen-Paap rk LM statistic
p-value
64.987
0.000
46.181
0.000
Weak Identification Test
Cragg-Donald Wald F statistic
(Stock and Yogo 2002)10% maximal IV size (Critical Value)
53.252
22.30
28.407
22.30
Test of Overidentifying Restrictions
Hansen’s J-statistic
p-value
0.468
0.791
1.748
0.417
Panel B: Second-Stage Regressions of Cost of Equity on Life Cycle Proxy
Explanatory Variable
Model 1
(RE/TA)
Potentially Endogenous Instrumented Variable
Life Cycle Proxy
-0.519***
(-6.17)
Unreported Control Variables Included in Regression
All Predetermined Variables in Main Specification
Yes
Year Fixed Effects
Yes
Firm Fixed Effect
Yes
Observation (N)
3735
Model 2
(RE/TE)
-0.276***
(-5.33)
Yes
Yes
Yes
3735
Hausman Test for the Effect of Life Cycle (Coefficient 2SLS = Coefficient OLS)
Cluster-robust F-statistic
p-value
54.842
0.000
44
53.454
0.000
Table 7: Sensitivity Analysis
Panel A: Age as an Alternative Life Cycle Proxy
Model 1
Easton 2004
RPEG
Model 2
Easton 2004
RMPEG
Model 3
OJ 2005
ROJ
Model 4
?
0.582***
(7.43)
0.543***
(7.03)
0.514***
(7.11)
0.561***
(6.98)
AGE
-
-0.003***
(-3.22)
-0.004***
(-3.48)
-0.004***
(-3.48)
-0.004***
(3.25)
SIZE
-
-0.018***
(-4.84)
-0.016***
(-3.93)
-0.014***
(-3.64)
-0.016***
(-4.28)
BM
+
0.034***
(7.50)
0.043***
(7.92)
0.040***
(8.14)
0.039***
(7.70)
BETA
+
0.006*
(1.70)
0.012***
(2.97)
0.011***
(2.93)
0.007*
(1.87)
LOSSt–1
+
0.037***
(4.14)
0.020**
(2.26)
0.016*
(1.96)
0.030***
(3.34)
LEV
+
0.017***
(3.51)
0.020***
(3.33)
0.017***
(3.75)
0.021***
(3.78)
ZSCORE
-
-0.004***
(-6.17)
-0.005***
(-5.73)
-0.004***
(-5.42)
-0.005***
(-6.39)
Year Dummy
Yes
Yes
Yes
Yes
Firm Fixed Effect
Yes
Yes
Yes
Yes
Adj. R-squared
0.754
0.778
0.765
0.751
Observations (N)
3,867
3,544
3,467
3,867
Number of Firms
681
658
639
681
Variables
Pred.
Sign
Intercept
Robust t-statistics in brackets
*** p < 0.01, ** p < 0.05, * p < 0.10
45
RAverage
Table 7: Sensitivity Analysis
Panel B: Alternative Estimation of Cost of Equity
Variables
Pred. Sign
Intercept
?
RE/TA
-
RE/TE
-
Introduction
+
Growth
-
Maturity
-
Decline
+
AGE
-
SIZE
-
BM
+
BETA
+
LOSSt – 1
+
LEV
+
ZSCORE
-
Year Dummy
Firm Fixed Effect
Adj. R-squared
Observations (N)
Number of Firms
Model 1
RPE
Model 2
RPE
Model 3
RPE
Model 4
RPE
0.010
(0.05)
-0.114**
(-1.97)
0.027
(-0.12)
0.223
(0.87)
0.406*
(1.65)
-0.047**
(-2.05)
0.017
(0.54)
-0.026**
(-2.18)
-0.024**
(-2.23)
0.219***
(3.01)
0.003
(0.28)
0.100***
(5.42)
0.011
(0.89)
-0.030*
(-1.51)
0.045**
(2.05)
-0.000
(-.77)
Yes
0.006
(0.48)
0.105***
(5.56)
0.009
(0.76)
-0.026
(-1.33)
0.022
(1.02)
-0.000
(-1.09)
Yes
-0.008
(-0.55)
0.100***
(5.79)
0.016
(1.32)
-0.019
(-0.97)
0.053**
(2.41)
-0.000*
(-1.68)
Yes
-0.007*
(-1.74)
-0.011
(-0.78)
0.105***
(5.83)
0.017
(1.34)
-0.008
(-0.42)
0.053**
(2.46)
-0.000*
(-1.53)
Yes
Yes
0.848
4,498
798
Yes
0.849
4,498
798
Yes
0.849
4,498
798
Yes
0.845
4,470
790
Robust t-statistics in brackets
*** p < 0.01, ** p < 0.05, * p < 0.10
46
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