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Investment, Q, and the Weighted Average Cost of Capital
Murray Z. Frank and Tao Shen∗
April 4, 2012
Abstract
Finance textbooks recommend evaluating investments by calculating the net presentvalue of the free cash flows using the weighted average cost of capital (WACC). Incontrast, scholarly studies estimate the impact of Q and cash flow on corporate in-vestment. This paper brings these together by examining the impact of WACC oninvestment regressions, using 440 alternative implementations of the WACC for USfirms from 1960 to 2010. WACC contains significant information not impoundedin empirical Q. When the common financial constraint indices are used, WACChas a similar impact on investment for both the constrained and the unconstrainedfirms. When WACC is decomposed, all elements have effects on investment. Theelasticities of investment with respect to leverage and taxation, are larger than theelasticities of investment with respect to Q and cash flow.
∗Murray Z. Frank, Piper Jaffray Professor of Finance, University of Minnesota, Minneapolis, MN55455. Tao Shen, Department of Finance, University of Minnesota, Minneapolis, MN 55455. We aregrateful to Heitor Almeida, Philip Bond, Bob Goldstein, Raj Singh, Andy Winton, and seminar partici-pants at the University of Minnesota, and North Carolina State for helpful comments and suggestions. Wealso thank Ken French and and John Graham for making useful data available. We alone are responsiblefor any errors.
Studies of corporate investment commonly focus on the impact of Q and cash flow, as
well as an index of financing constraints. There is an extensive debate over the common
finding that, despite the strong theoretical appeal of Q, empirical Q is less powerful
than theory suggests. Cash flow often matters. This is commonly attributed to either
financing constraints as studied by Hadlock and Pierce (2010) and Chen and Chen (2012),
or measurement error as studied by Almeida et al. (2010) and Erickson and Whited
(forthcoming).
However, practitioners do not think about investment in terms of Q. For decades
business students have been taught to evaluate investments by projecting cash flows and
discounting with the weighted average cost of capital (WACC). In surveys (AFP, 2011)
financial managers say that they do this. Of course, as observed by Gomes (2001), under
a strict interpretation, Q ought to fully impound the impact of these decisions. But it is
also well-known that empirical measures of Q are imperfect. So WACC might prove to
be important for investment even when Q is included.
In this paper we study the effect of WACC on corporate investment by US firms
1960-2010. As discussed by Bond and Van Reenen (2007) a number of different empirical
methods can be used to study corporate investment. In order to highlight the role of the
WACC we stick with the familiar investment regression approach that stems from Fazzari
et al. (1988). As discussed and updated by Lewellen and Lewellen (2011) this approach
continues to be a dominant methodology in the literature.
The key finding is that WACC contains empirically significant information about in-
vestment that is largely orthogonal to Q – neither subsume the other. This result is
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extremely robust to alternative methodological choices. Thus the observed investment
choices are broadly consistent with the survey evidence. This also implies that WACC
deserves attention when studying corporate investment.
Second, financial constraint indices do not disrupt the impact of the WACC. The
impact of WACC on investment is very similar for the financially constrained and the
financially unconstrained samples of firms. What is more, the components of the usual
financial constraint indices are very similar to the components of WACC, which raises
issues of interpretation.
Third, we study the impact of the components of WACC individually to see if they
all matter. Controlling for cash flows, investment is increasing in corporate tax, and
decreasing leverage, and the cost of debt. These effects line up correctly with the usual
textbook WACC. The effect of cost of equity is strongly sensitive to the approach used to
measure it. Seemingly equally plausible methods can produce opposite results.
In order to carry out this study it is necessary to measure WACC. Textbooks say that
this is easy1. But they provide only limited guidance regarding actual implementation. All
elements of the WACC can be measured in several ways. We have studies 440 alternative
ways of computing the WACC. Because the typical leverage ratio is about 0.3, the cost of
equity gets a weight of 0.7 in the WACC. Accordingly the cost of equity is of particular
importance. We study the textbook CAPM, the Fama and French (1993) 3 factor model,
1“You can often use stock market data to get an estimate of rE , the expected return demanded byinvestors in the company’s stock. With that estimate, WACC is not too hard to calculate, because theborrowing rate rD and the debt and equity ratios D/V and E/V can be directly observed or estimatedwithout too much trouble.” Brealey et al. (2006), page 514.
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the Fama-French 4 factor (or Carhart (1997)) model, the Gordon Growth model, the
‘implied cost of capital’ approach as in Gebhardt et al. (2001).
There are important systematic differences among the estimates. The historically
oriented measures (textbook CAPM, the Fama and French (1993) 3 factor model, the
Fama-French 4 factor model) have a higher average cost of capital than the forward looking
model based methods (Gordon Growth model, the implied cost of capital approach). The
historically based measures are often positively related to corporate investment. This
might be a reflection of firm-specific growth options as hypothesized by Da et al. (2012).
The forward looking methods are generally negatively related to corporate investment.
This is what should be observed if the proxies for future cash flow (Q, EBITDA, analyst
forecasts, etc.) are doing a good job of reflecting the expected future cash flows.
The usual financial constrained indices are by Lamont et al. (2001), Whited and Wu
(2006), and Hadlock and Pierce (2010). These are largely composed of elements of the
WACC and cash flow. But these factors enter the analysis at a different place. This
makes it hard to strictly distinguish ‘financially constrained’ firms from firms that simply
face a higher cost of capital. To some extent this difference is more a matter of degree
than of kind. A very high cost may not be all that different from an infinite cost as far
as the observable results are concerned.
Empirically we find surprisingly little difference between the financially constrained
and the financially unconstrained samples. This is true for each of the financing constraint
measures that we have tried. This is true whether we use pooled OLS, robust regressions,
Fama-MacBeth regressions, firm fixed effects, year fixed effects, or both firm and year
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fixed effects. In general inclusion of firm fixed effects is important for inferences about
the relative importance of Q and cash flow. But the choice about fixed effects is not so
important for recognition that WACC has an impact.
Because the financing constraints are often composed out of roughly the same factors
as the WACC/CF, it is of interest to examine the individual impacts of the components.
Accordingly we also ran investment regressions in which the individual components of the
WACC were included as regressors. The individual elements proved to be statistically
significant, and to have the expected sign according to the textbook WACC. The one
exception is the required return on equity. Some methods of computing the required
return on equity produce an impact on investment with a positive sign. Other methods
produce an impact with a negative sign. This choice really matters.
The WACC proves to be a fairly successful aggregation. The R2 is only a little bit
higher when we include the individual elements, as opposed to including the WACC
measure itself. Thus for practical purposes WACC provides a useful summary measure.
The rest of the paper proceeds as follows. Section I shows how to introduce the WACC
into the usual investment regression framework. Section II describes the practical issues
that arise in computing the WACC. Descriptive statistics are provided in Section III.
Basic regression results are provided in IV. Section V shows the relationship between
the WACC and financing constraint indices. In Section VI WACC is used to compute
firm level NPV creation. The connection between that NPV creation and firm value is
documented. The conclusion is provided in Section VII.
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I. Empirical Methodology
The Q-theory model dominates the empirical corporate finance literature on invest-
ment. The theoretical justification is due to Hayashi (1982). The usual empirical method-
ology was established by Fazzari et al. (1988). A version of the standard Q-theory deriva-
tion, is presented in Appendix 1.
The derivation involves a dynamic optimization problem with a standard capital ac-
cumulation equation. The firm choose an investment level. It is assumed that there is a
quadratic adjustment cost function so that optimal investment is given by a first order
condition. The first order condition gives investment as a function of Q. The coefficient
on Q has an interpretation as an inverse of an adjustment cost term.
Suppose that an additional financing constraint is added to the model, it might bind.
Cash flow ought to help alleviate the constraint. If it does, then Q will drop out and
instead the measure of the cash flow will matter in the regression equation.
Firms are sorted on an ex ante basis into financial constrained and financially uncon-
strained groups of firms. We do not expect the sorting to be perfect, but hopefully it will
be fairly successful. If it is successful, then among the unconstrained set of firms, Q will
matter and cash flow will not. Among the constrained firms cash flow will matter and Q
will not. Thus the test is a comparison of the coefficients on the two variables in the two
groups. (The WACC introduces a third consideration.)
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The usual investment regression can be written as,
Log(Ii,t/Ki,t) = α + βQLog(Qi,t−1) + βCFLog(CFi,t/Ki,t) +∑i
firmi +∑t
yeart + εi,t.
The fixed effects are intended to pickup the impact of otherwise omitted factors that
are either firm-specific or year-specific constants. Some papers estimate this equation in
levels, while other papers estimate it in logs. We have tried both. To save space we only
report the log versions. In general the inferences do not change, although some of the
parameters are affected. Some papers use GMM instead of fixed effects regressions. For
an assessment of the relative merits see Almeida et al. (2010) and Erickson and Whited
(forthcoming).
In this model βQ > 0, βCF = 0 is the usual prediction. The usual estimates depend on
the sample of firms and the time period to some degree. It is common to find βCF > 0.
Several measures have been proposed as indicators of financing constraints. Fazzari
et al. (1988) used dividends as their measure. A dividend paying firm is assumed not to be
constrained. More recently the popular measures are the Kaplan-Zingales, or KZ measure
(Lamont et al., 2001), the WW or Whited and Wu (2006) measure, and the Size-Age or
SA measure proposed by Hadlock and Pierce (2010). Empirically we find quite similar
results from all of these measures.
The WACC framework can also be used to motivate regression tests. To see this,
consider a firm with free cash flows denoted FCF . Let the value of the firm at date 0 be
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denoted by V0. Assume the cash flows grow at rate g, and that the WACC remains the
same in all periods. The traditional Gordon growth model is,
V0 = −I +∞∑t=1
FCFt(1 + rwacc,t)t
= −I +FCF
rwacc − g. (1)
With FCF , I, and rwacc are taken to be independent exogenous numbers, it is obvious
that ∂V0∂rwacc
< 0. As in the standard textbook presentation, this partial derivative is
assuming the exogeneity of FCF . If rwacc is correlated with FCF then the basic empirical
predictions might not hold.
The firm undertakes all investments with V0 > 0. On the last dollar that firm invests
V0 = 0 so,
It/Kt =FCFt+1/Kt
rwacc − g.
As rwacc increases, in order to maintain V0 = 0, less investment is selected.2
To get the expression into a convenient form, take the log of both sides of the equality.
Then the firm’s zero NPV condition can be reexpressed as a regression
Log(It/Kt) = α0 + α1Log(FCFt+1/Kt) + α2Log(rwacc − g) + εt.
This specification has the drawback that rwacc and g are grouped together inside the log
term. But we want to learn about the impact of rwacc itself. Of even greater concern,
2To fix ideas, think of a firm that has a production function FCF (I), with FCF ′ > 0, FCF ′′ < 0.
The firm problem is maxI{−I + FCF (I)rwacc−g}. The first order condition can be written as FCF ′ = rwacc. So
if rwacc increases, so must FCF ′. This requires a drop in I.
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Chan et al. (2003) have documented that the analyst forecasts of g are not very reliable.
Thus we might be adding noise. Or we might be adding systematically biased noise. To
avoid this one possibility is to simply assume that g = 0. Many papers implicitly or
explicitly do this. Empirically that is probably a reasonable approach. An alternative is
to linearize. Take a first order Taylor series expansion around the point g = 0. With the
inclusion of fixed effects, the resulting investment regression is,
Log(Ii,t/Ki,t) = α0 + α1Log(FCFi,t+1/Ki,t) + α2Log(rwacc) (2)
+α3(g/rwacc) +∑i
firmi +∑t
yeart + εi,t.
The predictions are α1 > 0, α2 < 0, α3 > 0. The specification in equation 2 is very close
to a conventional investment regression. So the next step is to merge equation 2 with the
investment model. To do this a couple of problems must be faced.
First, the same empirical proxies are common for cash flow (CF) and for free cash flow
(FCF). So these cannot really be meaningfully distinguished. EBITDA/K is a particularly
popular proxy for both.
Second, the cash flow timing assumptions differ. In the standard discounting model it
is future values of cash flows that matter for computing present values. In the financing
constraints model, the cash constraint matters when it binds. Thus it is the current
value of cash flow that is included.3 Yet another consideration is econometric exogeneity.
3Some papers assume that the constraint shows up in firm’s hedging in advance. If this is going onthen the timing effect is, or course, altered.
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From this perspective it is nice to have explanatory variables prior in time. That way we
can be sure that they are at least predetermined. In the contest of investment regressions
Lewellen and Lewellen (2011) provide evidence to an impact of lagged cash flow.
There is no perfect solution to the timing issue. We study each of these cash flow
timing alternatives: past, current and future. The timing does matter to some extent.
However the main conclusions are not affected.
Nesting the two perspectives gives the basic estimating equation,
Log(Ii,t/Ki,t) = α0 + α1Log(Qi,t−1) + α2Log(CFi,t/Ki,t) + α3Log(rwacc) (3)
+α4(g/rwacc) +∑i
firmi +∑t
yeart + εi,t.
In light of previous studies we expect to find that α1 > 0 and α2 > 0. If Q really is a
sufficient statistic, then only the coefficient on Q will matter. But empirically Q is not
likely to be so powerful.
Suppose that the standard discounting model is correct and further suppose that we
have a reasonable proxy for expected free cash flows. Then α3 < 0 as higher rwacc makes
fewer investments worthwhile.
A crucial empirical concern is whether the future cash flows have been adequately
taken into account. If our empirical proxies are inadequate, then the sign on α3 is not
pinned down. Part of the control for the future is in the g term. But due to Chan et al.
(2003) there is particular reason to worry about the quality of the available proxies for g.
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Suppose that g is poorly measured. Then α4 will primarily be driven by 1/rwacc which
in turn will depend on the curvature of the relationship between I/K and rwacc. There
does not seem to be a very strong theoretical presumption either way. In light of all this
we did not have a strong expectation regarding the likely sign of α4. If contrary to Chan
et al. (2003), g is well measured, then we would expect that α4 > 0.
In our basic estimating equation we have followed common practice of including firm
and year fixed effects. This is common, but not uniform. The motivation is to remove
the impact of otherwise omitted common factors. However, it is also possible that the
firm fixed effect could actually sever to dummy out the effect of the financing constraints.
To avoid this problem we have run all of our tests using four ways: with no fixed effects,
with only year fixed effects, with only firm fixed effects, and with both firm and year fixed
effects. The main results are not sensitive to which of these we use.
II. Computing WACC
For more than a generation, business students have been taught to evaluate corporate
investments using a standard model. They forecast free cash flows and then discount the
cash flows using the weighted average cost of capital (WACC).4 The required return on
equity in the WACC is computed using the CAPM.5 If the resulting net present value
4Myers (1974) already referred to it as ‘the textbook formula.’ The approach is taught by most moderncorporate finance textbooks such as Benninga (2008), Berk and DeMarzo (2011), Brealey et al. (2006),Koller et al. (2010), Damodaran (2002) and Ross et al. (2008).
5“in addition to being very practical and straightforward to implement, the CAPM-based approach isvery robust. While perhaps not perfectly accurate, when the CAPM does generate errors, they tend tobe small. Other methods, such as relying on average historical returns, can lead to much larger errors.”Berk and DeMarzo (2011), page 399.
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is positive, the investment is worthwhile and otherwise it is not worthwhile. In surveys,
senior managers – many of whom have business degrees – report using the WACC when
making investment decisions.6 However, the empirical literature on corporate investment7
has ignored the WACC in favor of tests of Tobin’s Q theory of investment – a theory that
is largely ignored in the teaching of business students.
It is helpful to recall the standard definition of WACC. Let E denote the value of
equity, D is the value of debt, V = D + E is the total value of the firm, rE is the equity
cost of capital, rD is the debt cost of capital, τc is the corporate tax rate, and rwacc is the
weighted average cost of capital,
rwacc =E
VrE +
D
VrD(1− τc) (4)
Computation of rwacc thus requires measuring rE, rD, E, D, V , and τc. For each of
these many seemingly plausible alternative proxies are available. Not surprisingly, while
some choices are more common than others, various practitioners report using a range
of alternative proxies in actual practice. We provide evidence for 440 different ways of
computing WACC. These alternatives generally produce reasonably similar average values.
However, they can produce sharply different second and higher moments. Furthermore
some alternative choices produce opposite signs in the investment regressions. Thus the
choice of proxies do seem to matter.
6See Graham and Harvey (2001) and AFP (2011) for good, relevant surveys.7For good examples see the survey by Bond and Van Reenen (2007), and Almeida and Campello
(2007), Erickson and Whited (2000), among many others.
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A particularly important choice is how to measure the expected return on equity, rE.
The most conventional method is to use the CAPM where several years of monthly data
is used to compute the firm’s β. Recently the Fama-French 3 factor model (Fama and
French, 1993), and the Fama-French 4 factor model (includes momentum) have become
increasingly popular. These methods rely on several years of historical data to compute
the required return on equity.
An alternative approach is to use a discounting structure and some basic assumptions
to impute the required return on equity. The classical imputation method is the Gordon
growth model, as taught in textbooks such as Benninga (2008). An increasingly popular
version is based on residual income accounting as proposed by Gebhardt et al. (2001)
(GLS) and further studied by Nekrasov and Shroff (2009), Hou et al. (2010), Lee et al.
(2010) and Lewellen (2010).
Generally, the Gordon growth model seems to work better than the more common
CAPM. A problem with the CAPM and related methods is that five years of monthly
data is still just 60 observations. Da et al. (2012) argue that the arrival of growth options
at the firm level may be causing problems even if individual projects satisfy the CAPM.
The method of computing the cost of debt rD can also matter. The most commonly
used method in practice is to use the actual yield on the debt the firm is currently
carrying. This method is particularly simple to compute and to interpret. However, the
method is frequently criticized since it does not necessarily reflect the current debt market
conditions facing the firm. The cost of debt computed this way will generally appear to
be much smoother than the actual debt market rates. As an alternative we compute the
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average yield of the firm’s incremental debt issued during the year. This method is still an
approximation, but it should more closely reflect current market conditions in the given
year.8
There is no consensus on how to correctly measure a firm’s target leverage. We examine
the firm’s actual book leverage, and market leverage. These would be correct if the firm is
always at the leverage target – a fairly strong assumption. It is well known that industry
effects are rather strong in the data. Accordingly we also considered an equally weighted
sum of the firm’s own leverage and the average leverage of the other firms in the same
Fama-French industry. Some scholars argue that cash should be regarded as negative
debt. This motivated consideration of market leverage with debt netted of cash. There is
an empirical literature devoted to studying which factors seem to help explain corporate
debt choices. Accordingly we also computed target leverage as in the model of Frank and
Goyal (2009).
These alternative methods can make an important difference for the CAPM and Fama-
French cost of equity methods. They make much less of a difference for the imputed cost
of capital estimates. The use of either the Frank and Goyal (2009) model, or the average
of the firm’s own leverage with the Fama-French industry average seem to work fairly
well. For the imputed cost of capital class of methods of computing the cost of equity,
any of the leverage methods seems to be fine.
8It is possible to use still other methods to estimate a cost of debt. For example it is possible toexamine the yield of newly issued rated debt. Then we could use similarly rated firm’s issue yield as aproxy for a given firm. Since many firms do not have credit ratings, it would be necessary to also estimatean imputed credit rating. This also leaves out the yield on bank loans. Thus this approach has bothstrengths and weaknesses. We have not used this method among our 440 alternatives.
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For taxation we consider the top statutory federal corporate income tax rate. This
has the advantage that it is actually exogenous to a given firm. However the tax code is
complex, and not all firms are paying to top marginal rate. Thus we also consider the
average income tax rate paid by a firm. This will be a good measure if the firm’s tax rate
is very persistent from year to year. More sophisticated measures are available for recent
years in the study by Graham and Mills (2008). We examined the impact of two measures
considered in that study. These measures include more of the tax code structure, but they
are not available for as long a time period. The alternative tax code measures do make
some difference, primarily for the CAPM and Fama-French cost of equity approaches.
Not all 440 methods of computing WACC are equally interesting. The Association
of Finance Professionals (AFP) provides a recent survey of the choices commonly made
by practitioners when computing WACC, see AFP (2011). The finance professionals
choices closely match the typical examples taught in corporate finance textbooks. We
highlight results for this method. We also highlight the results for the Gordon growth
model approach since it seems both simple to implement and it works rather well.
Computing standard errors is always controversial. Petersen (2009) provides a par-
ticularly helpful perspective. We started by estimating Fama-MacBeth style. Then we
considered robust regressions, fixed effects regressions with clustered standard errors, and
the use of instrumental variables to deal with potential measurement error in the WACC.
Measurement error is more important for some methods than for others. From these al-
ternative methods it seems clear that the effects that we have identified are coming both
from the cross-section and from the time-series variation in the data.
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The WACC can be regarded as a particular popular way to put together a number or
pieces of information for a firm considering an investment. Are all of the pieces equally
important? To address this question, year fixed effect linear regressions are run that
use the individual components of the WACC in place of the WACC. All of the WACC
components are statistically significant. Consistent with the earlier results, the choice of
the method to compute the required return on equity is a concern.
How do WACC and investment relate to the value of a firm? Suppose that firms
employ a given WACC to make the investment decisions, using the ordinary NPV rule.
Then a good WACC will result in more valuable firms. To examine this for each firm
we compute a median NPV using a measure of WACC across years. This provides an
estimate of the value created by a firm under the WACC measure. We sort firms into
quintiles by this measure. Within each of these quintiles we compute the value of Q as
an estimate of the market’s assessment of value created.
In these sorts we expected to see high NPV associated with high value creation. This
is not what is observed. Empirically Q is increasing in NPV. However there is an excep-
tion for the very lowest NPV quintile. Firms in the lowest NPV quintile also commonly
have high Q. Such firms are apparently not generating much actual profits, but must be
supported by the impact of hoped for growth option effects. The lack of a monotonic rela-
tionship between NPV creation and market value is true for alternative WACC measures
and does not seem to depend on a particular proxy for WACC.
We are not aware of any previous attempts to systematically study the impact of
the WACC on corporate investment. Indeed there are surprisingly few studies of the
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WACC altogether. Kaplan and Ruback (1995) study a sample of high leverage transac-
tions between 1983 and 1989 for which they have cost of capital and expected cash flow
information. Gilson et al. (2000) study a sample of firms in bankruptcy reorganization.
In both of these studies they have published cash flow forecasts. In both studies the
discounted cash flow analysis performs rather well.
A somewhat related study is Fama and French (1999). They carry out an ex post
analysis of the cost of capital and the return on investment. Since the analysis is ex post
they are able to side step the problems in computing the WACC and free cash flows.
Their results are somewhat comparable to our evidence on the connection between NPV
and Tobin’s Q.
It is well known that the CAPM has problems fully accounting for stock returns.
Da et al. (2012) argue that the CAPM is more useful at the project level than at the
firm valuation level. This can happen if firms get options to invest where the underlying
projects are themselves well accounted for by the CAPM. The idea that the CAPM
is missing the impact of growth options appears to be a natural interpretation for the
problematic results for the CAPM based version of WACC.
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A. Cost of Equity Using The Textbook CAPM
Practitioners routinely use the CAPM to get the cost of equity. We largely follow
the methods described in AFP (2011). To get this number we require several pieces of
information.
rE = rf + βE(rM − rf ) + ε
Several choices of the risk-free rate, rf , are possible.
Some people use a 3 month Treasury bill rate. But this entails rollover risk. Thus it is
more common to use a long term US government bond rates. To get βE it is usual to use
firm level regressions. most commonly a regression is run using either 3 years or 5 years
of monthly data.
Beta Industry Median Method. Sometimes the simple regressions give nonsensical
answers. In that case it is common to use an industry median value. Step 1. To do this
we first define an industry. We use the Fama-French industry definitions. Step 2. Then
for each firm in the industry compute the βE. Then unlever to get the βA as the beta of
assets (sometimes called the beta of an unlevered firm). To do this we must take a stand
on the firm’s leverage policy. Assuming the firm continuously maintains a leverage ratio,
then we use the Miles and Ezzell (1985) formula. Let βD be the beta of debt. Let V
denote the enterprize value. Under the assumption that the firm continuously rebalances
to maintain a target leverage ratio, βA = (EV
)βE + (DV
)βD. It is common in practice to
assume that βD = 0, which further simplifies things. This is probably not terrible for
many highly rated firms. Step 3. Take the industry median βA as applying to the assets
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of the firm under consideration. Step 4. Relever the βA using the firm’s own leverage ratio
to get an implied βE for the firm. Thus use that to compute the version of the return on
equity denoted by rE,IND.
Equity risk premium. This is hugely controversial. The most common proxies are:
long term arithmetic average return difference between the stock market (say S&P, or
CRSP VW or CRSP EW) and the risk free rate, long term geometric return difference,
an implied risk premium using the Gordon growth model as in Benninga (2008) section
2.7.3. For simplicity we have used the Fama-French measure from Ken French’s web
page.9 We have not explored alternatives on this dimension, and so it is always possible
that this could affect the results that we have found for the CAPM version of the WACC.
B. Cost of Equity Using The Gordon Growth Model
The Gordon growth model can be implemented in a number of ways. We have not
attempted to fine tune. Instead we follow Lee et al. (2010) which in turn draws on earlier
papers. As in that paper we considered two versions. A version with a single time period,
and a version with a five period horizon and a terminal value. Let EPSt denote earnings
per share at date t, and let DPSt denote dividends per share at date t and let κ denotes
the dividend payout ratio. The model discounts dividends for a few years and then adds
a ‘terminal value’.
9“Rm-Rf, the excess return on the market, is the value-weighted return on all NYSE, AMEX, andNASDAQ stocks (from CRSP) minus the one-month Treasury bill rate (from Ibbotson Associates)”
http://mba.tuck.dartmouth.edu/pages/faculty/ken.french/Data Library/f-f bench factor.html
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The basic model can be written as,
Pt =T−1∑i=1
DPSt+i(1 + re)i
+EPSt+T
re(1 + re)T−1,
where DPSt+1 = EPSt+1×κ. The dividend payout ratio, κ, is computed as in Hou et al.
(2010) and Gebhardt et al. (2001). If earnings are positive, then κ is current dividends
divided by current earnings. If earnings are negative, then κ is current dividends divided
by 0.06×total assets. The earnings per share can be taken from analyst forecasts from
IBES. This limits the number of firms that can be studied because not all firms have
analysts coverage. There are also questions about the quality of the analysts forecasting
abilities.
Recently Hou et al. (2010), and Lee et al. (2010) have found a fairly simple model
to predict earnings that seems to do rather well. We use that as the main method. It
computes earnings and the divides by number of shared to get EPS. Let EVj,t denote
the enterprize value of firm j in year t, TA is total assets, DIV is the value of dividends
paid, DD is a dummy for paying dividends, EARNj,t is earnings (before extraordinary
items) by firm j in year t, NegE is a dummy for negative earnings, ACC is total accruals
divided by total assets. The model is
EARNj,t+∆t = α0 + α1EVj,t + α2TAj,t + α3DIVj,t + α4DDj,t
+α5EARNj,t + α6NegEj,t + α7ACCj,t + εj,t+∆t.
19
Both papers estimate this model using pooled cross-section regressions using a rolling
prior ten years of data for each year. For comparability we do the same.10 A big advantage
of this model is that it gives the future earnings including growth.
III. Data and Summary Statistics
The data sources and data cleaning are described in Appendix 2, IX . Most of the
data is from standard sources, and we winsorize the data in each 1% tail. Using the Fama
and French (1997) industry definitions, we drop firms in utilities, banking, insurance, real
estate, trading, and with a missing industry code.
The descriptive statistics reported in Table 1 include several of the alternative proxies
for elements of the WACC. In most cases the proxies have fairly similar median values to
one another. The median of the proxies for leverage range from 0.21 to 0.34. The proxies
for the median cost of debt measures are 0.092 and 0.085. The median cost of equity
measures vary quite a bit, ranging from 0.05 to 0.19. The tax measures range from 0.32
to 0.41.
Because leverage is about 0.3, the cost of equity is crucial. The differences in the mea-
sure for the cost of equity are particularly notable. The ‘historical’ methods such as the
CAPM generally have a higher cost of equity. The ‘imputed’ methods such as the Gordon
10Given the presence of a lagged dependent variable, it ought to be possible to do better than simplyusing pooled cross-section regressions. Doing so would deviate from the earlier studies which, for ourpurposes is the more important consideration. Hence we stick with the approach from the literature.
20
Growth model generally give lower measures of the required return on equity. Some of
the methods give a higher standard deviation and skewness than do other methods.
Table II provides correlations among several of the factors. Column 1 shows that
some of the measures of the cost of equity are positively correlated with investment, while
other measures are negatively correlated. The CAPM based measure of the cost of equity
has a particularly strong positive correlation with investment (0.15), while the Gordon
growth model estimate has a particularly strong negative correlation (-.012). The leverage
measures are negatively correlated with investment. The top statutory tax is positively
correlated with investment, and the average tax has a negative correlation. In the later
regression analysis, all the tax measures are actually positively correlated with investment.
A perhaps surprising result is that the alternative measures of the cost of equity are
not all that highly correlated with each other. The CAPM and Fama-French 4 factor have
a correlation coefficient of 0.4. The Gordon growth model and the implied cost of capital
method (GLS) have a correlation of 0.54. But the other correlations are rather lower.
Table III shows what happens when we examine the investment of firms sorted into
quintiles by rwacc. To permit an impact of corporate cash flows in addition to sorting by
rwacc we also sort by either EBITDA/K (top two panels), or Q (bottom two panels). We
follow the literature in normalizing by the firm’s total capital (K) and studying I/K.
Since there are 440 measures of WACC we cannot report all the results. We report
results for WACCCAPM which uses the proxies that are fairly typical among the practi-
tioners by.AFP (2011) The min point of note is that it uses market leverage rather than
book leverage. This version of WACC is based on the CAPM and it is very close to the
21
typical description of how WACC is to be computed as found in most corporate finance
textbooks.
For comparison purposes we also report results for WACCGGM . This uses the Gordon
Growth model version of the cost of equity. This version performs particularly reliably in
the subsequent tests.
Within each cell the average value of I/K is computed. Differences in the mean values
of the high and low quintiles are also computed, along with statistical tests of the no
difference hypothesis.
Start with the first panel which gives results for WACCCAPM . The low WACC quintile
has low investment, while the high WACC quintile has high investment. Taken at face
value this is saying that firms invest more if investment is more costly. Clearly something
is amiss.
The most obvious hypothesis is that corporate earnings have not been taken into
account. Both EBITDA/K and Q can be viewed as (imperfect) proxies for free cash flow.
As might be expected high EBITDA/K and high Q are associated with greater corporate
investment. The differences are statistically significant. However, the problematic effect
of increasing investment as WACCCAPM increases is regularly found within each of the
cash flow quintiles. Thus to the extent that these proxies control for cash flow effects, the
problematic sign does not go away when we use proxies for future cash flows within the
sorting approach.
The problem could instead be due to the WACC measure. In the second panel of
Table III results for the WACCGGM (Gordon growth model version) are reported. For
22
this version of WACC, as the WACC increases investment drops. This is true in one-way
sorts. This is also true in two-way sorts using the same proxies as before (EBITDA/K
and Tobin’s Q).
This shows in a stark manner the potential importance of the choice of method for
computing the WACC. Depending on the choices of proxies, diametrically opposite im-
pacts can be obtained. This is despite the fact that all of the proxies are more-or-less
plausible. To some degree it may be the case that sorting is too blunt a technique. So we
next turn to regression based methods.
IV. Regression Results
There are several approaches to computing regressions that are popular in finance.
In empirical asset pricing, the Fama-MacBeth method is popular. In corporate finance,
following Petersen (2009), fixed effects models with standard errors clustered at the firm
level are popular. Some scholars are particularly concerned about empirical robustness.
We find all of these perspective compelling on their own terms. Rather than picking a
winner, and we ran all of our result for all WACC measures using each of these methods.
The robust regressions are particularly demanding of computer time. But all methods
generate very similar results for our topic. To report all of these results would try the pa-
tience of even a generous reader. Thus we report the results for the fixed effects regressions
with clustered standard errors.
23
Table IV reports the results of estimating equation 7. In the first column (CAPM)
the traditional CAPM is used as the cost of equity. In the second column (IND) industry
median β of assets is used to compute the firm’s cost of equity. In the third column (FF4)
the Fama French factors including momentum are used as the cost of equity. In column
four the Gordon Growth model is used. In the final column the implied cost of capital is
used. In all of these models firm and year fixed effects are used.
Some studies log the explanatory factors, while others do not do so. This affects the
numerical coefficients. We run in logs. The coefficients on the usual factors are similar to
those reported in earlier studies. In all of the models the coefficient on Q is around 0.2
and it is significantly different from zero at 1% level. In all of the models the coefficient
on cash flow (log(EBITDA/K)) is about 0.16 and it is also significant.
The key result of importance in Table IV are the coefficients on log(wacc). The message
here is that the choice of of cost of equity measure really matters. If the textbook CAPM
is used, a significant positive sign is found on WACC. If the industry median β is used a
negative sign is obtained. Thus how β is estimated really matters. In the Fama-French 4
factor model, as in the CAPM a positive sign is obtained. Both the Gordon growth model
and the implied cost of capital based estimates have negative coefficients. At this stage
it is not clear which is ‘better’. What is clear is that the sign on WACC is supposed to
be negative if future cash flow has been adequately controlled.
It may be helpful to think about the coefficients in terms of the elasticities. Thus in
Table IV we also report the associated elasticities on each coefficient. These are averages
across the observations that give the effect of a marginal change in the explanatory variable
24
on investment. The investment elasticity of Q is about 0.07 and for cash flow it is about
0.05. The elasticity of the WACC is, as expected, sensitive to how the cost of equity is
estimated. For the Gordon Growth Model the investment elasticity of WACC is -0.052
which is quite close to the value of the cash flow, but with the opposite sign.
Table IV reports fixed effects estimates. We have carried out the same estimations
using Fama-MacBeth, OLS, and Robust regression methods. These alternatives lead to
the same conclusions. To save space they are not tabulated separately in the paper.
Tables V and VI provides the estimated coefficients on WACC for various combina-
tions of the components. Several things are apparent. When the textbook CAPM, or the
Fama-French 3 factor or 4 factor models are used, the coefficient is usually positive, and
usually significant. The main exception is when the leverage target is computed from the
model, and the incremental cost of debt is used. When the implied cost of capital, or
the Gordon growth model is used, the coefficient is almost always negative and signifi-
cant. A particularly interesting case is the use of industry average to compute β. When
that is used in a CAPM (rE,IND) the coefficients are generally negative and statistically
significant. The choice of tax proxy, cost of debt measure, and leverage measures do not
seem to make all that much difference. From Tables V and VI it is apparent that the
CAPM and the GGM versions of the WACC are reasonably reflective of a broader group
of alternative ways of computing WACC.
In Table VII consideration is given to an alternative measure of cash flows. Instead of
using EBITDA, a direct Free Cash Flow measure is used. The coefficients on Q remain
essentially unchanged. The mean of the free cash flow variable is not the same as the
25
mean of the EBITDA, so the fact that the estimated coefficients differ is not a surprise.
The fact the cash flow comes through consistently and positively is important. Still more
importantly the estimated coefficients on the WACC measures are very close to being
unchanged. Thus the impact of the WACC measures on corporate investment is not
sensitive to the alteration of the cash flow measure. The R2 measures are generally higher
with EBITDA than with FCF, but the inferences to be drawn are not affected.
In the theoretical derivations of the regressions, the appropriate timing assumption on
the cash flow terms is an issue. In the financing constraints view, the cash flow measure
should be contemporaneous. In the WACC perspective it is future cash flow that matters.
Thus we tried using actual realized cash flows. If expectations are unbiased, the realization
ought to be a reasonable albeit noisy, proxy for what had been expected.
In the first five columns of Table VIII the future EBITDA is used. The results are
very similar to those in Table IV. The main difference is that the coefficients on EBITDA
are numerically closer to zero. The other coefficients are quite robust to the change. As
expected the R2 is somewhat reduced.
For econometric exogeneity purposes, it is natural to consider predetermined cash
flow measures. Thus in columns 6 to 10 of Table VIII lagged EDITDA is used. Again
there is a bit of a reduction in the R2. More interestingly the coefficients on the lagged
EBITDA are numerically very similar to the coefficients on the contemporaneous version
in Table IV. Thus there is a fair bit of robustness of the results to alternative cash flow
treatments. The main real difference is that the future values are biased towards zero.
This is consistent with the future being hard to forecast.
26
A. Instrumental Variable Approach
Investment can depend on many factors that we have only approximated in the con-
ventional investment regression. Accordingly it is natural to be concerned that the rwacc
measure might be correlated with the error term. Of particular concern is the idea that
there is a factor that affects the required return on equity, but which is omitted from
the particular model being estimated. If the covariance between rwacc,i,t and εi,t is not
zero then we do not get a consistent estimate of the coefficients. To some extent this is
a motivation for using fixed effects. But depending on how exactly the omitted factor
behaves, the fixed effects may not be enough.
To deal with this problem the method of instrumental variables is popular, see Roberts
and Whited (forthcoming) or Wooldridge (2010). The idea is that we need a variable z
that does not belong in the equation being estimated. There are two requirements. This
new variable must be uncorrelated with εi,t, the error term in the original equation being
estimated. In other words, it must be exogenous.
The second requirement is that z must do a good job of helping to statistically explain,
or be correlated with, rwacc. Recall the basic estimating equation,
Log(It/Kt) = α0 + α1Log(EBITDAt+1/Kt) + α2Log(rwacc,t) + εt. (5)
Then we need
Log(rwacc,t) = γ0 + γ1Log(EBITDAt+1/Kt) + γ2z + u. (6)
27
The linear projection error gives E(ut) = 0. It is critical that the coefficient on z, ie γ2 is
not zero.
The key question is thus where to get a suitable z, a variable that is correlated with
the cost of capital, but which does not belong in the investment regression given that
rwacc has been included? We have tried two ideas.
The first idea assumes that product markets are competitive. In that case the cost of
capital of other firms in the industry might serve as an instrument. The industry median
cost of capital ought to have similar factors at work to the specific firm’s cost of capital.
Thus it will likely be correlated with the firm’s cost of capital. In a competitive industry
what matters for decision making is your own cost of capital, not someone else’s. Thus
given the inclusion of the firm’s own cost of capital there is no reason for the cost of
capital of other firms to matter. The industry median does not belong in the investment
regression as a regressor. Thus we use the industry median value of a given cost of capital
measure as an instrument.
The second idea is arguably more tenuous, but seems to work well statistically. Sup-
pose that a given measure for WACC is the right measure of the cost of capital. Another
measure for WACC would then not belong in the estimating equation. However, the
second measure of WACC might well be correlated with the first measure.
This second approach is more tenuous for the following reason. Suppose that we
consider the IV in terms of an omitted variable interpretation. We would want z to be
uncorrelated with the omitted variable. But since an alternative proxy is itself also a
proxy, this assumption might well fail.
28
We report results for using WACCGGM,IBES5 and WACCGLS,IBE5 as instruments.
Both of these perform well in a variety of standard econometric tests for good instruments.
On the other hand, given their status as alternative proxy variables for WACC, there is
need for caution.
In Table IX the first stage regression results are reported. In each case main regressors
EBITDA/K and Tobin’s Q, are included along with the instrument. In all cases the F-tests
are far above the usual rule of thumb requirement of an F-statistic of at least 10. When
we have two instruments (in the second panel), the Hansen-Sargan statistic is generally
fine. The first stage results seem quite reasonable for both choices of instruments.
Table X reports the second stage results for the IV regressions. When the respective
industry medians are used as instruments the inferences do not change. We still get the
positive sign on WACCCAPM . We still get the negative sign on WACCGGM . Thus from
the perspective of the industry median instrument, it seems that measurement error in
WACC is not responsible for the findings.
When we use the two instruments from the second panel of Table IX, matters change.
Now all of the measure of WACC have a negative sign in the investment regression. Thus
from the perspective of the second panel instrumentation strategy, there was a problem
with the fixed effects regression estimates of the impact of WACCCAPM .
29
B. Decomposition of WACC
The WACC, while commonly taught, is a very specific model. It uses a number of
factors within a particular setting. It is therefore of some interest to ask whether the
elements are important only within the WACC specification.
To answer this question Table XI provides decomposition results. The components
of the respective WACC calculations are used as individual regressors in the investment
regression. It turns out that the individual components all matter. And they perform in
reasonable ways.
In addition to reporting the regression coefficients, we also report the respective elas-
ticities to provide a standardized means of comparison across factors. This is intended
to provide a partial answer to the question of whether the WACC component effects on
investment are minor when compared to the more familiar impacts of Q and cash flow.
As usual greater cash flow and greater Q are associated with higher investment. Both
of these have fairly consistent effects across columns 1 to 5. Both Q and cash flow have
investment elasticities of about 0.055. This suggests that in the current samples both
effects are about equally strong.
Higher leverage is associated with lower investment. This effect is uniformly strong
across all 5 columns. The coefficients are pretty stable. The elasticity of investment with
respect to to leverage is about -0.45. In other words changes in leverage have a much
stronger effect on investment than do either cash flow or Q. The model assumes that
30
leverage can be treated as an exogenous variable. To the extent that this assumption is
not valid, neither will the be the interpretation of the elasticity.
Higher cost of debt has a uniformly negative effect on investment. This effect is
statistically significant. But the elasticity is only about -0.005. So a fairly big interest
rate change would be needed to have much of an effect on corporate investment.
Higher top corporate tax rate is associated with more investment. Within the WACC
context this is supposed to reflect the role of tax shielding. When the tax rate is increased,
the effective cost of debt is reduced, making investment more attractive. Clearly taxes can
have other effects as well – particularly on the corporate cash flows. But it is interesting
to see the hypothesized WACC mechanism show up empirically.
The impact of an increase in tax requires a bit of care. The model is conditional on Q
and cash flow. In other words it is in effect assuming that cash flows are held fixed. This
rules out the impact of tax on the cash flows. Thus the current estimate might be better
interpreted as the impact of an increase in the tax shielding (benefits of tax).11
The estimated impact of the effect of the tax shielding on investment is remarkably
strong. The elasticity is estimated to be roughly 1. So a change in tax policy that
provides extra tax shields from investment is estimated to have a large effect on corporate
investment.
The inconsistent variable is once again the cost of equity. As might be expected
from the earlier tables, the CAPM and the Fama-French versions of the cost of equity
11Strictly speaking Q might fully impound the tax effect as well. If that were to happen, then thecoefficient on tax would be zero. What seems to happen in the data is that Q picks up the cash flowimpact more than it picks up the tax shielding effect. Exactly how and why this takes place deservesfurther study in its own right.
31
are positively associated with investment. The industry based CAPM and the Gordon
growth model cost of equity both have a negative sign. The elasticity of the cost of equity
is bigger than the cost of debt elasticity, but smaller than a number of the others. This
makes sense since debt is only about 30% of the financing, while equity is about 70%.
The decomposition results show that all aspects of the WACC are playing a role. None
are redundant. The fact that the leverage and the tax shielding terms come in so strongly
is interesting for future research on corporate investment.
V. Financial Constraints and the WACC
It is common to introduce financing constraints into investment regressions. Firms
are sorted into those that are ‘financially constrained’ and those that are not. Generally
it is reported that ‘financially constrained firms’ exhibit greater sensitivity of investment
to cash flow than do financially unconstrained firms even though Q has been included as
a regressor. Several different indices of financing constraints are in use. The KZ index is
from Lamont et al. (2001) and Bakke and Whited (2010). The WW index is from Whited
and Wu (2006). The SA index is from Hadlock and Pierce (2010).
From the perspective of WACC the popular KZ and WW indices are problematic.
They are composed of several elements that are basic to the WACC. The KZ index uses
cash flow, Q, leverage, dividends/K, and cash/K. The WW index uses cash flow, dividend
dummy, leverage, size, industry sales growth, firm sales growth.
32
Consider the KZ index from the standard WACC perspective cash flow and Q are
both plausible proxies for expected free cash flows. Leverage is a direct element of the
WACC. According to Frank and Goyal (2009) dividends are a reliable predictor of leverage.
Commonly cash is regarded as negative debt, and so it would belong in the leverage ratio
calculation as well. Thus all elements of the KZ index belong in the standard model of
the WACC, despite the fact that the WACC model assumes no financing constraints.
The WW index components have similar issues. Cash flow proxies for expected free
cash flow. The dividend dummy is a known predictor of leverage. Leverage is a component
of the WACC calculation. Size is another known predictor of leverage (Frank and Goyal,
2009). Both industry and firm sales growth seem to be very naturally viewed as proxies
for a firm’s expected future free cash flows.
The SA index consists of size and age both in the levels and squared. Firm size is an
established predictor of leverage. Firm age has been considered as a predictor of leverage
as well, although Frank and Goyal (2009) did not find it to be a reliable predictor in a
model that already included the other factors.
With this in mind we used each of the KZ, WW, and SA indices to separate firms
into constrained and unconstrained and reran the investment regressions in each group.
The results are extremely similar across indices, so we only report the KZ index results
in Table XII.
There is a question whether we should include firm and year fixed effects. It has been
argued that leaving out the fixed effects means that it is more likely that there is an
omitted factor causing trouble. On the other hand, it is also argued that the fixed effect
33
terms themselves can absorb the impact of the financing constraints. Table XII we report
results with both firm and year fixed effects (upper panel) and with neither (lower panel).
Table XIII the upper panel has only year fixed effect and the low panel has only firm fixed
effects.
The decision about whether to include fixed effects does matter. Start with the version
that includes both firm and year fixed effects (top panel of Table XII). The more con-
strained firms have a larger coefficient on Q than do the less constrained firms. The cash
flow coefficients are very similar in the two groups. We cannot reject the hypothesis that
the coefficients on cash flow are the same in the two groups. The coefficients on WACC
depend, as before, on the equity model. In general the constrained firms have a somewhat
stronger impact of WACC on investment when compared to the less constrained firms.
Overall the most striking fact is the stronger impact of Q among the more constrained
firms. This panel does not look like the ‘usual’ case of cash flow being relatively more
powerful than Q and more power among the constrained firms.
Next consider the pooled OLS results (lower panel of Table XII). This time the effect
of Q is about the same in the constrained and unconstrained firms. Cash flow is more
powerful that Q in the sense of having larger T statistics. Again WACC matters for both
groups of firms, and it is roughly of similar importance to Q, but less important than cash
flow. Apart form the case in which industry β is used to compute the cost of equity, the
sign on WACC is the same in the two groups.
In table XIII upper panel we have time fixed effects, but no firm fixed effects. This is
a fairly popular approach. This gives results that are more like the ‘traditional findings’.
34
Cash flow is more important than Q and it is more important for constrained firms than
it is for less constrained firms. In this setting WACC matters for both the more and the
less constrained firms. The coefficient on WACC is ‘more negative’ among the constrained
firms.
Finally in Table XIII lower panel we reverse things by including firm fixed effects but
no time fixed effects. This is less popular. In this setting Q matters more for constrained
firms than for unconstrained firms. Now cash flow is, if anything, weaker for the more
constrained firms. The WACC is again important for both groups, and a bit more negative
for the more constrained firms.
Where does this leave us? First observation. WACC matters both among the more
constrained and among the less constrained firms. In all four versions the Gordon Growth
model version of the WACC coefficient is always negative and statistically significant both
for the constrained and for the unconstrained firms. Generally WACC has a somewhat
stronger effect for the more constrained firms.12
Second observation. The ‘usual results’ seem to depend on which fixed effects you
choose to include. Inclusion of firm fixed effects really matters if we want to find that
cash flow is more important than Q. But the inclusion of firms fixed effects does not
change the conclusion that WACC matters for investment.
One way to think about the the results and the financing constraints might ‘split the
difference’. A constraint can be viewed as an extreme case of a cost. It happens when
12If the KZ index is really a reflection of WACC, then this suggests that WACC becomes more importantin decision making when it is higher. Exploring such a nonlinear impact is well beyond the scope of thecurrent paper. But it might deserve further attention in the future.
35
the cost becomes infinite. We are suggesting that the ‘financing constraints’ may really
reflect something that is a bit less extreme – ordinary high costs.13
VI. Value Creation?
Do firms that generate positive NPV have a high market value? If creating positive
NPV is a good thing, then high NPV firms ought to be worth more, and so have higher
Q.
To study this question Table XIV considers the CAPM and GGM measures of WACC.
In each case we compute the median value of the NPV created by a firm over all the
years that it is in the data. For each firm, the median NPV is calculated by using the
median EBITDA of a firm divided by the median WACC and then minus the median
of investment. In each case the firms are sorted into 5 by 5 groups basing on the NPV
quintile and the median EBITDA quintile. Within each quintile the median of firm’s
market-to-book ratio (Q) is calculated.
This basic NPV prediction is partly true. The bottom quintile does not match the
prediction. The bottom quintile firms have high value despite not creating much actual
NPV. Presumably these firms are expected to create high NPV in the future.
13A sharply different idea of a constraint would be the sort of thing that might happen in a searchmodel if the firm did not find a match. If that was the sort of thing at work, then the indicators oughtto be directly related to matching difficulties. To the best of our knowledge this has not been studied.
36
In the both panels of Table XIV, the “Total” in the sixth column is equivalent to the
one-way sort basing on NPV. Excluding the first row (lowest NPV), there is monotone
increasing relationship between the NPV and Q.
Outside of the bottom quintile high NPV firms are generally more highly valued by the
market. There is a partial departure from the general pattern for the CAPM version in
the higher EBITDA/K quintiles. For these the cells the high valuation extends beyond the
bottom NPV quintile. To some extent a similar effect is found for the highest EBITDA/K
quintile in the GGM version.
In summary, there is a U-shaped relation between the NPV and Q. This relationship
is not very sensitive to how WACC is measured. There are a significant number of firms
that have high values despite little actual NPV creation.
VII. Conclusion
In theory Q is supposed to be a sufficient statistic for the marginal incentive to invest.
But it is widely believed that the available proxies for Q are prone to error. Thus measures
that go beyond empirical Q are potentially important. This paper has examined the
impact of the Weighted Average Cost of Capital. This focus was motivated by the role
of WACC in MBA teaching as well as in practitioner answers to survey questions about
how they approach investment.
There is robust evidence that the WACC, or at least its components, have an important
impact in investment regressions that already include the usual Q and cash flow measures.
37
These extra determinants have very natural interpretations as discussed in the corporate
finance textbooks. In a sense, the scholarly literature on corporate investment can gain
from paying more attention to what we teach our students. This may not be so surprising
since our students become practitioners.
A number of specific effects are quite reliable and the impacts of leverage and corporate
tax have particularly large elasticities. Firms with higher cost of debt, and higher leverage,
invest less. In regressions that include proxies for future cash flows, firms facing a higher
tax rate invest more. The impact of the cost of equity is very sensitive to how that
cost is calculated. Seemingly equally reasonable alternative measures generate opposite
results. The WACC does a surprisingly good job of summarizing these effects. When the
component factors are aggregated into a WACC, there is some loss of information. But,
not all that much.
The investment literature has been heavily influenced by the idea that financing con-
straints are important. Popular financial constraint indices are used to sort firms con-
strained and unconstrained groups. The WACC has roughly similar impacts on investment
by both constrained and unconstrained firms.
38
VIII. Appendix 1: Q-Theory Review
Here is the standard Q-theoretic justification for an investment regression, as in Bondand Van Reenen (2007) and Cummins et al. (2006), among others. Markets are assumedto be perfectly competitive, and the firm has constant returns to scale.
Notation: Kt is capital stock at date t, It is investment at time t, βt is the discountfactor for date t, Et is the expectations operator as of time t, Vt is the value of the firmas of time t, Πt is net revenue function in period t, F () is the firm’s revenue function(F ′ > 0, F ′′ < 0), G(·, ·) is the adjustment cost function (assumed to be convex), δ is thecapital depreciation rate, λt is the shadow value of an extra unit of capital at date t, Qt
is (λt − 1), a and b are fixed parameters.The firm’s problem is given by,
Vt(Kt−1) = {maxIt
Πt(Kt, It) + βt+1EtVt+1(Kt)}
Πt(Kt) = F (Kt)−G(It, Kt)− It
The capital accumulation equation is
Kt = (1− δ)Kt−1 + It.
Optimization requires,
∂Πt
∂It= −λt
λt =∂Πt
∂Kt
+ (1− δ)βt+1Et[λt+1]
Note that λt = 11−δ
∂Vt∂Kt−1
is the shadow price on an extra unit of capital. The key featureis that it includes both the current period value and the implied effect on all future values.It is common to substitute λt+1 in repeatedly to calculate the shadow price as
λt = Et
∞∑s=0
(1− δ)sβt+s(∂Πt+s
∂Kt+s
).
From the net revenue function we have
∂Πt
∂It= −∂Gt
∂It− 1
so∂Gt
∂It= λt − 1.
The value of an extra unit of capital depends fundamentally on G, the structure of theadjustment cost function. Different adjustment cost functions might have sharply different
39
implications. From Hayashi (1982) the function G is assumed to be homogenous of degreeone in (It, Kt).
Empirical papers routinely assume that the adjustment cost function is a quadraticfunction14. The most common form (e.g. Gilchrist and Himmelberg (1995)) is
G(It, Kt) =b
2[(ItKt
)− a]2Kt.
As shown by Abel and Eberly (1994) if there are fixed transactions costs, then therecan be zones over which no investing is worth paying for, and so the linear regressionspecification will not be justified. This is usually assumed away in empirical papers. Withthis quadratic form of G, take the derivative with respect to It and then rearranging gives
ItKt
= a+1
b(λt − 1).
Or,ItKt
= a+1
bQt.
This is a simplified version of the basic derivation of the standard regression. Notice thata and b have specific interpretations in terms of the adjustment cost function. Due to thesimplicity of the structure a can also be reinterpreted as including additive errors. Thisprovides a method of interpreting the error term in the regression.
IX. Appendix 2: Data source and variable definition
The data USA firm level from 1950-2010 from the Compustat/CRSP merged file. AFP(2011) report that the typical firm uses the following proxies: leverage is a book debt toequity ratio, cost of equity is the CAPM estimated from monthly data over a 5 yearperiod, cost of debt is interest cost on outstanding debt, the tax rate is the company’sown ‘effective’ tax rate, the risk free rate is the 10-year Treasure bill rate, the equity riskpremium is about 5% or 6%.
All variables are winsorized at 1% level each tail every year
Cost of Debt Proxies
By far the most common proxy for the cost of debt is to take an historical ratio of theinterest payments to the the total debt of the firm. In the current version of the paper,we use two proxies:
14Abel and Eberly (2011) show that market power can be used as an alternative to quadratic adjustmentcost frictions.
40
• rD,INC : marginal cost of debt. It is constructed from CCMD data items: xint, dlc,dltt, dltr and dltis
xintt+1 − xintt = (dltist+1 + dlct+1) ∗ rD,INC,t+1 −xintt
dlttt + dlct∗ (dltrt+1 + dlct)
• rD,AV : average cost of debt.
rD,AV =xint
dltt+ dlc
It is well understood that this is a poor proxy since is is backwards looking. A firmcannot borrow today at the rates that it borrowed in the past. What matters today arethe current market conditions. For future work, we will also use the firm’s credit ratingto impute the rate, and the bond yield from the secondary market.
It is also possible to use a structural default adjusted method. These methods oughtto be more accurate, but they are relatively complex. We have not tried doing these.
Corporate Tax Rate
There are multiple ways to do this.
1. Actual historical average taxes paid by the firm
2. Historical top marginal tax rate
3. Use actual earnings and the tax code to impute the marginal tax cost
4. Use Graham’s model. These are simulated corporate marginal tax rates from 1980to now.
Here, we use four proxies for corporate tax rate:
• TaxSIM : pre-financing marginal tax rate simulated by Graham and Mills (2008).The webpage: (webpage).
• TaxOLS: OLS regression predicted pre-financing marginal tax rate by Graham andMills (2008) Table IV.
TaxOLS = 0.135 + 0.601*BookSimMTR – 0.028*USBookLossDummy –0.020*LowUSETR-Dummy –0.008*NOLDummy –0.016*BookLossDummy + 0.006*ForeignActivityDummy;
Variable definition:
1. USBookLossDummy =1 if Compustat #272 (or, #170 if #272 missing) ¡ 0, zerootherwise.
41
2. LowUSETRDummy = 1 if #63/#272 (or, #16/#170 if missing) ¡ 10 percent, zerootherwise.
3. NOLDummy =1 if #52 ¿ 0, zero otherwise.
4. BookLossDummy = 1 if nonmissing #170 ¡ 0, zero otherwise.
5. ForeignActivityDummy = 1 if —#273/#170— ¿ 5 percent, zero otherwise.
6. BookSimMTR = 0.345 –0.055*LowUSETRDummy–0.016*NOLDummy–0.103*BookLossDummy+ 0.026*ForeignActivityDummy
• TaxTop: top marginal tax rate in the corporation income tax brackets (1909-2002)(click here)
• TaxAV : corporate average tax rate. CCMD data item txt/pi, where txt is the totaltaxes and pi is the pretax income. Replace this rate by missing value if it is negativeor larger than 100% before winsorizing
Leverage
There are two natural candidate leverage ratios.Firm average value. For a given date we can multiply the number of shares by the
market value of share at that date to get Et. To get Dt it is common to simply use thebook value of debt.
Industry median. In the WACC calculation, the leverage ratio should be a long runtarget. The industry median could be one proxy for this target ratio.
Here we use five versions of leverage ratio (CCMD data items in the brackets):
• LevBK : annual realized firm leverage using book value of equity and book valueof debt. Book value of debt = Debt in Current Liabilities(dlc)+Long-Term Debt(dltt). Book value of equity followsDavis et al. (2000).
– book value of equity=stockholder equity (seq) +balance sheet deferredtaxes(txdb)+balance investment tax credit (itcb)-book value of preferred stock
– book value of preferred stock=in order: redemption(pstkrv), liquidation(pstkl),or par value(pstk) of preferred stock
– if stockholder equity (seq) is not available
∗ stockholder equity=book value of common equity(ceq)+par value of pre-ferred stock(pstk), or
∗ stockholder equity=book value of total assets(at)- book value of total lia-bility (lt)
• LevMKT : annual realized firm leverage using market value of equity and book valueof debt. Market value of equity=Shares Outstanding(shrout)* Price
42
• LevMKT,Net: annual realized firm leverage using market value of equity and bookvalue of debt net of cash holding. Book value of debt net of cash holding=Bookvalue of debt- cash holding (ch)
• LevWT : (LevIND+LevMKT )/2 where LevIND is the median leverage using LevMKT
of firms in the same industry every year. Industry definition follows Fama-French48-industry
• LevMKT,TGT : predicted leverage ratio following Frank and Goyal (2009) Table Vcolumn 9.
Cost of Equity Proxies
Stock Return/CAPM-Based Proxies
• rE,CAPM : cost of equity using CAPM model.
rE,CAPM = rf + βE(rM − rf )
The risk free rate rf is 10-year Treasury yield from FRED. To estimate firmβ, we run rolling window regressions using previous five years monthly stock re-turns. The dependent variable is the excess stock return (stock return from CRSP- risk free rate in Fama-French market excess return factor) and the indepen-dent variable is the Fama-French market excess return (from French’s webpage:http://mba.tuck.dartmouth.edu/pages/faculty/ken.french/ftp/F-F Research Data Factors.zip).E(rM − rf ) is the historical mean of the Fama-French market excess return, i.e. thedate t equity premium is the average of Fama-French market excess return fromtime t to the time 1.
• rE,CAPM,IND: the same as rE,CAPM except using the industry beta instead of firmbeta. We first calculate the firm asset beta as firm beta*market value of eq-uity/(market value of equity+book value of debt). Then we calculate the the medianof asset beta of each industry every year. The industry definition follows Fama-French 48-industry. Industry beta=median industry asset beta*(market value ofequity+book value of debt)/market value of equity
• rE,FF3: cost of equity using Fama-French 3-factor model. The calculation is similarto rE,CAPM but use two additional factors (small-big factor, high-low factor) fromFrench’s webpage.
• rE,FF4: cost of equity using Fama-French 3-factor model +momentum factor.Thecalculation is similar to rE,CAPM . The monthly momentum factor is from CRSP.
43
Accounting-Based Proxies
• rE,GGM,IBES,G: Gordon Growth Model (GGM) with IBES-based earnings per shareforecast. The earnings forecast of IBES ranges from one to five years, and a longterm growth rate is also provided for some firms. We use the median of earningsforecast for the first several years (when data is available), and then assume that thefirm will grow at the long term growth rate (when available; if not, then skip thisstep ) for the next five years, and then the firm will grow at some constant growthrate forever. The constant rate we use here is the risk free rate in Fama-Frenchmarket excess return factor. The payout ratio is assumed to be 60% constant. TherE,GGM,IBES,G is numerically solved such that stock price is equal to the sum ofdiscounted future cash flows, where the discount rate is rE,GGM,IBES,G and cashflows are the future payouts.
• rE,GGM,IBES1: GGM with T=1 and IBES-based earnings per share forecast.
• rE,GGM,IBES5: GGM with T=5 and IBES-based earnings per share forecast
To calculate the above two measures, we follow Lee et al. (2010)T=1:
Pt =EPSt+1
rE,GGM,IBES1
T=5:
Pt =4∑i=1
DPSt+i(1 + rE,GGM,IBES5)i
+EPSt+5
re(1 + rE,GGM,IBES5)4
DPSt+1 = EPSt+1 × κ
where dividend payout ratio: κ follows Hou et al. (2010) and Gebhardt et al. (2001): ifearnings are positive, κ is the current dividends divided by current earnings; if earningsare negative, κ is the current dividends divided by 0.06× total assets.
• rE,GLS,IBES: Residual Income Model (GLS) with IBES-based earnings per shareforecast.
We follow Gebhardt et al. (2001)and Hou et al. (2010)
Mt = Bt +11∑i=1
Et[(ROEt+i − re)×Bt+i−1]
(1 + rE,GLS,IBES)i+
Et[(ROEt+12 − re)×Bt+11]
rE,GLS,IBES(1 + rE,GLS,IBES)11
where Mt is the market value of equity, Bt is the book value of equity (defined above) and
Bt+i = Bt+i−1 + Et+i(1− κ)
where Bt and κ are defined the same as before.
44
Return on equity ROEt+i =
• from year one to year three: Et+i
Bt+i−1
• through year four to year twelve: interpolated value between ROEt+3 andindustrial median at time t; industrial median excludes firms with negativeearnings
• rE,GGM,HDZ1: GGM with T=1 and model-based forecast.
• rE,GGM,HDZ5 or simply rE,GGM : GGM with T=5 and model-based forecast.
• rE,GLS,HDZ or simply rE,GLS: GLS with model-based forecast.
For the three measures above, instead of using IBES-based forecast, we use the modelpredicted earnings. Recently Hou et al. (2010), and Lee et al. (2010) have found a fairlysimple model to predict earnings that seems to do rather well, and so we use that as well.
Let EVj,t denote the enterprize value of firm j in year t, TA is total assets, DIV isthe value of dividends paid, DD is a dummy for paying dividends, Ej,t is earnings (beforeextraordinary items) by firm j in year t, NegE is a dummy for negative earnings, ACCis total accruals divided by total assets. The model is
Ej,t+∆t = α0+α1EVj,t+α2TAj,t+α3DIVj,t+α4DDj,t+α5Ej,t+α6NegEj,t+α7ACCj,t+εj,t+∆t.
Both papers estimate this model using pooled cross-section regressions using a rollingprior ten years of data for each year. For comparability we do the same.∆t ranges from1 to 5.
• regression items in Hou et al. (2010) :
– E: net income or earnings before extraordinary items (ib)
– EV : total asset (at)+market value of equity-book value of equity
– DIV : dividend payment(dvt)
– TA: total asset (at)
– ACC: change in current assets (act)+ change in debt in current liability(dlc)-change in cash and short term investment(che)-change in current liabilities(lct),then scaled by total asset (at)
WACC
We have 11 measures on cost of equity, 4 measures on tax rate, 2 measures on costof debt and 3 measures on leverage ratio. In total, we have 264 different WACCs. The 5WACCs reported in the paper are constructed by the following way:
45
• waccCAPM = rE,CAPM × (1− LevWT ) + rD,INC × LevWT × (1− TaxTop)
• waccCAPM,IND = rE,CAPM,IND × (1− LevWT ) + rD,INC × LevWT × (1− TaxTop)
• waccFF4 = rE,FF4 × (1− LevWT ) + rD,INC × LevWT × (1− TaxTop)
• waccGGM = rE,GGM × (1− LevWT ) + rD,INC × LevWT × (1− TaxTop)
• waccGLS = rE,GLS × (1− LevWT ) + rD,INC × LevWT × (1− TaxTop)
In addition
• waccAFP = rE,CAPM × (1− LevBK) + rD,AV × LevBK × (1− TaxAV )
Free Cash Flow Proxies
Here are the cash flow proxies we use:
• Q: market value firm assets divided by ppegt
• EBITDA/K: CCMD data item ebitda divided by ppegt.
• FCF/K: CCMD data item (ebitda − dp) × (1 − taxrate) + dp − 4nwc where4nwct = (actt − lctt − cht)− (actt−1 − lctt−1 − cht−1)
Investment
• I/K : CCMD data items capx/ppegt
Financial Constraint
Three popular indices that gauge the extent of financial constraint are employed:
1. SA index. Following Hadlock and Pierce (2010), the SA index = −0.737 ∗ Size +0.043 ∗ Size2 − 0.040 ∗ Age where Size is the log of inflation adjusted (to 2004)book assets, and age is the number of years the firm has been on Compustat. Incalculating this index, Size is replaced with log($4.5 billion) and age with thirty-seven years if the actual values exceed these thresholds.
2. KZ index. Following Lamont et al. (2001), KZ index= -1.001909* [(Item 18 +Item 14)/ 8] +.2826389* [(Item 6 + CRSP Market Equity - Item 60 -Item 74)/Item 6] +3.139193* [(Item 9+Item 34) / (Item 9+Item 34 + Item 216)] -39.3678*[(Item 21 + Item 19)/Item 8] -1.314759* [Item 1/Item 8]. Item numbers refer toCOMPUSTAT annual data items described above. Data item 8 is lagged.
46
3. WW index. Following Whited and Wu (2006),WW index= 0.091*CF-0.062*DIVPOS+0.021*TLTD-0.044*LNTA+0.102*ISG-0.035*SG where CF=[(Item 18 + Item14)/ 8]; DIVPOS=1 if item127¿0;TLTD=[(Item 9+Item 34) / (Item 9+Item 34 +Item 216)] ; LNTA=log(item6); ISG is the firm’s three-digit industry sales growth;SG is the firm’s sales growth. Item numbers refer to COMPUSTAT annual dataitems described above. Data item 8 is lagged.
Data cleaning
In order:
• the variables constructed from Compustat/CRSP Merged Dataset (CCMD) werewinsorized at 1% level on each tail each year.
• drop the industry code 31(utility), 44(bank), 45(insurance), 46(real estate), 47(trad-ing) and 0 (not listed in Fama French 48 industries)
• keep the US firms (FIC code = USA)
• drop the firms without any measures on rE, or any measures on rD, or any measureson tax rate, or any measures on leverage
• every year drop the firms in bottom deciles of market size
47
Table I
Descriptive Statistics
This table presents the descriptive statistics of the main variables in the paper. The sample is all the U.S.
publicly traded firms from 1960 to 2010, excluding firms with industry code 31(utility), 44(bank), 45(in-
surance), 46(real estate), and 47(trading). The industry classification follows Fama-French 48 industries.
Variable definitions and construction are provided in the Appendix 3. The annual accounting data is from
CRSP-Compustat merged dateset; the monthly stock return data is from CRSP; the earnings forecast
data is from I/B/E/S. Variables are winsorized at 1% level in both tails of the distribution each year. The
small firms (bottom decile by market size every year) are also excluded. We construct 11 measures on
cost of equity rE , 2 measures on cost of debt rD, 5 measures on the leverage ratio Lev and 4 measures on
taxes Tax. In total, we have 440 different measures on WACCs. waccCAPM is computed using rE,CAPM ,
LevWT , rD,INC , TaxTop; waccGGM is computed using rE,GGM , LevWT , rD,INC , TaxTop;
count mean median std.dev. skewness
I/K 112909 0.144 0.111 0.117 2.042Q 113368 5.184 2.035 11.426 7.161C/K 96481 0.339 0.068 1.013 7.949EBITDA/K 114201 0.220 0.228 0.843 -3.847FCF/K 111659 0.111 0.139 0.694 -3.592rE,CAPM 79133 0.166 0.165 0.057 0.148rE,IND 114381 0.177 0.159 0.087 4.546rE,FF3 79133 0.193 0.189 0.082 0.351rE,FF4 79133 0.181 0.177 0.100 0.084rE,GGM,IBES5g 47929 0.113 0.104 0.049 1.099rE,GGM,HDZ1 63450 0.099 0.072 0.089 2.220rE,GGM 73173 0.120 0.091 0.096 1.887rE,GLS 66673 0.123 0.117 0.063 1.206rE,GGM,IBES1 40870 0.051 0.039 0.047 1.976rE,GGM,IBES5 29865 0.070 0.063 0.047 1.535rE,GLS,IBES 33894 0.098 0.092 0.056 1.496rD,INC 99501 0.219 0.092 0.604 6.321rD,AV 115490 0.114 0.085 0.138 6.013LevWT 114381 0.266 0.243 0.164 0.530LevMKT 114381 0.296 0.243 0.241 0.714LevBK 107987 0.367 0.336 0.263 0.912LevMKT,TGT 111785 0.289 0.288 0.113 0.158LevMKT,Net 95448 0.267 0.205 0.252 0.769TaxSIM 63960 0.318 0.350 0.126 -1.207TaxOLS 115661 0.319 0.364 0.065 -1.176TaxTop 100527 0.413 0.460 0.065 0.076TaxAV 105617 0.334 0.380 0.164 -0.880GIBES 52011 12.019 12.000 11.034 1.501waccCAPM 62578 0.150 0.139 0.084 7.007waccGGM 59281 0.112 0.091 0.093 5.361
no. of firms 12083 avg. firm-year 9.6
48
Tab
leII
:M
ain
Cor
rela
tion
sT
his
tab
lep
rese
nts
the
corr
elat
ion
coeffi
cien
tm
atr
ixof
main
vari
ab
les
wh
ich
are
use
din
the
regre
ssio
ns.
Th
esa
mp
leis
all
the
U.S
.p
ub
licl
ytr
aded
firm
sfr
om19
60to
2010
,ex
clu
din
gfirm
sw
ith
ind
ust
ryco
de
31(u
tili
ty),
44(b
an
k),
45(i
nsu
ran
ce),
46(r
eal
esta
te),
an
d47(t
rad
ing).
Th
ein
du
stry
clas
sifi
cati
onfo
llow
sF
ama-
Fre
nch
48in
du
stri
es.
Vari
ab
led
efin
itio
ns
an
dco
nst
ruct
ion
are
pro
vid
edin
the
App
end
ix3.
Vari
ab
les
are
win
sori
zed
at1%
level
inb
oth
tail
sof
the
dis
trib
uti
on
each
year.
Th
e5
mea
sure
son
cost
of
equ
ity
are
base
don
CA
PM
(rE,C
APM
),C
AP
Mw
ith
ind
ust
rym
edia
nβ
(rE,IN
D),
Fam
a-F
ren
ch-C
arh
art
4-f
act
or
(rE,F
F4),
GG
M(r
E,G
GM
)an
dG
LS
(rE,G
LS
).T
he
two
tax
rate
sare
top
stat
uto
ryfe
der
alco
rpor
ate
inco
me
tax
rate
(TaxTop)
an
dav
erage
rate
(TaxAV
)fr
om
firm
fin
an
cial
rep
ort
.T
he
leve
rage
rati
os
are
book
leve
rage
(Lev
BK
)an
dfi
rm-i
nd
ust
ryw
eigh
ted
lever
age
(Lev
WT
).B
othwacc
GGM
an
dwacc
CAPM
use
the
sam
eta
xra
te(TaxTop),
cost
of
deb
t(r
D,IN
C)
and
lever
age
(Lev
WT
).wacc
CAPM
use
sr E
,CAPM
wh
ilewacc
GGM
use
sr E
,GGM
asth
eco
stof
equ
ity.
To
save
space
,E/K
isth
eEBITDA/K
.*s
ign
ifica
nt
at5%
leve
l.**
sign
ifica
nt
at
1%
leve
l.
(1)
(2)
(3)
(4)
(5)
(6)
(7)
(8)
(9)
(10)
(11)
(12)
(13)
(14)
(15)
I/K
1.00
Q0.
24∗∗
1.00
E/K
0.02∗∗
-0.1
7∗∗
1.00
r E,C
APM
0.15∗∗
0.00
-0.0
5∗∗
1.00
r E,IN
D-0
.08∗∗
-0.0
8∗∗
-0.0
2∗∗
0.30∗∗
1.0
0r E
,FF4
0.08∗∗
-0.0
6∗∗
0.02∗∗
0.40∗∗
0.1
7∗∗
1.0
0r E
,GGM
-0.1
2∗∗
-0.1
3∗∗
-0.0
2∗∗
0.10∗∗
0.3
8∗∗
0.1
4∗∗
1.0
0r E
,GLS
0.03∗∗
0.10∗∗
-0.1
5∗∗
0.17∗∗
0.2
0∗∗
0.1
0∗∗
0.5
4∗∗
1.0
0r D
,IN
C0.
01∗∗
0.08∗∗
-0.0
3∗∗
0.01
-0.0
4∗∗
-0.0
2∗∗
-0.0
4∗∗
0.0
1∗1.
00
TaxTop
0.02∗∗
-0.1
6∗∗
0.09∗∗
0.38∗∗
0.2
1∗∗
0.2
0∗∗
0.3
4∗∗
0.2
2∗∗
-0.0
9∗∗
1.0
0TaxAV
-0.0
3∗∗
-0.2
2∗∗
0.34∗∗
0.05∗∗
-0.0
2∗∗
0.0
7∗∗
0.0
8∗∗
-0.1
1∗∗
-0.0
7∗∗
0.3
5∗∗
1.0
0Lev
WT
-0.2
3∗∗
-0.2
6∗∗
0.06∗∗
0.07∗∗
0.5
0∗∗
0.1
5∗∗
0.4
4∗∗
0.1
3∗∗
-0.1
1∗∗
0.1
9∗∗
0.1
2∗∗
1.0
0Lev
BK
-0.1
4∗∗
-0.0
9∗∗
-0.0
1∗
0.03∗∗
0.4
4∗∗
0.0
7∗∗
0.1
7∗∗
0.2
3∗∗
-0.1
1∗∗
-0.0
3∗∗
-0.1
2∗∗
0.6
4∗∗
1.0
0wacc
CAPM
0.09∗∗
0.05∗∗
-0.0
00.
44∗∗
0.0
3∗∗
0.1
5∗∗
-0.0
6∗∗
0.0
5∗∗
0.69∗∗
0.0
7∗∗
-0.0
1-0
.15∗∗
-0.1
1∗∗
1.0
0wacc
GGM
-0.0
9∗∗
-0.0
7∗∗
-0.0
10.
05∗∗
0.1
8∗∗
0.0
9∗∗
0.6
1∗∗
0.3
8∗∗
0.57∗∗
0.1
5∗∗
0.0
4∗∗
0.2
0∗∗
0.0
5∗∗
0.6
4∗∗
1.0
0∗p<
0.0
5,∗∗p<
0.01
49
Table III
I/K: Two-way sorts
The four panels in this table report the two-way sorts results of I/K. The variable definitions are providedin the Appendix. We sort the firms into 5×5 groups by one WACC measure (waccCAPM or waccGGM )and one control variable (EBITDA/K or Q). The median of I/K in each group is reported. High-Lowmeasures the mean differences between ”High” group and ”Low” group in each row/column. Assumingthat the two groups have different variance, we test whether the differences are significant. *significantat 5% level. **significant at 1 % level.
EBITDA/KwaccCAPM 1(Low) 2 3 4 5(High) Total High-Low
1 (Low) 0.058 0.076 0.089 0.099 0.117 0.085 0.057∗∗
2 0.064 0.084 0.099 0.111 0.130 0.097 0.057∗∗
3 0.073 0.088 0.107 0.116 0.138 0.106 0.053∗∗
4 0.074 0.092 0.112 0.127 0.145 0.114 0.058∗∗
5 (High) 0.092 0.096 0.118 0.137 0.164 0.124 0.058∗∗
Total 0.071 0.086 0.104 0.119 0.141 0.104 0.038∗∗
High-Low 0.042∗∗ 0.030∗∗ 0.036∗∗ 0.042∗∗ 0.043∗∗ 0.045∗∗
EBITDA/KwaccGGM 1(Low) 2 3 4 5(High) Total High-Low
1 (Low) 0.098 0.100 0.117 0.133 0.160 0.125 0.047∗∗
2 0.081 0.089 0.107 0.120 0.150 0.109 0.055∗∗
3 0.070 0.089 0.110 0.124 0.139 0.108 0.062∗∗
4 0.067 0.086 0.103 0.117 0.139 0.103 0.063∗∗
5 (High) 0.065 0.075 0.093 0.110 0.130 0.095 0.057∗∗
Total 0.076 0.088 0.106 0.121 0.144 0.107 0.038∗∗
High-Low -0.042∗∗ -0.026∗∗ -0.030∗∗ -0.028∗∗ -0.031∗∗ -0.034∗∗
QwaccCAPM 1(Low) 2 3 4 5(High) Total High-Low
1 (Low) 0.072 0.081 0.088 0.098 0.124 0.085 0.071∗∗
2 0.081 0.095 0.102 0.113 0.134 0.097 0.070∗∗
3 0.088 0.102 0.109 0.120 0.143 0.106 0.064∗∗
4 0.086 0.108 0.116 0.131 0.148 0.114 0.081∗∗
5 (High) 0.085 0.106 0.123 0.143 0.168 0.124 0.099∗∗
Total 0.081 0.098 0.108 0.123 0.146 0.104 0.105∗∗
High-Low 0.014∗∗ 0.027∗∗ 0.040∗∗ 0.047∗∗ 0.042∗∗ 0.045∗∗
QwaccGGM 1(Low) 2 3 4 5(High) Total High-Low
1 (Low) 0.082 0.108 0.115 0.135 0.160 0.125 0.088∗∗
2 0.085 0.099 0.111 0.126 0.155 0.109 0.081∗∗
3 0.087 0.104 0.114 0.125 0.150 0.108 0.081∗∗
4 0.085 0.102 0.110 0.125 0.144 0.103 0.087∗∗
5 (High) 0.076 0.092 0.105 0.117 0.132 0.095 0.078∗∗
Total 0.083 0.100 0.111 0.127 0.152 0.108 0.105∗∗
High-Low -0.010∗∗ -0.020∗∗ -0.010∗∗ -0.020∗∗ -0.020∗∗ -0.034∗∗
∗ p < 0.05, ∗∗ p < 0.0150
Table IV
Fixed Effect Panel Regressions
This table reports the estimates from the fixed effect panel regressions. The sample is all the U.S. publiclytraded firms from 1960 to 2010, excluding firms with industry code 31(utility), 44(bank), 45(insurance),46(real estate), and 47(trading). The industry classification follows Fama-French 48 industries. Variabledefinitions and construction are provided in the Appendix 3. Variables are winsorized at 1% level in bothtails of the distribution each year. The model we estimate is
Log(Ii,t/Ki,t) = α0 + α1Log(Qi,t−1) + α2Log(EBITDAi,t/Ki,t) + α3Log(wacci,t−1)
+α4(g/wacci,t−1) +∑i
firmi +∑t
yeart + εi,t.
The panel fixed effect estimator is used (first difference in firms) and year fixed effects are included. Thestandard errors are clustered at the firm level. Columns (1) to (5) contain the estimates for five differentWACC’s, all of which use the same tax rate (TaxTop), cost of debt (rD,INC) and leverage (LevWT ). Thedifference is the choice of cost of equity (rE). We suppress the subscripts indicating the choice of rE inwacc, and report them in the top row under the column number. The five measures on cost of equity arerE,CAPM (CAPM), rE,IND (IND), rE,FF4 (FF4), rE,GGM (GGM) and rE,GLS (GLS). The elasticitiesbetween the independent variables and investment are calculated, their standard errors are calculatedusing Delta-method and the z-values are in the parathesis. *significant at 5% level. **significant at 1 %level.
(1) (2) (3) (4) (5)CAPM IND FF4 GGM GLS
log(Q) 0.205∗∗ 0.215∗∗ 0.205∗∗ 0.193∗∗ 0.197∗∗
(21.54) (25.05) (21.20) (19.56) (19.02)elasticity 0.070∗∗ 0.080 0.070∗∗ 0.070∗∗ 0.075∗∗
(6.29) (1.65) (21.47) (3.75) (5.52)
log(EBITDA/K) 0.156∗∗ 0.155∗∗ 0.154∗∗ 0.162∗∗ 0.167∗∗
(22.37) (25.50) (21.92) (23.89) (23.07)elasticity 0.050 0.034∗ 0.043∗∗ 0.057 0.053
(0.49) (2.50) (7.72) (1.65) (1.57)
log(wacc) 0.040∗∗ -0.150∗∗ 0.045∗∗ -0.082∗∗ -0.024∗∗
(4.79) (-16.63) (7.27) (-13.10) (-3.96)elasticity 0.015∗∗ -0.091 0.038∗∗ -0.052∗∗ -0.015∗∗
(2.67) (-0.03) (8.70) (-3.37) (-3.39)
g/wacc 0.000 -0.017∗∗ 0.000 -0.001 -0.001(0.74) (-3.20) (0.30) (-0.94) (-1.39)
Yr and Firm Yes Yes Yes Yes YesN 56332 75049 55492 53630 50120No. of firms 5980 8372 5893 6460 6246average years 9.4 9.0 9.4 8.3 8.0within R2 0.157 0.161 0.157 0.170 0.163overall R2 0.146 0.142 0.145 0.167 0.157between R2 0.124 0.126 0.122 0.167 0.144
t statistics in parentheses∗ p < 0.05, ∗∗ p < 0.01
51
Tab
leV
:A
llW
AC
C’s
(Par
tI)
Tab
leV
and
VI
rep
ort
the
coeffi
cien
tson
WA
CC
’sfr
om
the
fixed
effec
tp
an
elre
gre
ssio
ns.
Th
esa
mp
leis
all
the
U.S
.p
ub
licl
ytr
ad
edfi
rms
from
1960
to20
10,
excl
ud
ing
firm
sw
ith
ind
ust
ryco
de
31(u
tili
ty),
44(b
an
k),
45(i
nsu
ran
ce),
46(r
eal
esta
te),
an
d47(t
rad
ing).
Th
ein
du
stry
clas
sifi
cati
onfo
llow
sF
ama-
Fre
nch
48in
du
stri
es.
Vari
ab
led
efin
itio
ns
an
dco
nst
ruct
ion
are
pro
vid
edin
the
Ap
pen
dix
3.
Vari
ab
les
are
win
sori
zed
at1%
leve
lin
bot
hta
ils
ofth
ed
istr
ibu
tion
each
year.
Th
em
od
elw
ees
tim
ate
is
Log
(Ii,t/K
i,t)
=α0
+α1Log
(Qi,t−
1)
+α2Log
(EBITDA
i,t/K
i,t)
+α3Log
(wacc
i,t−
1)
+α4(g/wacc
i,t−
1)
+∑ i
firm
i+∑ t
year t
+ε i
,t.
Th
eF
Ees
tim
ator
isuse
d(fi
rst
diff
eren
cein
firm
s)an
dye
ar
fixed
effec
tsare
incl
ud
ed.
Th
est
an
dard
erro
rsare
clu
ster
edat
the
firm
leve
l.E
ach
WA
CC
has
fou
rco
mp
onen
ts:
tax
rate
,le
vera
ge,
cost
of
deb
tan
dco
stof
equ
ity.
We
hav
e11
mea
sure
son
cost
of
equ
ity,
2m
easu
res
on
cost
of
deb
t,5
mea
sure
son
leve
rage
and
4m
easu
res
onta
xra
tes.
Th
eco
effici
ents
of
those
440
WA
CC
’s,
calc
ula
ted
by
the
com
pon
ents
inro
ws
an
dco
lum
ns,
are
rep
orte
d.
*sig
nifi
cant
at5%
leve
l.**si
gn
ifica
nt
at
1%
leve
l.
TaxSIM
Lev
BK
Lev
MK
TLev
WT
Lev
MK
T,N
et
Lev
MK
T,T
GT
r D,IN
Cr D
,AV
r D,IN
Cr D
,AV
r D,IN
Cr D
,AV
r D,IN
Cr D
,AV
r D,IN
Cr D
,AV
r E,C
APM
0.00
30.
181
**0.0
23**
0.1
94**
0.0
07
0.1
08**
0.0
24**
0.2
19**
-0.0
12
0.0
25
r E,F
F3
0.00
90.
074
**0.0
25**
0.0
91**
0.0
04
0.0
46**
0.0
26**
0.0
76**
-0.0
15*
-0.0
05
r E,F
F4
0.02
3**
0.069
**0.0
35**
0.0
86**
0.0
29**
0.0
61**
0.0
33**
0.0
73**
0.0
13*
0.0
31**
r E,G
GM
,IBES5g
-0.0
22**
0.10
6**
-0.0
07
0.3
48**
-0.0
16*
0.1
65**
-0.0
01
0.3
17**
-0.0
31**
0.0
21
r E,G
GM
,HDZ1
-0.0
48**
-0.0
96**
-0.0
58**
-0.0
76**
-0.0
54**
-0.0
79**
-0.0
53**
-0.0
60**
-0.0
44**
-0.0
75**
r E,G
GM
-0.0
67**
-0.1
59**
-0.0
84**
-0.1
18**
-0.0
91**
-0.1
64**
-0.0
78**
-0.1
13**
-0.0
75**
-0.1
57**
r E,G
LS
-0.0
25**
-0.0
03-0
.030**
0.0
53**
-0.0
33**
0.0
09
-0.0
28**
0.0
50**
-0.0
36**
-0.0
30
r E,G
GM
,IBES1
-0.0
64**
-0.1
63**
-0.0
82**
-0.1
31**
-0.0
69**
-0.1
26**
-0.0
81**
-0.1
17**
-0.0
58**
-0.1
09**
r E,G
GM
,IBES5
-0.0
59**
-0.1
43**
-0.0
75**
-0.0
84**
-0.0
70**
-0.1
19**
-0.0
80**
-0.0
73**
-0.0
61**
-0.1
30**
r E,G
LS,IBES
-0.0
51**
-0.0
32*
-0.0
57**
0.0
10
-0.0
61**
-0.0
37
-0.0
51**
0.0
10
-0.0
53**
-0.0
74**
r E,IN
D-0
.044
**-0
.047
*-0
.040**
0.4
09**
-0.1
24**
-0.7
91**
-0.0
53**
0.2
32*
-0.1
14**
-0.5
51**
TaxOLS
Lev
BK
Lev
MK
TLev
WT
Lev
MK
T,N
et
Lev
MK
T,T
GT
r D,IN
Cr D
,AV
r D,IN
Cr D
,AV
r D,IN
Cr D
,AV
r D,IN
Cr D
,AV
r D,IN
Cr D
,AV
r E,C
APM
-0.0
000.
148*
*0.0
27**
0.1
91**
0.0
07
0.1
01**
0.0
20**
0.2
14**
-0.0
12*
0.0
14
r E,F
F3
0.00
70.
071
**0.0
29**
0.1
02**
0.0
04
0.0
42**
0.0
25**
0.0
94**
-0.0
19**
-0.0
11
r E,F
F4
0.02
2**
0.076
**0.0
39**
0.0
90**
0.0
28**
0.0
67**
0.0
31**
0.0
75**
0.0
11*
0.0
35**
r E,G
GM
,IBES5g
-0.0
19**
0.08
5**
-0.0
14*
0.3
07**
-0.0
17*
0.1
31**
-0.0
08
0.2
94**
-0.0
30**
-0.0
14
r E,G
GM
,HDZ1
-0.0
52**
-0.0
84**
-0.0
56**
-0.0
53**
-0.0
59**
-0.0
76**
-0.0
61**
-0.0
46**
-0.0
47**
-0.0
87**
r E,G
GM
-0.0
69**
-0.1
49**
-0.0
79**
-0.0
84**
-0.0
85**
-0.1
57**
-0.0
81**
-0.1
00**
-0.0
79**
-0.1
72**
r E,G
LS
-0.0
31**
-0.0
26**
-0.0
28**
0.0
65**
-0.0
37**
0.0
01
-0.0
33**
0.0
53**
-0.0
39**
-0.0
53**
r E,G
GM
,IBES1
-0.0
67**
-0.1
78**
-0.0
82**
-0.1
43**
-0.0
69**
-0.1
37**
-0.0
81**
-0.1
25**
-0.0
58**
-0.1
21**
r E,G
GM
,IBES5
-0.0
62**
-0.1
57**
-0.0
75**
-0.0
89**
-0.0
68**
-0.1
20**
-0.0
80**
-0.0
75**
-0.0
58**
-0.1
32**
r E,G
LS,IBES
-0.0
53**
-0.0
72**
-0.0
58**
-0.0
30
-0.0
57**
-0.0
65**
-0.0
50**
-0.0
18
-0.0
56**
-0.0
93**
r E,IN
D-0
.065
**-0
.108
**-0
.057**
0.3
06**
-0.1
33**
-0.9
53**
-0.0
63**
0.1
24
-0.1
42**
-0.6
73**
∗p<
0.05
,∗∗p<
0.01
52
Tab
leV
I:A
llW
AC
C’s
(Par
tII
)
TaxTop
Lev
BK
Lev
MK
TLev
WT
Lev
MK
T,N
et
Lev
MK
T,T
GT
r D,IN
Cr D
,AV
r D,IN
Cr D
,AV
r D,IN
Cr D
,AV
r D,IN
Cr D
,AV
r D,IN
Cr D
,AV
r E,C
APM
0.03
1**
0.199
**0.0
73**
0.2
98**
0.0
40**
0.2
02**
0.0
64**
0.3
32**
0.0
09
0.0
81**
r E,F
F3
0.03
0**
0.102
**0.0
63**
0.1
53**
0.0
26**
0.0
76**
0.0
55**
0.1
19**
-0.0
04
0.0
10
r E,F
F4
0.04
3**
0.098
**0.0
62**
0.1
15**
0.0
45**
0.0
81**
0.0
53**
0.0
98**
0.0
25**
0.0
49**
r E,G
GM
,IBES5g
-0.0
17*
0.14
9**
0.0
08
0.4
26**
-0.0
05
0.2
45**
0.0
17
0.4
09**
-0.0
18*
0.0
76
r E,G
GM
,HDZ1
-0.0
44**
-0.0
49**
-0.0
44**
-0.0
00
-0.0
49**
-0.0
45**
-0.0
43**
0.0
02
-0.0
44**
-0.0
71**
r E,G
GM
-0.0
65**
-0.1
18**
-0.0
70**
-0.0
21
-0.0
82**
-0.1
29**
-0.0
65**
-0.0
46**
-0.0
82**
-0.1
67**
r E,G
LS
-0.0
15*
0.04
1**
-0.0
09
0.1
67**
-0.0
24**
0.0
71**
-0.0
09
0.1
45**
-0.0
31**
-0.0
11
r E,G
GM
,IBES1
-0.0
72**
-0.1
69**
-0.0
90**
-0.1
52**
-0.0
73**
-0.1
45**
-0.0
88**
-0.1
39**
-0.0
58**
-0.1
27**
r E,G
GM
,IBES5
-0.0
63**
-0.1
46**
-0.0
80**
-0.0
99**
-0.0
76**
-0.1
47**
-0.0
83**
-0.0
88**
-0.0
62**
-0.1
69**
r E,G
LS,IBES
-0.0
61**
-0.0
76**
-0.0
57**
0.0
02
-0.0
68**
-0.0
48
-0.0
60**
-0.0
03
-0.0
64**
-0.0
84**
r E,IN
D-0
.052
**-0
.042
*-0
.018*
1.1
55**
-0.1
50**
-0.8
41**
-0.0
32**
1.0
26**
-0.1
55**
-0.6
75**
TaxAV
Lev
BK
Lev
MK
TLev
WT
Lev
MK
T,N
et
Lev
MK
T,T
GT
r D,IN
Cr D
,AV
r D,IN
Cr D
,AV
r D,IN
Cr D
,AV
r D,IN
Cr D
,AV
r D,IN
Cr D
,AV
r E,C
APM
-0.0
000.
114*
*0.0
34**
0.2
13**
0.0
13
0.1
35**
0.0
30**
0.1
88**
-0.0
09
0.0
31*
r E,F
F3
0.00
70.
063
**0.0
33**
0.0
99**
0.0
08
0.0
36**
0.0
30**
0.0
88**
-0.0
16**
-0.0
13
r E,F
F4
0.02
5**
0.072
**0.0
45**
0.0
85**
0.0
32**
0.0
68**
0.0
38**
0.0
74**
0.0
15**
0.0
38**
r E,G
GM
,IBES5g
-0.0
23**
0.10
1**
-0.0
09
0.2
92**
-0.0
22**
0.1
40**
-0.0
01
0.2
73**
-0.0
30**
0.0
01
r E,G
GM
,HDZ1
-0.0
49**
-0.0
88**
-0.0
55**
-0.0
43**
-0.0
55**
-0.0
71**
-0.0
51**
-0.0
37**
-0.0
48**
-0.0
86**
r E,G
GM
-0.0
71**
-0.1
43**
-0.0
76**
-0.0
76**
-0.0
85**
-0.1
53**
-0.0
81**
-0.0
93**
-0.0
78**
-0.1
72**
r E,G
LS
-0.0
31**
-0.0
13-0
.027**
0.0
65**
-0.0
37**
-0.0
01
-0.0
32**
0.0
54**
-0.0
37**
-0.0
58**
r E,G
GM
,IBES1
-0.0
67**
-0.1
56**
-0.0
82**
-0.1
26**
-0.0
74**
-0.1
25**
-0.0
81**
-0.1
13**
-0.0
56**
-0.1
14**
r E,G
GM
,IBES5
-0.0
57**
-0.1
41**
-0.0
77**
-0.0
67**
-0.0
70**
-0.1
05**
-0.0
80**
-0.0
60**
-0.0
61**
-0.1
22**
r E,G
LS,IBES
-0.0
56**
-0.0
69**
-0.0
53**
-0.0
28
-0.0
56**
-0.0
69**
-0.0
51**
-0.0
23
-0.0
57**
-0.0
97**
r E,IN
D-0
.080
**-0
.170
**-0
.049**
0.1
33
-0.1
40**
-0.9
71**
-0.0
73**
0.0
05
-0.1
32**
-0.6
94**
∗p<
0.05
,∗∗p<
0.01
53
Table VII
Fixed Effect Panel Regressions
This table reports the estimates from the fixed effect panel regressions. The sample is all theU.S. publicly traded firms from 1960 to 2010, excluding firms with industry code 31(utility),44(bank), 45(insurance), 46(real estate), and 47(trading). The industry classification followsFama-French 48 industries. Variable definitions and construction are provided in the Appendix3. Variables are winsorized at 1% level in both tails of the distribution each year. The modelwe estimate is
Log(Ii,t/Ki,t) = α0 + α1Log(Qi,t−1) + α2Log(FCFi,t/Ki,t) + α3Log(wacci,t−1)
+α4(g/wacci,t−1) +∑i
firmi +∑t
yeart + εi,t.
The panel fixed effect estimator is used (first difference in firms) and year fixed effects are
included. The standard errors are clustered at the firm level. Columns (1) to (5) contain the
estimates for five different WACC’s, all of which use the same tax rate (TaxTop), cost of debt
(rD,INC) and leverage (LevWT ). The difference is the choice of cost of equity (rE). We suppress
the subscripts indicating the choice of rE in wacc, and report them in the top row under the
column number. The five measures on cost of equity are rE,CAPM (CAPM), rE,IND (IND),
rE,FF4 (FF4), rE,GGM (GGM) and rE,GLS (GLS). *significant at 5% level. **significant at 1 %
level.
(1) (2) (3) (4) (5)CAPM IND FF4 GGM GLS
log(Q) 0.266∗∗ 0.277∗∗ 0.265∗∗ 0.248∗∗ 0.255∗∗
(25.46) (31.67) (25.58) (23.32) (22.75)
log(FCF/K) 0.049∗∗ 0.051∗∗ 0.050∗∗ 0.048∗∗ 0.052∗∗
(11.62) (13.39) (11.70) (10.99) (11.42)
log(wacc) 0.037∗∗ -0.156∗∗ 0.047∗∗ -0.080∗∗ -0.023∗∗
(4.10) (-16.91) (7.17) (-12.13) (-3.49)
g/wacc 0.000∗∗ -0.020∗∗ -0.000 -0.000 -0.002(6.33) (-4.03) (-0.01) (-0.98) (-1.21)
Yr and Firm Yes Yes Yes Yes YesN 51594 68753 50789 50019 46748No. of firms 5998 8704 5912 6584 6353average years 8.6 7.9 8.6 7.6 7.4within R2 0.142 0.147 0.145 0.147 0.139overall R2 0.119 0.116 0.119 0.127 0.120between R2 0.091 0.085 0.087 0.097 0.089
t statistics in parentheses∗ p < 0.05, ∗∗ p < 0.01
54
Tab
leV
III:
Fix
edE
ffec
tP
anel
Reg
ress
ions:
Diff
eren
tT
imin
gin
Cas
hF
low
sT
his
tab
lere
por
tsth
ees
tim
ates
from
the
fixed
effec
tp
an
elre
gre
ssio
n.
Th
esa
mp
leis
all
the
U.S
.p
ub
licl
ytr
ad
edfi
rms
from
1960
to2010,
excl
ud
ing
firm
sw
ith
ind
ust
ryco
de
31(u
tili
ty),
44(b
an
k),
45(i
nsu
ran
ce),
46(r
eal
esta
te),
and
47(t
rad
ing).
Th
ein
du
stry
class
ifica
tion
foll
ows
Fam
a-F
ren
ch48
ind
ust
ries
.V
aria
ble
defi
nit
ion
san
dco
nst
ruct
ion
are
pro
vid
edin
the
Ap
pen
dix
3.
Vari
ab
les
are
win
sori
zed
at
1%
level
inb
oth
tail
sof
the
dis
trib
uti
onea
chye
ar.
Th
em
odel
we
esti
mate
is
Log
(Ii,t/K
i,t)
=α0
+α1Log
(Qi,t−
1)
+α2Log
(EBITDA
i,T/K
i,t)
+α3Log
(wacc
i,t−
1)
+α4(g/wacc
i,t−
1)
+∑ i
firm
i+∑ t
year t
+ε i
,t
Th
ep
anel
fixed
effec
tes
tim
ator
isu
sed
(firs
td
iffer
ence
infi
rms)
an
dyea
rfi
xed
effec
tsare
incl
ud
ed.
Th
est
an
dard
erro
rsare
clu
ster
edat
the
firm
leve
l.C
olu
mn
s(1
)to
(5)
conta
inth
ees
tim
ate
sfo
rfi
ved
iffer
ent
WA
CC
’sfo
rca
shfl
ows
tim
eat
T=
t+1.
Colu
mn
s(6
)to
(10)
conta
inth
ees
tim
ates
for
five
diff
eren
tW
AC
C’s
for
cash
flow
sti
me
at
T=
t-1.
All
WA
CC
su
seth
esa
me
tax
rate
(TaxTop),
cost
of
deb
t(r
D,IN
C)
an
dle
vera
ge(Lev
WT
).T
he
diff
eren
ceis
the
choi
ceof
cost
of
equit
y(r
E).
We
sup
pre
ssth
esu
bsc
rip
tsin
dic
ati
ng
the
choic
eofr E
inwacc
,an
dre
por
tth
emin
the
top
row
un
der
the
colu
mn
nu
mb
er.
Th
efi
vem
easu
res
on
cost
of
equ
ity
arer E
,CAPM
(CA
PM
),r E
,IN
D(I
ND
),r E
,FF4
(FF
4),r E
,GGM
(GG
M)
andr E
,GLS
(GL
S).
*sig
nifi
cant
at
5%
leve
l.**si
gn
ifica
nt
at
1%
leve
l.
futu
reca
shfl
ows
lagged
cash
flow
s(1
)(2
)(3
)(4
)(5
)(6
)(7
)(8
)(9
)(1
0)
CA
PM
IND
FF
4G
GM
GL
SC
AP
MIN
DF
F4
GG
MG
LS
log(Q
)0.
239∗∗
0.24
2∗∗
0.2
37∗∗
0.2
29∗∗
0.2
35∗∗
0.1
75∗∗
0.1
91∗∗
0.1
76∗∗
0.1
59∗∗
0.1
59∗∗
(24.
82)
(27.
37)
(24.2
2)
(22.8
1)
(22.2
7)
(17.0
5)
(21.0
8)
(16.9
3)
(15.0
7)
(14.2
1)
log(EBITDA/K
)0.
078∗∗
0.08
2∗∗
0.0
77∗∗
0.0
78∗∗
0.0
86∗∗
(12.
37)
(14.
76)
(12.1
2)
(12.4
6)
(12.8
6)
log(wacc
)0.
048∗∗
-0.1
41∗∗
0.0
51∗∗
-0.0
71∗∗
-0.0
14*
0.0
30∗∗
-0.1
49∗∗
0.0
41∗∗
-0.0
81∗∗
-0.0
33∗∗
(5.4
1)(-
14.7
7)(7
.72)
(-11.0
5)
(-2.2
7)
(3.5
9)
(-16.9
4)
(6.6
2)
(-13.4
3)
(-5.3
4)
log(EBITDA/K
)0.1
57∗∗
0.1
41∗∗
0.1
56∗∗
0.1
66∗∗
0.1
76∗∗
(20.5
0)
(21.6
7)
(20.1
3)
(21.3
0)
(21.5
2)
Yr
Fir
man
dg
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
N52
927
7012
552136
50239
46953
56691
75571
55867
54078
50428
No.
offi
rms
5531
7738
5458
5981
5770
6019
8463
5935
6542
6307
aver
age
year
s9.
69.
19.6
8.4
8.1
9.4
8.9
9.4
8.3
8.0
wit
hinR
20.
140
0.14
40.1
41
0.1
49
0.1
45
0.1
50
0.1
52
0.1
52
0.1
64
0.1
58
over
allR
20.
133
0.13
20.1
32
0.1
51
0.1
44
0.1
35
0.1
27
0.1
35
0.1
54
0.1
47
bet
wee
nR
20.
117
0.12
40.1
13
0.1
41
0.1
33
0.1
04
0.1
00
0.1
03
0.1
31
0.1
18
tst
atis
tics
inp
aren
thes
es∗p<
0.0
5,∗∗p<
0.01
55
Table IX
Two-Stage Least Squared: First Stage
This table reports the first stage estimates from 2SLS regressions. The sample is all the U.S. publiclytraded firms from 1960 to 2010, excluding firms with industry code 31(utility), 44(bank), 45(insurance),46(real estate), and 47(trading). The industry classification follows Fama-French 48 industries. Variabledefinitions and construction are provided in the Appendix 3. Variables are winsorized at 1% level inboth tails of the distribution each year. Upper panel: we use the industry median of each WACC asthe excluded instrument for each WACC. Since the exact identification, no Hansen-Sargan statistics arereported. Lower panel: we use waccGGM,IBES5 and waccGLS,IBES as the excluded instruments for thosefive WACC’s, and Hansan-Sargan p-values are reported. In both panels: g/wacc, Q, EBITDA/K are theincluded instruments; F statistics are reported; FE estimator is used and year fixed effects are included;the standard errors are clustered at the firm level. *significant at 5% level. **significant at 1 % level.The first stage regression is
Log(wacci,t−1) = α0 + α1Log(Qi,t−1) + α2Log(EBITDAi,t/Ki,t) + α3Log(waccIV,t−1)
+α4(g/wacci,t−1) +∑i
firmi +∑t
yeart + εi,t.
(1) (2) (3) (4) (5)CAPM,MED IND,MED FF4,MED GGM,MED GLS,MED
log(Q) 0.030∗∗ -0.034∗∗ 0.043∗∗ -0.176∗∗ -0.084∗∗
(5.66) (-10.14) (4.94) (-20.83) (-9.61)
log(EBITDA/K) 0.011∗∗ 0.001 0.020∗∗ 0.024∗∗ 0.034∗∗
(3.12) (0.23) (3.59) (4.20) (6.29)
log(waccCAPM,MED) 0.746∗∗ 0.935∗∗ 0.848∗∗ 0.614∗ 0.780∗∗
(28.58) (45.45) (30.59) (27.41) (26.31)
Yr Firm and g Yes Yes Yes Yes YesN 55346 73634 54508 52486 48895F statistics 816.7 2065.6 935.8 751.1 692.0R2 0.208 0.278 0.131 0.170 0.184
(1) (2) (3) (4) (5)CAPM IND FF4 GGM GLS
log(Q) 0.056∗∗ 0.014 0.099∗∗ -0.078∗∗ -0.014(5.11) (1.56) (3.63) (-4.73) (-0.88)
log(EBITDA/K) 0.011 0.008 0.054∗∗ 0.023 0.005(1.76) (1.48) (2.96) (1.91) (0.46)
log(waccGGM,IBES5) 0.280∗∗ 0.376∗∗ 0.324∗∗ 0.707∗∗ 0.281∗∗
(10.24) (21.25) (12.18) (25.82) (12.19)
log(waccGLS,IBES) 0.048∗∗ 0.075∗∗ 0.103∗∗ 0.102∗∗ 0.362∗∗
(2.64) (6.35) (4.07) (5.02) (13.48)
Yr Firm and g Yes Yes Yes Yes YesN 8841 11676 8622 9398 8771F statistics 70.7 405.9 356.8 1841.6 355.6Sargan p value 0.651 0.556 0.337 0.420 0.001R2 0.741 0.655 0.221 0.650 0.672
t statistics in parentheses∗ p < 0.05, ∗∗ p < 0.01
56
Tab
leX
:T
wo-
Sta
geL
east
Squar
ed:
Sec
ond
Sta
geT
his
tab
lere
por
tsth
ese
con
dst
age
esti
mat
esfr
om2S
LS
regr
essi
ons.
Th
esa
mp
leis
all
the
U.S
.p
ub
licl
ytr
ad
edfi
rms
from
1960
to20
10,
excl
ud
ing
firm
sw
ith
ind
ust
ryco
de
31(u
tili
ty),
44(b
ank),
45(i
nsu
ran
ce),
46(r
eal
esta
te),
and
47(
trad
ing)
.T
he
ind
ust
rycl
assi
fica
tion
foll
ows
Fam
a-F
ren
ch48
ind
ust
ries
.V
aria
ble
defi
nit
ion
san
dco
nst
ruct
ion
are
pro
vid
edin
the
Ap
pen
dix
3.
Var
iab
les
are
win
sori
zed
at1%
level
inb
oth
tail
sof
the
dis
trib
uti
onea
chye
ar.
Col
um
ns
(1)
to(5
)co
nta
ins
the
esti
mate
su
sin
gth
ein
du
stry
med
ian
as
the
excl
uded
inst
rum
ents
inth
efi
rst
stag
e.C
olu
mn
s(6
)to
(10)
conta
ins
the
esti
mate
su
sin
gth
ewaccGGM,IBES
5an
dwaccGLS,IBES
asth
eex
clu
ded
inst
rum
ents
inth
efi
rst
stag
e.F
Ees
tim
ator
isu
sed
and
year
fixed
effec
tsare
incl
ud
ed.
Th
est
and
ard
erro
rsare
clu
ster
edat
the
firm
leve
l.A
llW
AC
Cs
use
the
sam
eta
xra
te(TaxTop),
cost
of
deb
t(rD,INC
)an
dle
vera
ge(LevWT
).T
he
diff
eren
ceis
the
choi
ceof
cost
ofeq
uit
y(rE
).W
esu
ppre
ssth
esu
bsc
rip
tsin
dic
atin
gth
ech
oice
ofr E
inwacc
,an
dre
port
them
inth
eto
pro
wu
nd
erth
eco
lum
nnu
mb
er.
Th
efi
vem
easu
res
onco
stof
equ
ity
arer E
,CAPM
(CA
PM
),r E
,IND
(IN
D),r E
,FF
4(F
F4),
r E,GGM
(GG
M)
an
dr E
,GLS
(GL
S).
*sig
nifi
cant
at5%
leve
l.**
sign
ifica
nt
at1
%le
vel.
Th
ese
con
dst
age
regre
ssio
nis
Log
(Ii,t/Ki,t)
=α
0+α
1Log
(Qi,t−
1)
+α
2Log
(EBITDAi,t/Ki,t)
+α
3Log
(waccFIT,t−
1)
+α
4(g/wacci,t−
1)
+∑ i
firmi+∑ t
year t
+ε i,t.
(1)
(2)
(3)
(4)
(5)
(6)
(7)
(8)
(9)
(10)
CA
PM
IND
FF
4G
GM
GL
SC
AP
MIN
DF
F4
GG
MG
LS
log(Q
)0.2
85∗∗
0.32
4∗∗
0.27
9∗∗
0.25
8∗∗
0.32
4∗∗
0.29
1∗∗
0.307∗∗
0.301∗∗
0.259∗∗
0.284∗∗
(26.5
7)
(33.
40)
(25.
07)
(20.
94)
(28.
86)
(11.
85)
(15.1
8)
(11.
42)
(11.
82)
(11.
92)
log(EBITDA/K
)0.0
98∗∗
0.09
1∗∗
0.08
9∗∗
0.10
7∗∗
0.09
7∗∗
0.11
6∗∗
0.104∗∗
0.125∗∗
0.103∗∗
0.094∗∗
(13.0
4)
(13.
97)
(11.
58)
(14.
62)
(12.
46)
(6.6
3)(7
.45)
(6.5
8)
(6.4
6)(5
.72)
log(wacc
)0.2
90∗∗
0.18
8∗∗
0.35
7∗∗
-0.2
80∗∗
0.09
9∗-0
.285∗∗
-0.1
80∗∗
-0.2
03∗∗
-0.1
11∗∗
-0.1
21∗∗
(5.6
2)
(5.0
5)(1
1.46
)(-
7.35
)(2
.44)
(-6.
56)
(-8.4
6)
(-7.9
6)
(-9.0
4)
(-6.9
9)
Yr
Fir
man
dg
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
N5534
673
634
5450
852
486
4889
588
41116
7686
2293
9887
71F
irm
s507
971
0650
0153
8751
0616
82230
7164
8185
6173
0A
dj.R
20.1
510.
155
0.10
00.
162
0.17
50.
178
0.2
07
0.1
28
0.2
00
0.19
1
tst
atis
tics
inp
aren
thes
es∗p<
0.0
5,∗∗p<
0.01
57
Table XI
Fixed Effect Panel Regressions: Decomposition
This table reports the estimates from the fixed effect panel regressions. The sample is all the U.S. publiclytraded firms from 1960 to 2010, excluding firms with industry code 31(utility), 44(bank), 45(insurance),46(real estate), and 47(trading). The industry classification follows Fama-French 48 industries. Variabledefinitions and construction are provided in the Appendix 3. Variables are winsorized at 1% level in bothtails of the distribution each year. The model estimated is
Log(Ii,t/Ki,t) = α0 + α1Log(Qi,t−1) + α2Log(EBITDAi,t/Ki,t) + α3Log(LevWT,i,t−1) + α4Log(rD,INC,i,t−1)
+α5Log(TaxTop,t−1) + α6Log(rE,i,t−1) +∑i
firmi +∑t
yeart + εi,t.
The panel fixed effect estimator is used (first difference in firms) and year fixed effects are included. Thestandard errors are clustered at the firm level. All WACCs use the same tax rate (TaxTop),cost of debt(rD,INC) and leverage (LevWT ). The difference is the choice of cost of equity (rE). We suppress thesubscripts indicating the choice of rE in wacc, and report them in the top row under the column number.The five measures on cost of equity are rE,CAPM (CAPM), rE,IND (IND), rE,FF4 (FF4), rE,GGM (GGM)and rE,GLS (GLS). The elasticities between the independent variables and investment are calculated, theirstandard errors are calculated using Delta-method and the z-values are in the parathesis.*significant at5% level. **significant at 1 % level.
(1) (2) (3) (4) (5)CAPM IND FF4 GGM GLS
log(EBITDA/K) 0.198∗∗ 0.183∗∗ 0.196∗∗ 0.201∗∗ 0.206∗∗
(26.92) (28.95) (26.46) (27.76) (26.76)elasticity 0.045∗∗ 0.035 0.046∗∗ 0.057∗ 0.057∗∗
(12.15) (1.96) (3.81) (2.04) (6.24)
log(Q) 0.064∗∗ 0.089∗∗ 0.065∗∗ 0.066∗∗ 0.066∗∗
(6.36) (9.71) (6.38) (6.11) (6.05)elasticity 0.052∗∗ 0.061∗∗ 0.051∗∗ 0.052∗∗ 0.055∗∗
(21.33) (5.72) (12.81) (5.21) (17.80)
log(LevWT ) -0.252∗∗ -0.239∗∗ -0.243∗∗ -0.248∗∗ -0.277∗∗
(-22.62) (-22.89) (-21.46) (-21.57) (-22.68)elasticity -0.450∗∗ -0.500∗ -0.439∗∗ -0.443∗∗ -0.485∗∗
(-34.53) (-2.11) (-31.81) (-24.66) (-31.19)
log(rD,INC) -0.023∗∗ -0.020∗∗ -0.021∗∗ -0.022∗∗ -0.024∗∗
(-8.62) (-8.47) (-7.66) (-7.73) (-8.07)elasticity -0.005∗∗ -0.004∗∗ -0.005∗∗ -0.006∗∗ -0.006∗∗
(-4.03) (-2.99) (-3.01) (-4.35) (-4.04)
log(TaxTop) 0.685∗∗ 1.045∗∗ 0.795∗∗ 0.983∗∗ 0.927∗∗
(18.25) (28.52) (21.13) (25.74) (24.01)elasticity 0.777∗∗ 1.137∗∗ 0.880∗∗ 1.089∗∗ 1.096∗∗
(30.03) (5.15) (33.19) (28.98) (35.63)
log(rE) 0.205∗∗ -0.133∗∗ 0.061∗∗ -0.034∗∗ 0.023∗∗
(14.41) (-7.94) (8.67) (-4.46) (3.16)elasticity 0.232∗∗ -0.033 0.101∗∗ -0.023∗∗ 0.029∗∗
(19.64) (-0.52) (16.59) (-3.74) (3.62)
Observations 52110 69568 50926 50078 46746Adjusted R2 0.139 0.142 0.132 0.143 0.144
t statistics in parentheses∗ p < 0.05, ∗∗ p < 0.01
58
Tab
leX
II:
Fin
anci
alC
onst
rain
tP
anel
Reg
ress
ions:
KZ
Index
Th
ista
ble
rep
orts
the
esti
mat
esfr
omth
ep
anel
regre
ssio
ns.
Th
esa
mple
isall
the
U.S
.pu
bli
cly
trad
edfi
rms
from
1960
to2010,
excl
ud
ing
firm
sw
ith
ind
ust
ryco
de
31(u
tili
ty),
44(b
ank),
45(i
nsu
ran
ce),
46(r
eal
esta
te),
an
d47(t
rad
ing).
Th
ein
du
stry
class
ifica
tion
foll
ows
Fam
a-F
ren
ch48
ind
ust
ries
.V
aria
ble
defi
nit
ion
san
dco
nst
ruct
ion
are
pro
vid
edin
the
Ap
pen
dix
3.
Vari
ab
les
are
win
sori
zed
at
1%
leve
lin
both
tail
sof
the
dis
trib
uti
onea
chye
ar.
We
sort
firm
-yea
rin
toth
ree
gro
up
sby
KZ
ind
ex,
an
da
firm
-yea
ris
”le
ss(m
ore
)co
nst
rain
ed”
ifit
fall
sin
the
top
(bot
tom
)33
%gr
oup
.C
olu
mn
s(1
)to
(5)
conta
inth
ees
tim
ate
sfo
rle
ssco
nst
rain
edfi
rms.
Colu
mn
s(6
)to
(10)
conta
inth
ees
tim
ate
sfo
rm
ore
con
stra
ined
firm
s.T
he
cash
flow
her
eis
EB
ITD
A.
All
WA
CC
su
seth
esa
me
tax
rate
(TaxTop),
cost
of
deb
t(r
D,IN
C)
an
dle
ver
age
(Lev
WT
).T
he
diff
eren
ceis
the
choi
ceof
cost
ofeq
uit
y(r
E).
We
sup
pre
ssth
esu
bsc
rip
tsin
dic
ati
ng
the
choic
eofr E
inwacc
,an
dre
port
them
inth
eto
pro
wu
nd
erth
eco
lum
nnu
mb
er.
Th
efi
vem
easu
res
on
cost
of
equ
ity
arer E
,CAPM
(CA
PM
),r E
,IN
D(I
ND
),r E
,FF4
(FF
4),r E
,GGM
(GG
M)
an
dr E
,GLS
(GL
S).
Th
eu
pp
erp
anel
isu
sin
gfi
xed
effec
tes
tim
ate
sw
ith
both
tim
ean
dfi
rmfi
xed
effec
t.T
he
low
erp
an
elis
usi
ng
Poole
dO
LS
wit
hn
ofi
xed
effec
t.*s
ign
ifica
nt
at5%
level
.**
sign
ifica
nt
at
1%
leve
l.
Les
sC
on
stra
ined
More
Con
stra
ined
(1)
(2)
(3)
(4)
(5)
(6)
(7)
(8)
(9)
(10)
CA
PM
IND
FF
4G
GM
GL
SC
AP
MIN
DF
F4
GG
MG
LS
log(Q
)0.
150∗∗
0.16
1∗∗
0.1
43∗∗
0.1
34∗∗
0.1
44∗∗
0.2
45∗∗
0.2
49∗∗
0.2
46∗∗
0.2
57∗∗
0.2
46∗∗
(9.6
7)(1
0.62
)(9
.22)
(8.9
4)
(9.0
3)
(11.4
2)
(13.9
1)
(11.2
4)
(11.9
9)
(10.5
8)
log(EBITDA/K
)0.
117∗∗
0.11
5∗∗
0.1
16∗∗
0.1
17∗∗
0.1
13∗∗
0.1
25∗∗
0.1
13∗∗
0.1
23∗∗
0.1
26∗∗
0.1
32∗∗
(7.7
4)(9
.02)
(7.6
0)
(8.2
1)
(7.4
5)
(10.6
4)
(10.7
4)
(10.4
6)
(11.1
0)
(10.9
5)
log(wacc
)0.
016
-0.0
31∗
0.0
27∗
-0.0
84∗∗
-0.0
41∗∗
0.0
23
-0.2
24∗∗
0.0
49∗∗
-0.0
94∗∗
-0.0
29∗
(1.0
0)(-
2.11
)(2
.04)
(-6.8
9)
(-3.5
4)
(1.6
0)
(-13.6
5)
(4.1
6)
(-8.5
3)
(-2.5
2)
Yr
Fir
man
dg
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
N16
560
2218
516294
16662
15571
16560
22184
16293
16661
15570
No.
offi
rms
2831
4152
2777
3052
2894
3533
4889
3483
3838
3660
aver
age
year
s5.
85.
35.9
5.5
5.4
4.7
4.5
4.7
4.3
4.3
wit
hinR
20.
135
0.13
30.1
34
0.1
42
0.1
35
0.1
14
0.1
32
0.1
16
0.1
36
0.1
24
over
allR
20.
143
0.15
20.1
42
0.1
76
0.1
64
0.0
91
0.1
00
0.0
90
0.1
19
0.1
07
bet
wee
nR
20.
134
0.17
10.1
31
0.1
89
0.1
80
0.0
77
0.0
75
0.0
74
0.1
14
0.0
93
Les
sC
on
stra
ined
More
Con
stra
ined
(1)
(2)
(3)
(4)
(5)
(6)
(7)
(8)
(9)
(10)
CA
PM
IND
FF
4G
GM
GL
SC
AP
MIN
DF
F4
GG
MG
LS
log(Q
)0.
056∗∗
0.11
6∗∗
0.0
64∗∗
0.0
65∗∗
0.0
69∗∗
0.0
42∗∗
0.1
01∗∗
0.0
46∗∗
0.0
48∗∗
0.0
59∗∗
(8.3
4)(1
9.98
)(9
.27)
(8.8
6)
(9.3
6)
(4.5
1)
(12.5
4)
(4.9
0)
(5.1
7)
(5.9
9)
log(EBITDA/K
)0.
203∗∗
0.18
7∗∗
0.2
00∗∗
0.2
24∗∗
0.2
22∗∗
0.2
05∗∗
0.1
70∗∗
0.2
06∗∗
0.2
03∗∗
0.2
18∗∗
(25.
64)
(27.
10)
(24.7
2)
(28.5
8)
(26.8
0)
(25.4
5)
(24.1
3)
(25.2
2)
(25.7
4)
(26.2
6)
log(wacc
)0.
229∗∗
0.16
2∗∗
0.1
07∗∗
-0.0
79∗∗
-0.0
05
0.1
55∗∗
-0.1
78∗∗
0.0
75∗∗
-0.1
69∗∗
-0.0
59∗∗
(19.
84)
(12.
31)
(10.0
5)
(-8.8
7)
(-0.4
2)
(12.4
4)
(-13.7
6)
(7.8
2)
(-18.7
5)
(-5.4
1)
gY
esY
esY
esY
esY
esY
esY
esY
esY
esY
esO
bse
rvat
ion
s16
560
2218
516294
16662
15571
16560
22184
16293
16661
15570
Ad
just
edR
20.
111
0.12
30.0
95
0.1
21
0.1
02
0.0
68
0.0
61
0.0
62
0.0
84
0.0
69
tst
atis
tics
inp
aren
thes
es∗p<
0.05
,∗∗p<
0.0
1
59
Tab
leX
III:
Fin
anci
alC
onst
rain
tP
anel
Reg
ress
ions:
KZ
Index
Th
ista
ble
rep
orts
the
esti
mat
esfr
omth
ep
anel
regre
ssio
ns.
Th
esa
mple
isall
the
U.S
.pu
bli
cly
trad
edfi
rms
from
1960
to2010,
excl
ud
ing
firm
sw
ith
ind
ust
ryco
de
31(u
tili
ty),
44(b
ank),
45(i
nsu
ran
ce),
46(r
eal
esta
te),
an
d47(t
rad
ing).
Th
ein
du
stry
class
ifica
tion
foll
ows
Fam
a-F
ren
ch48
ind
ust
ries
.V
aria
ble
defi
nit
ion
san
dco
nst
ruct
ion
are
pro
vid
edin
the
Ap
pen
dix
3.
Vari
ab
les
are
win
sori
zed
at
1%
leve
lin
both
tail
sof
the
dis
trib
uti
onea
chye
ar.
We
sort
firm
-yea
rin
toth
ree
gro
up
sby
KZ
ind
ex,
an
da
firm
-yea
ris
”le
ss(m
ore
)co
nst
rain
ed”
ifit
fall
sin
the
top
(bot
tom
)33
%gr
oup
.C
olu
mn
s(1
)to
(5)
conta
inth
ees
tim
ate
sfo
rle
ssco
nst
rain
edfi
rms.
Colu
mn
s(6
)to
(10)
conta
inth
ees
tim
ate
sfo
rm
ore
con
stra
ined
firm
s.T
he
cash
flow
her
eis
EB
ITD
A.
All
WA
CC
su
seth
esa
me
tax
rate
(TaxTop),
cost
of
deb
t(r
D,IN
C)
an
dle
ver
age
(Lev
WT
).T
he
diff
eren
ceis
the
choi
ceof
cost
ofeq
uit
y(r
E).
We
sup
pre
ssth
esu
bsc
rip
tsin
dic
ati
ng
the
choic
eofr E
inwacc
,an
dre
port
them
inth
eto
pro
wu
nd
erth
eco
lum
nnu
mb
er.
Th
efi
vem
easu
res
on
cost
of
equ
ity
arer E
,CAPM
(CA
PM
),r E
,IN
D(I
ND
),r E
,FF4
(FF
4),r E
,GGM
(GG
M)
an
dr E
,GLS
(GL
S).
Th
eu
pp
erp
anel
isu
sin
gP
ool
edO
LS
wit
hti
me
fixed
effec
ton
ly.
Th
elo
wer
pan
nel
isu
sin
gP
oole
dO
LS
wit
hfi
rmfi
xed
effec
ton
ly.
*sig
nifi
cant
at5%
leve
l.**
sign
ifica
nt
at1
%le
vel
.
Les
sC
on
stra
ined
More
Con
stra
ined
(1)
(2)
(3)
(4)
(5)
(6)
(7)
(8)
(9)
(10)
CA
PM
IND
FF
4G
GM
GL
SC
AP
MIN
DF
F4
GG
MG
LS
log(Q
)0.
135∗∗
0.18
8∗∗
0.1
47∗∗
0.1
42∗∗
0.1
48∗∗
0.0
67∗∗
0.1
19∗∗
0.0
68∗∗
0.0
69∗∗
0.0
79∗∗
(17.
66)
(28.
60)
(19.1
7)
(18.5
1)
(18.6
5)
(7.1
5)
(14.8
4)
(7.2
5)
(7.5
3)
(8.1
1)
log(EBITDA/K
)0.
148∗∗
0.13
8∗∗
0.1
41∗∗
0.1
63∗∗
0.1
61∗∗
0.1
88∗∗
0.1
60∗∗
0.1
89∗∗
0.1
86∗∗
0.2
03∗∗
(17.
96)
(19.
29)
(16.8
8)
(20.5
3)
(18.9
1)
(23.5
9)
(23.1
0)
(23.4
2)
(24.2
1)
(24.8
9)
log(wacc
)0.
135∗∗
0.04
6∗∗
0.0
51∗∗
-0.1
43∗∗
-0.0
59∗∗
0.0
95∗∗
-0.2
83∗∗
0.0
45∗∗
-0.2
35∗∗
-0.1
02∗∗
(10.
81)
(3.2
4)(4
.72)
(-16.1
5)
(-5.4
4)
(7.2
0)
(-21.0
5)
(4.6
7)
(-25.6
3)
(-9.4
3)
Yr
and
gY
esY
esY
esY
esY
esY
esY
esY
esY
esY
esO
bse
rvat
ion
s16
560
2218
516294
16662
15571
16560
22184
16293
16661
15570
Ad
just
edR
20.
151
0.16
60.1
46
0.1
88
0.1
68
0.1
06
0.1
15
0.1
05
0.1
47
0.1
23
Les
sC
on
stra
ined
More
Con
stra
ined
(1)
(2)
(3)
(4)
(5)
(6)
(7)
(8)
(9)
(10)
CA
PM
IND
FF
4G
GM
GL
SC
AP
MIN
DF
F4
GG
MG
LS
log(Q
)0.
050∗∗
0.08
5∗∗
0.0
41∗∗
0.0
50∗∗
0.0
58∗∗
0.2
34∗∗
0.2
71∗∗
0.2
35∗∗
0.2
67∗∗
0.2
49∗∗
(5.3
2)(1
0.07
)(4
.34)
(4.8
8)
(5.5
5)
(15.7
3)
(20.7
4)
(15.6
2)
(17.5
0)
(15.4
0)
log(EBITDA/K
)0.
193∗∗
0.18
3∗∗
0.1
93∗∗
0.1
94∗∗
0.1
89∗∗
0.1
52∗∗
0.1
38∗∗
0.1
52∗∗
0.1
59∗∗
0.1
64∗∗
(21.
73)
(23.
37)
(21.5
5)
(21.9
1)
(20.2
0)
(17.2
8)
(17.2
6)
(16.9
4)
(17.7
3)
(17.5
3)
log(wacc
)0.
156∗∗
0.12
2∗∗
0.0
98∗∗
-0.0
26∗
0.0
18
0.0
81∗∗
-0.1
47∗∗
0.0
73∗∗
-0.0
60∗∗
-0.0
07
(13.
03)
(9.5
9)(8
.97)
(-2.4
9)
(1.6
7)
(6.4
0)
(-10.9
5)
(7.4
2)
(-6.1
4)
(-0.6
3)
Fir
man
dg
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Ob
serv
atio
ns
1656
022
185
16294
16662
15571
16560
22184
16293
16661
15570
Ad
just
edR
20.
448
0.46
80.4
45
0.4
43
0.4
37
0.4
16
0.4
04
0.4
14
0.4
08
0.4
02
tst
atis
tics
inp
aren
thes
es∗p<
0.05
,∗∗p<
0.0
1
60
Table XIV
Q: Two-way sort by NPV and EBITDA/K
This table reports the two-way sorts results of Q. The sample is all the U.S. publicly traded firms from1960 to 2010, excluding firms with industry code 31(utility), 44(bank), 45(insurance), 46(real estate),and 47(trading). The industry classification follows Fama-French 48 industries. Variable definitions andconstruction are provided in the Appendix 3. Variables are winsorized at 1% level in both tails of thedistribution each year. We sort the firms into 5×5 groups by one NPV measure and EBITDA/K, andthe median of Q in each group is reported. (4)-(2) measures the mean differences between ”group 4” and”group 2” in each row/column. Assuming that the two groups have different variance, we test whetherthe differences are different from zero. *significant at 5% level. **significant at 1 % level.
EBITDA/KNPVCAPM 1 2 3 4 5 Total (4)-(2)
Low High
1 (Low) 1.659 1.068 1.467 2.791 3.787 1.348 1.212∗∗
2 0.761 0.916 1.443 2.552 6.626 1.016 2.412∗∗
3 0.857 1.016 1.351 2.074 3.787 1.435 1.1.259∗∗
4 0.794 1.077 1.543 2.183 3.190 2.106 1.264∗∗
5 (High) 1.194 0.977 1.751 2.513 4.586 3.861 1.504Total 1.291 0.960 1.415 2.212 4.234 1.740 1.265∗∗
(4)-(2) 0.236 0.044∗∗ 0.007 -1.103∗∗ -1.169∗∗ 1.123∗∗
EBITDA/KNPVGGM 1 2 3 4 5 Total (4)-(2)
Low High
1 (Low) 1.813 0.863 1.145 1.656 7.306 1.251 1.471∗∗
2 0.787 0.887 1.225 1.534 2.813 1.002 784∗∗
3 0.936 1.080 1.345 1.734 2.389 1.382 0.735∗∗
4 2.391 1.371 1.751 2.179 2.766 2.162 -0.3625 (High) 0.964 2.642 2.457 2.989 5.192 4.111 -6.373∗∗
Total 1.342 0.966 1.418 2.212 4.245 1.753 1.265∗∗
(4)-(2) 3.143∗∗ 1.364∗∗ 0.453∗∗ 0.544∗∗ 0.621∗∗ 1.231∗∗
∗ p < 0.05, ∗∗ p < 0.01
61
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