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

1

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.

2

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

3

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.

4

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.)

5

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

6

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.

7

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.

8

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.

9

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.

11

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

12

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.

13

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

15

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

17

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

18

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

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I/K

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Q0.

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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

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0r E

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0.17∗∗

0.2

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4∗∗

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00

TaxTop

0.02∗∗

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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

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-0.1

1∗∗

1.0

0wacc

GGM

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9∗∗

-0.0

7∗∗

-0.0

10.

05∗∗

0.1

8∗∗

0.0

9∗∗

0.6

1∗∗

0.3

8∗∗

0.57∗∗

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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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