The Relation Between the Cost of Capital and Economic Profit
Michael S. Pagano*
Villanova University
College of Commerce and Finance
800 Lancaster Avenue
Villanova, PA 19085
Michael.Pagano@villanova.edu
(610) 519-4389
JEL Classification: G32, G31, G3
Keywords: Cost of Capital, Capital Budgeting, Corporate Finance, Empirical Analysis
Current Version: January, 2003
* - The author wishes to thank Ivan Brick, Steve Cochran, Javier Estrada, Victoria
McWilliams, Bob Patrick, Dave Stout, and seminar participants at the 2002 Financial
Management Association Annual Meeting, Rutgers University, and Villanova University
for helpful comments, as well as Craig Coulter for capable research assistance. A
Summer Research Fellowship from Villanova University supported this research. Please
do not quote or cite without permission of the author.
The Relation Between the Cost of Capital and Economic Profit
Please do not quote or cite without permission
Abstract
This paper develops empirical estimates of the average cost of capital for 58 U.S.
industries during 1990-1999. A simple, parsimonious theoretical relation between an
industry’s weighted average cost of capital (WACC) and the industry’s economic profit
is used to obtain empirical estimates of the WACC for these 58 industries. We show that
our technique requires fewer data inputs for deriving ex post WACC estimates than the
conventional (or “textbook”) cost of capital technique and can be applied to firm-level as
well as industry data. We find that our estimates are positively correlated with an
industry’s cost of capital estimated via conventional methods and that differences
between the two sets of estimates are related to industry-specific differences in growth
opportunities and profitability. The model’s estimates are also more positively related to
realized stock returns and perform better in out-of-sample forecasts than estimates based
on the conventional method. Overall, the results suggest our technique can be a more
expedient, descriptive, and precise method of deriving estimates of an industry’s (or
firm’s) weighted average cost of capital and economic profit.
Estimating a firm’s weighted average cost of capital (WACC) is of critical
importance to managers who evaluate investment projects for capital budgeting purposes
as well as to investors who wish to assess the overall riskiness and expected return from a
company’s activities for valuation purposes. For example, corporate finance textbooks
typically devote several chapters to the problems of capital budgeting, cash flow
estimation, and the determination of a firm’s cost of capital. However, it can be difficult
in practice to obtain reliable estimates of the inputs required to perform capital budgeting
as recommended by the textbooks. As Fama and French (1997, 1999) point out, some of
these practical difficulties exist because there is considerable uncertainty in estimating a
firm’s (or even an industry’s) cost of capital. This uncertainty is similar to the risk faced
by the firm when projecting a project’s cash flow. In addition, surveys of corporate
finance practitioners indicate there is wide variation in corporate WACC estimation
methods, primarily due to managers’ differences in estimating a firm’s cost of equity
capital (e.g., see Bruner, Eades, Harris, and Higgins, 1998). Thus, a simple,
parsimonious, less-subjective, and accurate method of estimating the WACC for a firm or
industry can be a useful tool to managers interested in capital budgeting problems and
investment decision-making in general.1 We present such a method and perform
empirical tests based on this technique for 58 U.S. industries.
In addition, our method provides estimates of economic profit (also referred to as
“economic value added” or EVA® by the Stern Stewart and Co. consulting firm). These
estimates of economic profit can be useful for analysts who wish to study the long-term
performance of corporations before and after an important financial event. For example,
our model’s economic profit estimates might be helpful in identifying (via an event study
format) the long-term over- or under-performance of firms issuing new securities or
merging with other firms.
1
We can define a “simple” method as one that is less intensive in terms of the time and computations
required to obtain a WACC estimate when compared to the conventional textbook method. Likewise, a
“parsimonious, less-subjective” method can be defined as one that requires fewer inputs and/or calculations
that are based on subjective judgments made by the analyst and / or the firm’s management.
The conventional approach to identifying a firm’s WACC is based on estimating
the costs of the individual components of the firm’s sources of financing.2 For example,
computing the WACC for a company with debt and common equity in its capital
structure entails estimating: 1) the relative weights of debt and equity in the capital
structure, 2) the required after-tax return on the firm’s debt securities, and 3) the required
return on the company’s common equity. One of the difficulties in implementing the
above method is that it is sometimes hard to identify the correct weights of the capital
structure components because the market values of many debt securities (e.g., bank loans,
privately placed debt) might not be known. In addition, estimating the required returns
on the debt securities can be problematic due to the general paucity of data related to
corporate debt instruments.
Further, as Fama and French (1997, 2002) confirm, estimating the required return
on common equity can be difficult due to the statistical noise inherent in estimating an
asset pricing model’s time-varying factor loadings and risk premiums. Using dividend
and earnings growth models, Fama and French (2002) show that the expected equity
premium for 1951-2000 is probably much lower than estimates based on realized stock
returns (e.g., 2.55% – 4.32% versus the 7.43% estimate based on actual stock returns).
This result is due to the statistical problems associated with the use of realized returns as
proxies for expected returns. Recent results reported in Elton (1999) also suggest the use
of historical returns as a proxy for ex ante returns is not appropriate when one examines
the long-term performance of various securities such as U.S. government bonds and Tbills.
This study addresses the issues described above by proposing a method for
estimating a firm’s cost of capital that neither requires estimating the firm’s capital
structure nor the firm’s required return on debt and equity securities. The approach is
based on the microeconomic concept of “economic profit” first posited by Alfred
Marshall (1890) over a century ago. Recent work on economic value added (EVA®) by
Stewart (1991) has revived interest in estimating the economic profit of a firm or
2
See Ehrhardt (1994) for an in-depth discussion of the practical application of various methods of cost of
capital estimation.
2
industry. Marshall described economic profit as the excess of the entity’s marginal
revenue over its marginal cost. Thus, a firm or industry that is generating returns greater
than those required by investors is said to be earning economic profits or, in Stewart’s
terminology, adding economic value. Conversely, a firm or industry that yields returns
less than those required by investors is destroying economic value or generating
economic losses. We use the economic profit concept to derive an implicit relation
between economic profit and the firm’s weighted average cost of capital. This relation
can then be used to estimate firm- or industry-level WACC estimates. These estimates
can be obtained via regression analysis using relevant data from the firm’s financial
statements. To be more precise, the technique provides an ex post historical average of
the firm’s or industry’s marginal cost of capital over the estimation period. By using this
method, the analyst is freed from making several (potentially subjective) assumptions
about the firm’s capital structure and the costs of these capital components.3 In turn, this
historical average of the marginal WACC can be used to formulate ex ante WACC
estimates when the firm’s or industry’s WACC fluctuates fairly predictably over time.
We identify five main results from testing this new estimation method. First, we
find that the average WACC across all 58 industries during 1990-1999 is 11.01% with a
general increase in the cost of capital over the two 5-year sub-periods of the sample (i.e.,
10.42% in 1990-1994 and 11.34% during 1995-1999). When the model’s average
economic profit is restricted to zero (i.e., the model’s intercept equals zero), the estimates
also possess small standard errors (0.50-0.67%) and typically explain a large proportion
of the variance in the industries’ after-tax operating income (i.e., usually over 90% of the
variation). These WACC estimates are statistically more precise than those reported in
prior research and suggest that our approach can be used as an aid to practitioners in realworld capital budgeting / security valuation problems. Second, the model’s WACC
estimates are significantly positively related to realized stock returns of value-weighted
portfolios of the stocks that comprise the 58 industries. The model’s estimates are also
more effective in generating out-of-sample forecasts of future levels of industry
3
As Weaver (2001) notes, there is considerable cross-sectional variability in how real-world firms try to
estimate their respective cost of capital and economic profit. Weaver finds that no two firms (out of a
sample of 29) use the same method to estimate their firms’ cost of capital and EVA®.
3
profitability. This is in contrast to WACC estimates published by Ibbotson Associates
using the conventional textbook method. These latter estimates show no significant
relation to realized industry stock returns and are poorer predictors of future industry
profitability, thus suggesting that our model may be more descriptive of real-world
returns to capital. Third, consistent with the finding related to stock returns and our
WACC estimates, we find that our WACC estimates are also more closely correlated
with relevant financial variables related to profitability and growth opportunities than
published estimates based on the conventional textbook method. Thus, our approach
holds the potential of providing WACC estimates that are closer descriptions of the
actual financial costs facing a firm or industry when compared to using the conventional
textbook method of WACC estimation.
Fourth, our 1995-1999 results are corroborated by out-of-sample tests for the
1990-1994 period.4 Our approach is therefore robust to the choice of time period. We
also find evidence that WACC estimates vary over time in a predictable manner.
Specifically, we report statistically significant mean-reversion in our WACC estimates
during 1990-1999. This is particularly encouraging in terms of being able to use our ex
post averages of the industries’ WACC in order to develop out-of-sample ex ante WACC
estimates.
Fifth, the technique proposed here also allows us to estimate a firm’s or industry’s
average annual economic profit (or EVA®). We find that the average industry generated
$2.37 billion in annual excess profit during 1995-1999 and effectively zero EVA® during
1990-1994. This finding appears to be consistent with the strong economic growth and
above-normal stock returns experienced in the U.S. during the latter time period.
Although the approach presented here simplifies the amount of data required to
estimate a firm’s WACC, it typically requires reliance on financial accounting data that
might not always reflect economic reality due to accounting conventions such as accruals
and revenue/cost matching principles. However, the proposed methodology simplifies
4
Due to the limitations on the Compustat and Ibbotson Associates data available to us, we focus our
analysis on the 1990-1999 time period. Clearly, more data for periods earlier than 1990 would be helpful
to document the stability of the relations reported here. However, the main thrust of the paper (i.e., the use
of the economic profit relation to estimate the weighted average cost of capital) can be demonstrated
effectively with the 1990-1999 data.
4
the estimation problem considerably and removes most of the potentially subjective
decisions required by the conventional WACC estimation method. Thus, the gains in
simplicity and objectivity appear to outweigh the potential drawbacks of using
accounting data.5 This paper therefore contributes to the cost of capital literature by
providing a new estimation method that can be used to complement or supplement the
textbook approach.
The rest of the study is organized as follows. Section I reviews some of the
research relevant to our analysis. Section II develops the theoretical relations that are
then tested using the data and methodology described in Section III. Section IV reports
the results of our tests while Section V presents some concluding remarks and avenues
for future research.
I. Relevant Research
As noted in the previous section, there have been several attempts in recent years
to estimate the cost of capital of U.S. companies at the industry level. Most notably,
Poterba (1998), Fama and French (1997, 1999, 2002), and Gebhardt, Lee, and
Swaminathan (2001) use different approaches to tackle the problems associated with
estimating the cost of corporate capital. Using the Fama-French (1993) three-factor
model, Fama and French (1997) estimated the cost of equity capital for 48 industries and
found that, on average, the excess return on equity capital (i.e., the return above the riskfree rate) is 6.64% with a large degree of variability (e.g., standard errors of typically
greater than 3.0%). Indeed, the authors claim that the large degree of imprecision in the
excess returns makes these estimates useless in practice for corporate discounted cash
5
For example, analysts frequently argue that accounting data might not reflect the true market value of a
firm’s activities. However, since we are looking at WACC as a relative measure based on the relation
between net operating profits and firm capital, our accounting-based WACC might be as accurate as a
market-based estimate when the biases inherent in accounting profits and capital are offsetting.
Given recent accounting scandals reported in the popular press, it is comforting to know that, for
our methodology, most of management’s accounting choices (including fraudulent ones) are naturally
offsetting in terms of accounting profits and the book value of the firm’s total capital. For example, if a
company under-states its expenses by fraudulently capitalizing these costs, then both reported profits and
total capital are inflated because over-stated profits also lead to over-stated common equity via the retained
earnings account. Thus, our method is relatively insensitive to these potential problems with accounting
data.
5
flow analysis. In addition, economy-wide WACC estimates are also relatively imprecise
with Fama and French (1999) reporting standard errors ranging from 1.67% to 2.21%.
The authors admit that even these standard errors are probably under-estimates of the
true standard errors.
Fama and French (2002) show that equity premiums based on fundamentals such
as dividend and earnings growth can yield more precise estimates of equity premiums
than those based on realized stock returns. For example, the standard error of dividend
growth during 1951-2000 was 0.74% and is much smaller than the standard error of
2.43% for average stock returns during this time period. This recent evidence from Fama
and French (2002) is consistent with our findings that using fundamental data can lead to
more precise estimates of a firm’s cost of capital.
Gebhardt et al. (2001) estimate the cost of equity capital but use a dividend
discount model (DDM) methodology and IBES earnings estimates. They find that the
cost of equity capital for large, U.S. publicly traded companies ranged between 10% and
12% during 1979-1995, depending on the assumptions used with the DDM approach.
Interestingly, Myers and Borucki (1994) obtain the same range of estimates for the cost
of equity capital of a limited sample of U.S. utility companies using a DDM-type method.
Similar to Claus and Thomas (2001), Easton, Taylor, Shroff, and Sougiannis (2001)
employ a less-restrictive version of the model used by Gebhardt et al. (2001) and find
somewhat higher estimates of the industry-level cost of equity capital with an average
value of around 13% during 1981-1998 for publicly traded stocks that are followed by
the I/B/E/S information service. However, these papers require analyst forecasts that
Claus and Thomas (2001), among others, find to be biased upward (i.e., analysts typically
over-estimate the actual growth rate of earnings).
Fama and French (1999) and Poterba (1998) are recent examples of research
focused on estimating WACC rather than simply a firm’s equity capital.6 Poterba (1998)
uses aggregate financial flow of funds data from 1959-1996 to estimate the annual
inflation-adjusted WACC for the entire U.S. macroeconomy. He reports an inflation-
6
These papers follow in path of the seminal empirical work on cost of capital estimation presented in
Miller and Modigliani (1966).
6
adjusted WACC of 5.1% which translates to a nominal WACC estimate between 8% and
9%. Fama and French (1999) use Compustat data for 1950-1996 to estimate the annual
WACC for large, publicly traded U.S. companies using the discounted cash flow
technique. Their estimates of 7.1% - 7.3% for the inflation-adjusted WACC are
somewhat higher than those reported by Poterba (1998). On a nominal basis, Fama and
French (1999) show estimates that range from 10.7% to 11.8%. As Fama and French
note, the difference between the two sets of estimates could be driven by Fama-French’s
selective sample of larger, publicly traded U.S. companies when compared with
Poterba’s more comprehensive data set. In effect, Poterba’s estimate captures smaller,
private companies as well as the large, publicly traded companies analyzed in Fama and
French (1999). If these small, private firms are less risky and less profitable than their
larger, public peers, then one could explain the observed difference between the two sets
of WACC estimates in terms of differences in the sample of companies employed.
As noted in the previous section, Ehrhardt (1994) and Bruner et al. (1998)
identify several areas where the conventional textbook approach can force analysts to
make subjective judgments. For example, Ehrhardt (1994) notes that choices related to
the selection of asset pricing model, market factor proxy, periodicity of returns, and
capital structure can all cause WACC estimates to vary widely. Bruner et al. (1998) and
Weaver (2001) confirm these observations by surveying large corporations about their
WACC methodologies. Both sets of authors find that significant differences exist in
estimating the equity capital component of the firm, particularly via the use of the
CAPM. Ideally, we desire a less-subjective WACC method that allows the results of
actual firm-specific economic activities to “speak for themselves” and removes as many
ad hoc judgments made by analysts and / or the firm’s managers as possible from the
estimation process. As will be described in greater detail in the following section, our
approach proposes a solution to several of the problems that have confronted researchers
in this area.
7
II. Theoretical Framework
As noted above, we can use the EVA framework first detailed in Stewart (1991)
to derive an empirical relation that is useful for obtaining estimates of a firm’s or an
industry’s WACC:
EVAit = NOPATit - WACCit ⋅ TOTAL CAPITALit-1
(1)
where, EVAit = economic value added for the i-th firm at time-t,
NOPATit = net operating profit after taxes for the i-th firm at time-t,7
WACCit = weighted average cost of capital for the i-th firm at time-t, and
TOTAL CAPITALit = book value of long-term debt, common stock, and preferred
stock for the i-th firm at time-(t-1).8, 9
7
The basic definition of NOPAT is defined as Earnings Before Interest but after Taxes (i.e., NOPAT =
EBIT – Taxes) generated at time-t. NOPAT is defined as the quarterly Compustat data item, Operating
Income after Depreciation, which is derived by subtracting Cost of Goods Sold (Q30), SG&A Expense
(Q1), and Depreciation (Q5) from Sales (Q2). Taxes are defined as the difference between Pretax Income
(Q23) and Net Income (Q69). For simplicity, we follow the typical financial convention and assume that
this flow variable is received at one point in time (i.e., at time-t) even though, in reality, NOPAT is most
likely generated over the entire period between time-t-1 and time-t. As Stewart (1991) discusses,
adjustments to the NOPAT definition can be used to tailor the NOPAT figure to a specific firm or industry.
Note that Depreciation Expense is not added back to EBIT to obtain NOPAT. This is because depreciation
is viewed as a true economic cost that represents the amount of money that the firm must spend to maintain
its existing set of assets. See Peterson and Peterson (1996) and Stewart (1991) for a detailed discussion of
how to estimate NOPAT, as well as TOTAL CAPITAL. Depending on the company, Peterson and
Peterson note that numerous adjustments can be made to the basic NOPAT formula. In our case, data on
most of these adjustments are not available on a quarterly basis. Consequently, we focus our analysis on
the basic definition of NOPAT.
8
As Peterson and Peterson (1996) point out, the relevant estimate of a firm’s total capital is based on book
values, not market values, when the analyst is attempting to assess the historical performance of a firm in
terms of EVA®. This is based on the notion that market values (particularly for equity) include forwardlooking estimates of the value of future growth prospects. However, the NOPAT figure is based on
historical accounting data that are derived from existing assets. Thus, using market value data for TOTAL
CAPITAL will bias EVA® estimates downward because NOPAT will appear relatively low since it does
not directly include future growth opportunities. This situation further simplifies our estimation process
because market values for many debt instruments are frequently difficult to obtain. By using book values,
the problem of finding market values for debt securities is avoided. Also, the TOTAL CAPITAL variable
which is lagged one period in Equation (1) to avoid counting the current portion of Retained Earnings as
part of the firm’s capital at the beginning of the current period. The quarterly Compustat data items used
for long-term debt, preferred stock, and common equity are Q51, Q55, and Q59, respectively.
9
Note that we do not include short-term debt (Q45) in our specification because many textbooks, as well
as most practitioners, focus on the long-term sources of corporate financing (long-term debt, preferred
stock, common stock) when estimating a firm’s cost of capital. For example, Gitman and Vandenberg
(2000) find in a survey of large U.S. firms that most practitioners focus on the long-term debt and common
equity components of the capital structure when estimating their firms’ respective WACC. As will be
discussed in the Empirical Results section, our results are not affected materially by the inclusion or
exclusion of short-term debt from the TOTAL CAPITAL calculation.
8
Damodoran (1996) describes in detail how (1) can be viewed as an equilibrium relation
for a value-maximizing firm that has established an optimal capital structure and
generates sufficient perpetual, non-growing cash flows that satisfy investors’ required
returns on the firm’s securities. If, for example, the return generated by the firm’s equity
does not meet investors’ required return, then investors will exert selling pressure on the
firm’s common stock so that, in equilibrium, the firm’s stock price falls to a level that
equates the investors’ required equity return with the expected return on the firm’s stock.
Growth in NOPAT can be accommodated in (1) by assuming a constant growth
rate, g, and including it within the WACC term. In this case, WACC = (NOPAT /
TOTAL CAPITAL) + g. This is similar in spirit to Gordon’s (1961) constant growth
model for equity valuation. Non-constant growth can also be incorporated into the
definition but this makes the WACC term more complicated and requires additional
assumptions by the analyst. For the sake of simplicity, we use the perpetual, zero growth
definition included in (1) for our analysis. To the extent that growth in NOPAT is large
and variable, our estimates of WACC will differ from the “true” WACC figures. Indeed,
we perform tests to determine which financial variables can explain differences in our
WACC estimates with those developed using the conventional textbook approach and
published by a commercial financial analysis firm, Ibbotson Associates (see the
following Data section for more details).
It should also be noted that our WACC estimates based on (1) are unbiased when
growth is a constant (g) and the firm’s dividend/profit retention policy is irrelevant for
valuation purposes. For example, it can be shown that the WACC estimates will be
unchanged if growth is constant and can be estimated via a conventional formula such as:
g = (after-tax net operating profit retention ratio ⋅ WACC). Plugging this formula into a
constant growth model of total firm valuation (i.e., firm value = [(1 – retention ratio) ⋅
NOPAT] / (WACC – g)) yields a relation between firm value and WACC that is
independent of the growth rate. That is, using a conventional constant growth model and
inserting the above assumptions about growth and WACC yields the relation that firm
value = NOPAT / WACC. Thus, our simplified model presented in (1) might also be
9
relatively accurate when the above conditions hold for a particular firm or industry with
non-zero growth.10 [NOTE to Reviewer: Please see the attached supplement at the end
of the paper that demonstrates algebraically and numerically the independence between
value and growth when the above assumptions are met.]
Another perspective for interpreting (1) can be traced to Marshall (1890). As is
well known from microeconomic theory, in a perfectly competitive industry, equilibrium
occurs when marginal revenue equals marginal cost. In terms of Equation (1), we can
view NOPATit as the firm’s marginal return on capital and WACCit ⋅ TOTAL CAPITALit
as the marginal cost of capital. Thus, in equilibrium, EVAit should be zero. However, as
Marshall (1890) noted, firms and/or industries might be in temporary disequilibrium
because a new product or technological innovation can convey economic, or “abnormal,”
profits on a firm/industry that, ultimately, attracts competitors that, in turn, eventually
erode these profits and force EVAit back to zero. We can view EVAit in Equation (1) as
an estimate of the Marshallian concept of economic profit.
Re-arranging (1) and including a stochastic disturbance term, eit, yields a more
useful relation for the purposes of estimating WACC:11
NOPATit = EVAi + WACCi ⋅ TOTAL CAPITALit-1 + eit
(2)
In the above specification, we can interpret EVAi and WACCi as parameters to be
estimated via a bivariate regression analysis, where NOPATit is the dependent variable
and TOTAL CAPITALit-1 is the independent variable. To account for possible
heteroskedasticity and autocorrelation in the residuals, we use the Newey-West (1984)
10
Note that there is more than one way to demonstrate the irrelevance of the growth factor when specific
assumptions are used to constrain a constant growth valuation model. In our case, we use some standard
textbook definitions of the dividend payout ratio and the growth rate to show the independence between
growth and value. Other approaches can also arrive at the same conclusion using different definitions and
the constancy of factors such as operating profitability, a capital requirement ratio, and the investment in
capital. Since other approaches yield the same conclusion as ours, we prefer to use our original
formulation because it is more closely aligned with the standard textbook definitions of the components of
a constant growth valuation model. We thank an anonymous referee for pointing out the possibility of
these alternative approaches.
11
The stochastic disturbance term is included because unusual, non-recurring errors might be contained in
the historical financial data. For example, a major revision in an accounting standard might significantly
affect NOPAT and/or TOTAL CAPITAL for a specific quarter or year. Or, the firm/industry might have
an unusually good or bad quarter due to a merger, strike, lawsuit, etc. Thus, the eit term attempts to capture
these random idiosyncracies in the accounting data.
10
generalized method of moments (GMM) estimator of the model’s variance-covariance
matrix. When the instrumental variables used in the analysis are the same as the
independent variables in Equation (2), the GMM parameters are identical to those
obtained via OLS but the standard errors are adjusted for heteroskedasticity and
autocorrelation.
Strictly speaking, a regression’s parameter estimates of our model described
above in Equation (2) are ex post averages over time of the marginal cost of capital and
marginal economic profit related to a specific industry or firm. When the markets for
physical and financial capital are efficient, investors can use the realized levels of
NOPAT and TOTAL CAPITAL as reliable indicators of a firm’s or industry’s cash flows
and invested capital. In this case, the regression parameter estimates from (2) can be
interpreted as the average levels of EVA and WACC during the estimation period. That
is, we can view the intercept and slope parameters of Equation (2) as measures of the
average relationship between an industry’s NOPAT and TOTAL CAPITAL over the
sample period. In Equation (2), the estimated intercept is an expected value of the
average level of EVA over the sample period that has a standard error associated with it.
Likewise, the slope parameter estimate can be interpreted as the expected WACC over
the sample period that also possesses a standard error. Therefore, the estimated intercept
and slope parameter in Equation (2) should not be interpreted as being literally constant
over the entire sample period. Instead, these parameter estimates should be viewed as
econometric theory defines them: that is, as measures of the average relationship between
NOPAT and TOTAL CAPITAL that minimizes the sum of squared residuals. Viewed in
this light, we can see that EVA and WACC do not have to be constant for every quarter
within our sample period in order for us to obtain reliable parameter estimates via
Equation (2).12
12
While we agree that one needs to make certain assumptions in order to use the EVA relation for
empirical estimation purposes as defined by Equation (2) (e.g., a constant growth framework and efficient
markets), we would like to point out that, based on fundamental econometric theory, the intercept term of
our bivariate regression, EVA, is equal to: EVA = average of NOPAT - (WACC parameter estimate *
average of TOTAL CAPITAL). Thus, the intercept can be interpreted as follows: the average level of an
industry's EVA is literally a function of the average levels of NOPAT, WACC, and TOTAL CAPITAL and
does not have to be constrained to a constant value for all time periods within the sample period. So, our
model is amenable to empirical testing because, based on the econometric relationship noted above, we do
not require EVA (or WACC for that matter) to be constant for all time periods.
11
We can use time series accounting data for a firm or industry to estimate the
parameters of Equation (2).13 The slope parameter of this regression provides us with an
estimate of the relevant firm’s or industry’s average WACC for the time period analyzed.
For example, we can use quarterly accounting data for 1995-1999 to estimate the 5-year
average of the marginal WACC for an industry during the late 1990s. This estimate is
obtained simply (via generalized method of moments, GMM) and less subjectively
(because there is less room for analyst judgment in the choice of data inputs).14 As noted
earlier, Equation (2) shows that the intercept term of a bivariate regression yields an
estimate of the firm’s or industry’s average EVA® over the estimation period. One can
view this estimate as the 5-year average of the economic value added by the firm or
industry. For example, if we use annual accounting data, then the EVA® estimate from
(2) is an estimate of the average annual marginal economic profit generated by the firm
or industry.15
13
Equation (2) can also be estimated cross-sectionally at a point in time. For example, we could estimate
the WACC for an industry during a specific quarter or year by using a cross-section of quarterly or annual
financial statement data for firms within that industry. Similarly, one could also estimate an economy-wide
WACC by using a cross-section of industry-level financial statement data. In either case, weighted least
squares (WLS) would be appropriate for these cross-sectional analyses in order to account for differences
in the size of firms within an industry or the size of industries within a macroeconomy. To conserve space,
we focus on the time series application of Equation (2).
14
In Equation (2), the “true” value of NOPAT may be measured with error whereas the TOTAL CAPITAL
variable is more or less directly observable since it is based on book values (as theory suggests). As
Greene (1993) notes, the measurement error of NOPAT is not a problem in terms of biasing our parameter
estimates since NOPAT appears as the dependent variable in (2). Therefore, the effect of measurement
error in our model is reflected in a more volatile error term rather than biased parameter estimates. As we
will see in the Empirical Results section of the paper, the relatively tight fit of our model suggests that
NOPAT’s measurement error is not a significant problem in our sample.
15
It should be noted that the model can expanded to accommodate increased complexity, such as timevarying interest rates, via explicit risk premiums for an industry’s cost of debt and equity. However, we
think that such a model departs from our original objective of constructing a simple, parsimonious model
that does not require the analyst to choose a specific asset pricing model for the cost of debt and equity. By
choosing a specific asset pricing model, we would be moving towards a potentially more accurate model
but one that is decidedly more complex and more taxing on the analyst in terms of developing inputs and
assumptions for the model. This is the classic trade-off in financial modeling between simplicity /
tractability and realism. Our position is that we prefer to use a simpler, possibly more stylized model given
the inherent difficulties in developing sensible inputs and results when a model is too detailed. Thus, we
use the model described by Equation (2) but readily admit that the model can be expanded upon if an
analyst has specific preferences related to the choice of asset pricing model. We thank an anonymous
referee for pointing out this possibility.
12
Another relation implied by (2) also pertains to the intercept term, EVAi. If we
suppress the intercept term of the regression of (2), then we are, in effect, estimating a
restricted form of (2) where the WACC slope parameter can be interpreted as an estimate
of the “required” WACC for a firm/industry based on a rational expectations equilibrium.
In addition, the approach ensures that the average NOPAT is equal to the expectation of
NOPAT generated by the right hand side of Equation (2). As Muth (1961) first noted,
market participants form rational expectations when, on average, their expectations are
indeed realized over time and there are no systematic errors in their forecasts. Thus,
according to Muth (1961), for an estimate to be a rational expectation it simply has to
have no systematic biases. That is, when the EVAi parameter is suppressed in our
regression, we are estimating what return, on average, rational investors would have
required on the firm’s/industry’s assets in order to earn a “fair” return (i.e., a return which
yields an NPV of zero, which is equivalent to yielding an average EVA of zero over the
period of analysis).
It should also be noted that we are not claiming that the restricted form of our
model will yield the “true” WACC for an industry or firm. Our objective in suppressing
the intercept is to estimate a “required” WACC value for a given industry over a
specified sample period, which might not be equal to the “true” unobserved WACC
because of measurement error or other modeling problems. That is, when the intercept is
suppressed, we are stating that EVA is, on average, zero over the sample period and that
the resulting slope parameter estimate is consistent with a rational investor’s unbiased
expectation of an industry’s WACC during this time period. Given the properties of the
OLS and GMM estimators, our WACC estimates satisfy this requirement. In addition,
our estimates are preferable to other rational expectations estimates because our estimates
also satisfy the criterion of minimizing the sum of squared residuals. When we suppress
the intercept and estimate our “required” WACC values for each industry, we are not
requiring EVA to be zero for all periods and we are not trying to estimate the
unknowable “true” WACC. Our more modest goal is to show that the model can be used
to uncover what WACC a rational expectations investor would require so that EVA
would be, on average, zero during the sample period. Note also that this does not require
the investor to have perfect foreknowledge since there is an error term contained within
13
our model. Thus, a rational investor can make forecasting errors, as long as there is no
systematic bias in these errors. Accordingly, we can re-estimate (2) a second time
without the intercept term in order to obtain estimates of the relevant WACCs required
by investors within a rational expectations framework.
It is also important to note that suppressing the intercept in our model does not
imply that one can estimate the firm’s WACC by algebraically manipulating Equation
(2). For example, one cannot calculate the firm’s WACC by simply dividing the firm’s
average NOPAT by the firm’s average TOTAL CAPITAL (i.e., WACC ≠ average
NOPAT ÷ average TOTAL CAPITAL). As Greene (1993) and Kennedy (1998)
demonstrate, the mean of a dependent variable in a bivariate regression (e.g., a random
variable denoted as y) will not equal the product of the slope’s parameter estimate and the
mean of the random independent variable (denoted as x) when the intercept is set to zero.
Both Greene and Kennedy show that the slope parameter is estimated in this case via the
equation: slope = Σyx / Σx2. Only by coincidence would this slope parameter estimate be
equal to the ratio of the means of y and x. Thus, one must estimate the slope parameter
(in our model, the WACC parameter) via regression and cannot be estimated by simply
dividing the historical averages of NOPAT and TOTAL CAPITAL.
In theory, it is the above estimates of the “required” WACC that should be used
in corporate decision-making rather than ex post, unrestricted WACC estimates based on
historical realizations of the firm’s cash flows. To the extent that these required WACC
estimates change slowly and predictably over time, these historical estimates can be
useful to an analyst who wishes to forecast the future level of WACC for a firm or
industry. In our discussion of the empirical results (Section IV), we report the results of
this required WACC estimation process as well as the results based on the unrestricted
form of Equation (2). Thus, we develop two estimates of WACC via Equation (2), an ex
post required return (using the restricted equation) and an ex post realized return (based
on the unrestricted equation).
Given (2), we can gather the relevant time series of accounting data for a set of
companies and estimate the WACCi and EVAi parameters. However, we must verify
whether or not these estimates are realistic by comparing our WACC figures to WACC
estimates derived from the conventional cost of capital approach. In the ideal case, our
14
approach would be of great use to analysts and managers if it could generate reasonably
accurate WACC estimates but without the need for subjective judgments and timeconsuming data collection required by the conventional method. Thus, we can generate
another set of WACC estimates using the conventional approach and then compare these
estimates with the WACC figures derived from (2). Our expectation is that our WACC
estimates will be positively correlated with the conventional cost of capital figures.
III. Data and Empirical Methodology
A. Data
The data used to estimate Equation (2) were obtained from the Standard & Poor’s
Compustat database. We use quarterly data for 1990-1999 to compute NOPAT and
TOTAL CAPITAL for 58 U.S. industries (based on the primary two-digit SIC
designations of individual firms).16 The NOPAT and TOTAL CAPITAL figures for each
company within an industry are summed to obtain quarterly industry-wide estimates of
NOPAT and TOTAL CAPITAL.17 We then use these data to estimate industry-specific
WACCs for three time periods (1990-1994, 1995-1999, and 1990-1999). To create
annual estimates of WACC and EVA®, we form four-quarter moving sums of the
NOPAT variable.18 In this way, the slope and intercept terms of (2) can be directly
interpreted as annual estimates of the relevant industry’s WACC and EVA®.19 This
16
See the Appendix for the Standard Industry Classification (SIC) definitions of the 58 industries.
17
To reduce survivorship bias, we do not require each company to have data for all years in the sample. A
firm’s data are included as long as it has data for any quarter during January 1990 – December 1999.
18
According to the EVA® proponents at Stern Stewart and Co., there are numerous alternative definitions
of NOPAT that can be used. Yook (1999) attempts to estimate NOPAT and TOTAL CAPITAL using five
of the most common adjustments recommended by Stern Stewart and Co. We find a very high correlation
between our simple definitions of NOPAT and TOTAL CAPITAL noted earlier and those computed using
Yook’s method. For example, our simple definitions of NOPAT and TOTAL CAPITAL have statistically
significant correlations of 0.94 and 0.86 with Yook’s method of calculating these variables. Due to very
high positive correlation between these alternative definitions, we prefer to use the simpler forms of
NOPAT and TOTAL CAPITAL described earlier for the tests reported here.
19
It should be noted that some of our WACC and EVA® estimates could be biased downward if there are
numerous small, young firms within an industry. This type of firm typically has low or negative NOPAT
yet can have relatively high levels of TOTAL CAPITAL. This problem is mitigated by the fact that we use
2-digit SIC codes (rather than 3- or 4-digit SICs) and thus our industry categories are rather broad and
contain, on average, over 60 firms in each industry group. Thus, the 2-digit SIC groups are much more
15
approach also has the advantage of smoothing out some of the quarter-to-quarter
volatility present in NOPAT, thus reducing the potential distortionary effects of
cyclical/seasonal variations in NOPAT. In addition, the use of the GMM estimation
technique helps adjust the model’s standard errors to account for any autocorrelation and
heteroskedasticity that the moving sum of NOPAT might create so that proper inferences
about the model parameters can be made.
To develop a benchmark WACC estimate for each industry to compare with our
estimates, we use the annual editions of the Ibbotson Associates’ Cost of Capital
Quarterly (CCQ) publication. This source provides five different estimates of WACC for
the 58 two-digit SIC industries employed in our analysis. The CCQ estimates are all
calculated using the textbook approach described earlier. The five estimates correspond
to different methods of estimating an industry’s cost of equity capital.20 For example,
CCQ publishes WACC estimates based on the conventional CAPM, a “size-adjusted”
CAPM, Fama and French’s (1993) three-factor model, as well as two estimates based on
discounted cash flow techniques (see Ibbotson Associates, 1999, or their web site,
www.ibbotson.com for more details on these estimation methods).21
The firms included in our 58 industry estimates are matched with the firms
included in Ibbotson’s CCQ reports on an annual basis. We then form 5-year averages of
these annual WACC estimates for the 1995-1999 period and across Ibbotson’s five
estimation methods. As noted earlier, firms are allowed to enter and leave the industry
groups over our sample’s time horizon, thus minimizing potential survivorship bias. The
above matching procedure yields a total of 3,653 companies across the 58 industries.
However, our sample is limited to publicly traded firms and therefore our results are not
directly applicable to privately held companies that might operate in these industries.
likely to include a representative mix of large and medium-sized, established firms rather than be
dominated by smallish, young start-ups.
20
Similar to our model’s WACC estimates, Ibbotson’s estimates are value-weighted within each industry
to ensure comparability between our method and theirs.
21
The analysts at Ibbotson Associates also adjust their estimates based on “reality checks”. For example,
WACC estimates less than the yield on a 20-year U.S. Treasury bond or greater than 100% are omitted
altogether.
16
B. Empirical Methodology
B. 1) Estimating the Cost of Capital
To estimate Equation (2), we first use quarterly Compustat data for 1995-1999 for
each company within a two-digit SIC industry to compute aggregate, industry-wide
values for NOPAT and TOTAL CAPITAL. Therefore, we have 58 quarterly values for
these two variables for each of the 20 quarters that comprise the January, 1995 –
December, 1999 time period. In effect, we form 58 time series (one for each industry)
where each series comprises 20 quarters of data. We then perform separate regression
analyses based on (2) to obtain WACC estimates for each of the 58 industries. These
WACC estimates are the 5-year average of marginal WACCs for the relevant industries
during the 1995-1999.22 For corporate managers, this historical estimate can be of use in
determining how their firm’s WACC compares with its relevant industry. For example,
industries such as public utility companies might find the above estimates useful in
determining how to set utility rates within a particular operating region.
B. 2) Two Types of Out-of-Sample Tests
One way to test the robustness of our model is by re-estimating (2) for a time
period outside the original 1995-1999 sample period. For example, we can perform an
out-of-sample test of (2) to obtain required WACCs for each of the 58 industries during
an earlier time period (e.g., 1990-1994). We can compare these WACC estimates to the
1995-1999 estimates to see if there are substantial differences over the two time periods.
However, we cannot compare the 1990-1994 estimates to Ibbotson’s figures because
Ibbotson Associates did not begin publishing the CCQ report until 1995. Nevertheless,
the out-of-sample tests can be useful for replicating the model’s 1995-1999 results and to
study the dynamics of how WACC estimates change over time.
We have also developed a second out-of-sample test of our model’s validity by
using the following relation to forecast NOPAT one quarter ahead over the entire 20quarter 1995-1999 period:
22
As described in the previous section, we can re-estimate (2) a second time without an intercept term in
order to derive estimates of the required WACC.
17
NOPATi,t = EVAi + (WACCi * TOTAL CAPITALi,t-1)
(3)
Where the right-hand-side estimates of EVAi and WACCi are based on a regression using
1990-1994 data for the i-th industry. We then use actual quarterly data for TOTAL
CAPITAL during the 1995-1999 period to estimate NOPAT for each quarter (and each
industry) of this out-of-sample period. For example, we use the actual TOTAL CAPITAL
at the end of the fourth quarter of 1994, along with our model’s parameter estimates for
EVAi and WACCi, to forecast NOPAT for the first quarter of 1995. (We can use the
actual TOTAL CAPITAL level for the previous quarter because the above relation
specifies that TOTAL CAPITAL is lagged one quarter.) We then use the actual TOTAL
CAPITAL for the first quarter of 1995 (along with the same 1990-1994 parameter
estimates for EVAi and WACCi) to forecast NOPAT for the second quarter of 1995, and
so on. We can compare these forecasts of NOPAT with the actual values of NOPAT to
compute the statistics reported later in Table 4 of the Empirical Results section. Note
that we do not re-estimate our model’s parameters using additional information contained
in the quarterly data within the 1995-1999 period. The parameters are effectively
“frozen” at the end of 1994 and are not allowed the benefit of, for example, the additional
information contained in the first quarter of 1995 to forecast NOPAT for the second
quarter of 1995, and so on. Thus, our test is a particularly strict one that works against
our model’s estimates in terms of developing accurate out-of-sample forecasts.
For the Ibbotson WACC estimates, we compute the forecast statistics using the
only data available to us (i.e., the 1995-1999 Average and Median estimates). Thus, we
are stacking the test further in favor of Ibbotson’s estimates because these estimates are
based on data contained within the out-of-sample test period of 1995-1999. As noted
earlier, we are forced to use these data because Ibbotson did not start developing WACC
estimates until 1995. Also, the test favors Ibbotson’s estimates because these estimates
are based on updated information and are not “frozen” like our estimates. For example,
Ibbotson’s 1996 WACC estimates contain information for 1995 while our forecasts do
not. Given that more information is better than less information in terms of generating
accurate forecasts, our model’s forecasts are at a distinct disadvantage when compared to
Ibbotson’s.
18
B. 3) Comparing the Cost of Capital Estimates with Realized Stock Returns
Another way to test the robustness of the model is by comparing our WACC
estimates with realized stock returns for each of the industry groups. We expect our
WACC estimates to be positively related to realized stock returns because the definition
of a firm’s cost of capital shows that WACC is a positive linear function of the firm’s
cost of equity capital. Thus, on average, an industry’s realized stock returns should be a
reasonable proxy for the cost of equity capital that, in turn, implies a positive correlation
between our WACC estimates and realized stock returns. In addition, we can compare
the correlation of our WACC estimates with stock returns to the correlation of Ibbotson’s
WACC estimates with these same stock returns. If our technique provides a closer
approximation of the industry’s “true” (but unobservable) WACC, then we would expect
our WACC estimates to be more positively related to realized stock returns than
Ibbotson’s estimates.23
B. 4) Comparing the Cost of Capital Estimates with Ibbotson’s Estimates
Once the WACC estimates are computed according to Equation (2), we can
compare them to the Ibbotson CCQ estimates to determine whether or not our
methodology yields estimates that are consistent with those derived via the textbook
approach. The non-parametric Wilcoxon test can be performed in order to make these
comparisons. Since we do not know whether our WACC estimates or those from
Ibbotson Associates are the nearest approximations of the “true” unobservable WACCs,
we can use simple correlation analysis to see which set of estimates are more closely
23
It should be noted that, ideally, it would be better to compare our WACC estimates with the total returns
to both stockholders and debtholders. However, we cannot obtain reliable estimates of the return to
debtholders because we do not have sufficient data on the average yield to maturity (YTM) of each firm’s /
industry’s debt load. We therefore do not think approximations such as estimating the cost of debt via the
division of interest payments by the book value of outstanding debt are appropriate because this method
does not capture: a) the current YTM facing the firm (instead, it represents the current yield at the time the
debt was issued), b) sudden changes in financial leverage that might cause interest payments to appear very
high (or very low) relative to end-of-period debt figures (thus creating unreasonably high, or low, cost of
debt estimates), and c) bond-related capital gains. In addition, from a statistical perspective, the returns on
equity will typically be much more volatile than the returns on debt. Thus, the correlations between our
WACC estimates and the industry’s total returns to both stockholders and debtholders will be driven
largely by the correlations between our WACC estimates and the industry’s stock returns. So, the use of
stock returns rather than returns to both shareholders and debtholders is most likely not that problematic for
our purposes.
19
correlated to key financial variables related to stock returns, profitability, growth
opportunities, risk, and liquidity.24 The set of estimates that are most closely correlated
with these variables can be interpreted as a more accurate description of the industry’s
actual cost of capital. This follows from the premise that the true cost of capital should
be influenced by factors such as profitability, growth opportunities, risk, and liquidity.
In addition to the univariate tests described above, we can estimate a crosssectional regression using the differences between our 58 average required WACC
estimates and the 5-year averages (or medians) of the Ibbotson WACCs as the dependent
variable.25 These differences in the WACC estimates can then be regressed on a set of
variables based on the factors noted above. For example, we can estimate the following
cross-sectional regression:
Required WACCi - Ibbotson Average WACCi =
DIFFMEANi = f(Growth Opportunitiesi, Profitabilityi, Riski, Liquidityi) + vi
(4)
where,
Required WACCi = WACCi estimated via Equation (2) with the intercept suppressed,
Ibbotson Average WACCi = 5-year average of WACCi estimated via Ibbotson CCQ’s
five techniques,26
Growth Opportunitiesi = proxy variables such as the Market-to-Book Equity ratio
(MB) and the percentage of sales derived internationally (FORSALE),27
24
Since theory does not provide us with an explicit set of factors that affect a firm’s cost of capital, we
have chosen those influences that have been typically cited in the literature.
25
Using differences between Ibbotson’s and our model’s WACC estimates provides a more parsimonious
and efficient way of identifying differences between the two sets of WACC estimates when compared to
estimating Equation (4) below using the means and medians of the two sets of WACC estimates in separate
regressions. The results of performing separate regressions of Equation (4) for Ibbotson’s and our model’s
WACC estimates are qualitatively similar to those reported in Table 8 and are not reported here in order to
conserve space.
26
This variable is calculated by taking annual averages of the five average WACC estimates Ibbotson
Associates reports in its annual CCQ report based on five different asset pricing models and then averaging
these annual estimates over the entire 1995-1999 period. Similarly, we can form a 5-year average of the
annual medians of the five Ibbotson estimates to create an alternate dependent variable, DIFFMEDIANi.
Thus, DIFFMEDIANi = Required WACCi – 5-year average of Ibbotson’s Median WACCi.
27
FORSALE can be viewed as a proxy for growth opportunities since extensive international sales imply
large, growing markets for the industry’s goods and services. In addition, FORSALE can be viewed as a
20
Profitabilityi = Return on Common Equity (ROE),
Riski = Stock Price Volatility (VOL) and Assets-to-Common Equity ratio
(LEVERAGE),28
Liquidityi = Share trading volume (VOLUME), and
vi = stochastic disturbance term for the i-th industry.
To be consistent with the dependent variable, the independent variables are computed as
5-year averages of annual data during 1995-1999.29 As described in the theoretical
framework of Section II, our model of WACC found in Equation (2) is most directly
applicable to firms with zero growth (or to firms with constant growth-- assuming
dividend/profit retention policy is irrelevant). Thus, differences between Ibbotson’s and
our WACC estimates might be due to differences related to growth (e.g., industryspecific growth opportunities and profitability). In addition, the riskiness of an industry’s
equity, financial leverage (possibly serving as a proxy for financial distress costs), and
liquidity can also affect the cost of capital estimates. As noted above, since theory does
not give us clear guidance about the factors to be included in (3), we have chosen those
variables that are typically cited in the empirical literature as proxies for these four
influences.
If our model’s estimates are valid measures of the “true” WACC, then the
parameter estimates for MB, FORSALE, ROE, VOL, and LEVERAGE should be
positive (due to the direct relation between WACC and factors such as growth
opportunities, profitability, risk, and financial distress costs). In contrast, the parameter
estimates for VOLUME should be negative due to the inverse relation between WACC
proxy for risk (due to the diversification possibilities of international operations as well as the risks related
to foreign currency movements and international politics).
28
VOL is defined as the difference between the annual high and low stock price divided by the prior year’s
year-end stock price and is reported in Compustat as a measure of stock price risk. Other market-based
risk measures, such as a market-weighted industry average beta, were also tested. However, VOL
exhibited the strongest relation with the dependent variable and thus is the market-based measure reported
here.
29
The 5-year averages of the independent variables, MB, ROE, VOL, LEVERAGE, are obtained from the
annual market value-weighted averages of the relevant variables for each industry. For VOLUME and
FORSALE, data for individual firms within an industry are simply summed each year and then averaged
over the 5-year period.
21
and liquidity. So, if we find statistically significant parameters consistent with these
expectations, then we can infer that our model’s WACC estimates are more responsive to
the above factors than Ibbotson’s estimates. This finding would provide indirect
evidence that our model generates WACC estimates that are more descriptive of realworld variations in key financial variables. In addition, this result would suggest that our
assumption of zero growth in Equation (2) is not that restrictive since our model can,
even with this assumption, provide WACC estimates that are more responsive to
important financial variables than the conventional approach.
Conversely, if we find that the parameters for these variables are statistically
significant and are of opposite sign to those noted above, then we can infer that our
model’s WACC estimates are not good descriptions of the true WACC. Likewise, if we
find that the parameters are not statistically significant, then we can infer that the above
factors affect our WACC and Ibbotson’s WACC estimates in a similar manner and that
differences in the two estimates are not attributable to those factor(s).
In sum, if we find differences between our estimates and those of Ibbotson, then
the correlation and regression analyses should confirm which variables related to growth
opportunities, profitability, risk, and liquidity explain a substantial portion of
DIFFMEAN (or DIFFMEDIAN). In turn, these analyses should help us answer the
question regarding the relevance of Equation (2) in estimating industry-specific costs of
capital.
IV. Empirical Results
A. The Cost of Capital Estimates
Before discussing the results of the various tests described in the previous section,
it should be noted that diagnostic tests were performed on the two key variables found in
Equation (2). Namely, we performed unit root and cointegration tests for each of the 58
industry-specific time series of NOPAT and TOTAL CAPITAL. These tests are based
on Phillips and Perron (1988) and Phillips and Ouliaris (1990), respectively. None of the
58 pairs of NOPAT and TOTAL CAPITAL variables are cointegrated or non-
22
stationary.30 Thus, we can proceed with our tests knowing that these econometric
problems are not biasing our results.
Panel A of Table 1 provides summary statistics of the industry WACC estimates
based on Equation (2) and the textbook approach, while Panel B contains statistics for
selected cross-sectional financial variables. This table shows that the average WACC for
the entire set of 58 industries during the 1995-1999 time period was 10.09% based on
estimating (2) in its unrestricted form (referred to as the Ex Post WACC).31 However, the
estimates based on this form are relatively noisy with a large average standard error of
2.67%. This wide variation is consistent with the notion that the estimates are essentially
realized return estimates which, by their nature, will typically be more volatile than
investors’ ex ante returns. Despite the noisiness of the Ex Post WACC figures, the
unrestricted form of (2) has the side-benefit of providing an estimate of the average
annual EVA® generated by the firms that comprise the 58 industries used in our analysis.
As Table 1 reports, the average annual economic value added was $2.367 billion during
1995-1999. This figure is statistically significant at the 1% confidence level. This
postive EVA® finding is not that surprising given the exceptionally strong economic
conditions and stock market performance during the late 1990s.
We also show in Table 1 that, based on the restricted form of (2), the average
required WACC required by investors was 11.34% (referred to as the Required WACC in
the table).32 In effect, this is the return that would have set the average EVA® equal to
30
Results are available, on request, from the author.
31
We refer to the unrestricted form’s WACC estimate as the “Ex Post WACC” because this estimate is
based on realized values of NOPAT and TOTAL CAPITAL and therefore represents an estimate of the
actual cost of capital realized by investors rather than a required return on invested capital.
32
Note that our model’s WACC estimates reported here and in subsequent tables are based on the
exclusion of short-term debt from the TOTAL CAPITAL calculation and the inclusion of debt-related tax
benefits in our NOPAT computation. Thus, strictly speaking, our resulting slope parameter estimates can
be viewed as an estimate of the before-tax WACC for each industry. When we re-estimate the restricted
model with the debt-related tax benefits excluded from NOPAT to estimate an after-tax WACC, we find, as
expected, that the average required WACC is lower (10.51% vs. 11.34%) but that the precision of the
WACC estimates remains essentially unchanged.
Likewise, when short-term debt is included in the TOTAL CAPITAL figure, the WACC estimates
are lower by 93 basis points (10.41% vs. 11.34%) but the dispersion and precision of the estimates are
effectively unchanged. For the unrestricted model, the WACC estimates are affected in a similar manner
with the average estimate falling from 10.09% to 9.84% and 9.60% when the debt-related tax shields are
excluded and when short-term debt is included, respectively. These results suggest that our model can
23
zero during the 1995-1999 period for our sample of 58 industries. As will be discussed
in more detail below, these estimates are also the most precise ones reported in Table 2.
Despite the Required WACC’s relatively precise parameter estimates, the WACCs
themselves exhibit considerable cross-sectional dispersion. Figure 1 plots the
distribution of Required WACC estimates for our sample. This graph shows substantial
variation in WACCs across industries, with most estimates clustered between 8% and
14%.
Panel A of Table 1 also reports the median and average Ibbotson WACC
estimates for the aggregate set of five estimation techniques (referred to as Ibbotson
Average and Ibbotson Median in the table) as well as the median and average WACC
estimates for each of the five asset pricing approaches (referred to as: CAPM for the
WACC estimates based on equity capital estimates derived from the Capital Asset
Pricing Model, Adjusted CAPM for the size-adjusted CAPM, Fama-French for the 3factor Fama-French model, Discounted CF for the 1-stage discounted cash flow model,
and 3-Stage DCF for the 3-stage discounted cash flow model).
Although there is some modest variation in these models’ WACC estimates, their
dispersion is noticeably smaller than that reported for estimates based on Equation (2).
For example, the Ibbotson average of all five techniques is 12.69% with a standard
deviation of 1.69% (the median estimates are quite similar to the average with values of
12.64% and 1.35%, respectively). These estimates are somewhat higher than our
model’s estimates as well as those reported in other studies (e.g., 10.7-11.8% in Fama
and French, 1999, and 8-9% in Poterba, 1998). As Figure 2 demonstrates, the Ibbotson
estimates are also more tightly clustered between 10% and 14% than our model’s
estimates. This result might be due to the “reality checks” performed by Ibbotson
Associates to remove high and low WACC estimates from their reports. It is possible the
less-disperse results shown in Figure 2 are due also to analysts’ conservatism and
easily accommodate these alternative definitions of NOPAT and TOTAL CAPITAL since the inclusion or
exclusion of debt-related tax shields and / or short-term debt lowers the overall average WACC estimates
by less than 1 percentage point. We report the results of these alternative definitions here to conserve
space and because our focus is on presenting the simplest, most parsimonious model that can be readily
used by analysts.
24
subjectivity when estimating the components of WACC via the conventional textbook
method.
Panel B of Table 1 displays summary statistics for several financial variables that
are relevant to estimating Equation (4). Overall, these statistics suggest that the
industries in our sample were profitable (e.g., average ROE of 11.0%), large (average
assets of $51.6 billion), and rewarded shareholders (average annual stock return of
25.6%). The data underlying these statistics are used to estimate (4). The results of these
tests are presented in Table 8 and will be discussed in detail later.
Table 2 displays various WACC estimates and their standard errors for each of
the 58 industries. The first six columns contain estimates based on the restricted and
unrestricted forms of (2), while columns 7-10 show average and median Ibbotson
estimates. Columns 3 and 6 report the adjusted “raw” R2 statistics for the two forms of
our model. The final two columns of Table 2 present the EVA® estimates and their
standard errors based on the unrestricted form of (2). The average and standard deviation
for each column is presented at the bottom of the table to summarize the results across all
58 industries.
What is most striking about Table 2 are the low standard errors and high
explanatory power of the Required WACC estimates. For example, the Required WACC
standard errors are nearly half as large as those reported for the Ibbotson estimates
(0.50% versus 0.90-0.98%).33 The average t-statistic for these parameter estimates is also
quite large at 22.50 when compared to the average t-statistics for the Ex Post WACC
(3.78), Ibbotson Average (12.95), and Ibbotson Median (14.04) estimates. Further, the
average Required WACC estimates are consistent with those published in other studies
such as Fama and French (1999) and Poterba (1998). However, the standard errors for
the Required WACC estimates are relatively small when compared to the estimates
reported in Fama and French (1999). For example, Table 2 shows that the average
standard error of the Required WACC provides a much tighter confidence interval
33
The standard errors reported for the Ibbotson estimates are probably under-estimated because these
standard errors are based on five different WACC estimates that have standard errors themselves.
However, Ibbotson does not publish the standard errors for each of the five WACC estimates. In addition,
as noted earlier, Ibbotson analysts will omit unusually high or low WACC estimates in their “reality
checks”, thus further exacerbating the under-estimation of standard errors.
25
compared to Fama-French’s (1999) standard errors of 1.67-2.21%. In addition, the
explanatory power of our model, measured by what Aigner (1971) calls “raw” R2, is
remarkably good.34 Panel A shows that the average adjusted R2 for the restricted form of
(2) is .9348 while the unrestricted form’s average adjusted R2 is .9627. Thus, our method
appears to provide a more precise set of WACC estimates when compared to other
studies.
Overall, the table indicates that our model’s WACC estimates are generally lower
and more widely dispersed than the Ibbotson estimates. For example, the average
difference between the Required WACC and Ibbotson estimates is 1.30-1.35% (and is
statistically significant at the 1% level according to a conventional t-test). However, the
Required WACC column contains three estimates (for SICs equal to 10, 62, and 78) that
are below 6.0%. Admittedly, these estimates are probably unrealistically low. If these
three estimates are omitted, the average required WACC rises to 11.74% and its
difference of 0.90-0.95% with the Ibbotson figures is no longer statistically significant.
Further, from the perspective of economic significance, the average estimates from the
restricted form of (2) and Ibbotson Associates are quite close with a difference of no
more than 135 basis points. However, an inspection of the industry-specific WACC
estimates suggests the average figures might be masking greater variation at the
industry/SIC level. We examine these differences between our model’s and the textbook
method’s WACC estimates in more detail later in Section IV. C.
B. The Results of the Two Out-of-Sample Tests
When the intercept is suppressed, the regular definition of R2 ( ∑ ( yˆ − yˆ ) 2 / ∑ ( y − y ) 2 ) loses its
interpretation as a measure of the explained variance of the dependent variable. However, Aigner (1971)
shows that the “raw” R2 (defined as ∑ yˆ 2 / ∑ y 2 ) does represent the proportion of the dependent
34
variable’s variance that is explained by the model. Consequently, we report the raw R2 statistics for the
restricted and unrestricted forms of (2) in order to present a proper comparison of the two forms of the
model. We adjust these statistics for degrees of freedom to create adjusted raw R2 statistics. Chow tests of
the two forms’ raw R2 statistics for each of the 58 industries indicates that 33 (or 57%) of the R2 pairs are
statistically different from each other. Nevertheless, even these differences are not sizable, particularly
when viewed from the perspective of economic significance. For example, the average difference between
the two forms’ R2 is only .0279 (i.e., .9348 versus .9627).
26
We continue our investigation of the model described in Equation (2) by
performing our first out-of-sample test based on industry data for 1990-1994. Table 3
displays the Required WACC estimates for the 58 industries based on three time periods
(1990-1994, 1995-1999, and the full 10-year period, 1990-1999). The results show that
the average Required WACC is lower during 1990-1994 (10.42% versus 11.34% for
1995-1999) but this difference is not significant at the 5% level. In addition, the
variability in WACC estimates is essentially the same for the two 5-year periods (3.8%
vs. 3.7%). The precision of the 1990-1994 WACCs is similar to 1995-1999 with an
average standard error of 0.67% and an average adjusted R2 of .8959 (vs. 0.50% and
.9348 for the later period).35 Further, a Wilcoxon test confirms that the two sets of
WACC estimates are not statistically different from each other. Thus, the earlier period’s
results replicate those obtained for 1995-1999 and suggest that our model’s findings are
not a statistical artifact of a specific sub-sample. Lastly, the WACC estimates for the full
10-year period yield a similar average cost of capital figure of 11.01% but, as expected
when a larger sample is used, the cross-sectional dispersion and standard errors are lower
(i.e., 3.41% and 0.51%, respectively).
The estimates presented in Table 3 also indicate that industry-specific WACCs
might vary over time in a predictable fashion. For example, WACCs might exhibit
mean-reverting behavior similar to that observed by Blume (1975) for empirical
estimates of market betas. Thus, we run a Blume-type cross-sectional regression of the
1995-1999 WACCs on the 1990-1994 WACC estimates to determine whether or not the
earlier period’s estimates can explain the future period’s cost of capital. To conserve
space, we report the results of this regression at the bottom of Table 3. The statistically
significant slope parameter estimate of 0.582 is consistent with the hypothesis that our
WACC estimates exhibit mean-reverting behavior because this parameter, as in Blume
(1975), is significantly lower than 1.0 at the 1% confidence level. With an adjusted R2 of
.3451, the regression also possesses relatively good explanatory power. Overall, the out35
Interestingly, the EVA estimate for 1990-1994 of –$1.01 billion is substantially lower than the 19951999 EVA estimate of +$2.37 billion. However, the 1990-1994 EVA figure is effectively zero because
this parameter estimate is not statistically significant. Thus, in contrast to the early 1990s, there appears to
be a significant increase in EVA during the late 1990s.
27
of-sample tests reported in Table 3 provide further evidence of the validity of our model.
In addition, the tests have identified mean-reverting, predictable variations in the cost of
capital over time. This information, coupled with the technique described by (2), might
be able to help practitioners develop more accurate ex ante forecasts of a firm’s or
industry’s cost of capital.
For our second test, we report in Table 4 the superior out-of-sample forecasting
ability of our model in terms of predicting future industry profitability, as measured by
NOPAT. Table 4 reports the root mean squared error (RMSE), mean absolute error
(MAE), Theil’s U-statistic (U), along with four other measures of forecast reliability
suggested by Theil (the R2, Bias, Variance, and Covariance of the model’s forecasts).
Ideally, we would like to see values close to zero for all of these measures except the R2
and Covariance statistics (which are ideally close to 1).36 These seven standard measures
of forecast accuracy are presented for four sets of WACC estimates. In panel A of Table
4, the first two rows of the table display the forecast statistics based on our model using
the restricted and unrestricted forms, respectively. The next two rows of Panel A of
Table 4 show the forecast statistics based on using Ibbotson’s Average and Median
WACC estimates, respectively. Panel B reports statistics for the same four sets of
WACC estimates after making a first-order, AR(1), autoregressive correction in the
quarterly NOPAT forecasts to remove any autoregressive tendency in the NOPAT time
series. A quick review of these panels shows that the restricted model’s forecast statistics
are uniformly closer to the ideal levels than the other three WACC estimates. Panels C
and D repeat the same rows as in panels A-B in order to report the percentage
improvements in the forecast statistics when our restricted model’s WACC estimates are
used to forecast NOPAT for the 1995-1999 period. For example, the RMSE of the
36
Theil’s (1971) U-statistic can be decomposed into three components (Bias, Variance, and Covariance)
that sum to 1. The Bias statistic indicates the percentage of the U-statistic that is associated with any
systematic bias in the quarterly NOPAT forecasts. The Variance and Covariance figures represent the
model’s ability to duplicate NOPAT’s actual variability and the model’s random error, respectively. As
noted above, a “good” model is one where Bias and Variance are near zero (indicating no systematic bias
and an exact replication of NOPAT’s variability) and Covariance is near one (suggesting that all forecast
errors are simply caused by random fluctuations). The R2 statistic suggested by Theil is based on a
regression of actual and forecasted values of NOPAT and, ideally, should be equal to 1 in order to show
that the model’s forecasts closely fit the actual out-of-sample data.
28
restricted model’s estimates are between 16% and 27% smaller than those reported for
the Ibbotson forecasts.
Despite the inherent advantages Ibbotson’s estimates have in this out-of-sample
test, we find that our restricted, or “required”, WACC model’s estimates of NOPAT are
consistently superior to Ibbotson’s estimates across all seven measures of forecast
accuracy. In addition to the restricted model’s lower RMSE forecast errors, the other
forecast statistics such as the MAE and Theil’s U-statistic show similar (and many times,
greater) levels of improvement in panels C and D of the table. Interestingly, the Bias
statistic indicates that our restricted model’s systematic bias is virtually negligible (0.01
and 0.02 in Panels A and B, respectively). This lack of bias confirms our earlier claim
that the Required WACC estimates can be interpreted as WACC estimates based on a
rational expectations framework. The positive results for our model are true regardless of
whether or not an AR(1) error correction is employed to remove any autoregressive
pattern in the data. Our unrestricted model’s NOPAT forecasts do not perform as well as
our restricted model’s forecasts but the former model still performs on a par with the
Ibbotson estimates. In sum, Table 4’s strong results in favor of our model (despite the
aforementioned disadvantages of our forecasts when compared to Ibbotson’s) provide
compelling evidence that our model can be useful in terms of developing out-of-sample
forecasts and generating more accurate estimates than Ibbotson’s conventional approach.
C. Cross-Sectional Comparisons of the Model’s and Ibbotson’s Cost of Capital Estimates
Despite Table 2’s confirmation that the average estimates of Equation (2) and
Ibbotson’s CCQ report are relatively close, we still find that less than half of the industryspecific Required WACC estimates are within +/- 200 basis points of either Ibbotson’s
average or median estimates (i.e., 25 or 43% of the total). Thus, there appear to be a
significant number of large deviations between our model’s and Ibbotson’s industryspecific estimates. Table 5 confirms this observation by reporting the results of nonparametric Wilcoxon tests comparing the Required WACC industry estimates with the
average and median Ibbotson figures. Both tests indicate that the industry-specific
WACC estimates are significantly different at the 1% confidence level. Even when the
29
three “low” Required WACCs are omitted from the tests, the p-values for the Wilcoxon
z-statistics are still .0133 and .0107 for the Ibbotson average and median estimates,
respectively.
Another way to examine the usefulness of our model’s WACC estimates is by
comparing these estimates with realized stock returns. As noted earlier, we expect our
WACC estimates to be positively correlated with stock returns because the cost of capital
formula is a linear function of a firm’s or industry’s cost of equity capital. In addition,
Fama (1981), among others, has shown that stock returns are statistically related to
economic activity, inflation, and the return on capital. We test the above hypothesis by
regressing, on a cross-sectional basis, the 5-year (1995-1999) value-weighted total
returns for the common stocks that comprise each of the 58 industry groups on our
model’s Required WACC estimates (as well as Ibbotson’s average and median
estimates).37 The results of these regressions are reported in Table 6 and show that the
parameter estimates for the Required WACC estimates (both for 1990-1994 and 19951999) are consistently significant and positive (see Tests 1 and 2) whereas both sets of
the Ibbotson estimates are insignificant (Tests 3 and 4). In fact, Tests 5 and 6 of the table
show that when the 1995-1999 Required WACC and one of the Ibbotson WACC
estimates are included in the same regression, the only significant parameter is the one
for the Required WACC estimates.
From the set of six tests shown in Table 6, it appears that the 1995-1999 Required
WACC estimates provides the best description of realized stock returns during 19951999 (as reported in Test 2 of the table). The 1990-1994 Required WACC estimates are
also significant but have lower explanatory power than the 1995-1999 Required WACC
estimates. This latter result suggests that our model’s WACC estimates might have, in
addition to exhibiting the mean-reverting behavior shown in Table 3, some predictive
power for explaining future industry-level stock returns. This intriguing result might be
explained by the fact that industry-level WACCs can change slowly over time. Thus, the
inherent serial correlation of the WACCs due to mean-reversion might be correlated with
37
Similar tests based on the average 1-year total stock returns for each industry yield results similar to
those reported in Table 6 and are therefore not reported here in order to conserve space.
30
future stock returns. Overall, the above tests provide relatively clear evidence of the
greater explanatory power of our model’s WACC estimates when compared to those that
are based on the conventional WACC method used by Ibbotson.
In order to investigate further the differences between our model and Ibbotson’s
method, we also calculate the simple correlations between the four types of WACC
estimates reported in Table 2 and various financial variables discussed in Section III
related to growth opportunities, profitability, risk, and liquidity. In addition, the average
annual stock return and total revenue for the industries are included in the analysis to
gauge the various WACC estimates’ correlations with actual equity market values and
the relative size of the industries (proxied for by average total revenue for each industry).
Table 7 reports these correlations.
The first column of this table shows the correlations between our Required
WACC estimates, the other WACC estimates, and the financial variables. All of the
correlations in this column (except total revenue and stock volatility) are statistically
significant at the .05 level. The Required WACC is the only variable that is significantly
correlated with nearly all other variables in Table 7. For example, the three other WACC
estimates are correlated with only six or eight of the 12 variables listed in Table 7.
Interestingly, the Required WACC estimates are not only positively correlated with the
Ex Post and Ibbotson WACC estimates (.43, .26, and .33) but also strongly correlated
with the financial variables related to growth opportunities (MB, FORSALE),
profitability (ROE), and financial leverage (LEVERAGE). In addition, our model’s
WACC estimates exhibit a greater amount of simple correlation with stock returns (.28
and .45) than the Ibbotson estimates (.03 and .28). These latter results are not surprising
given the results found earlier in Table 6.
In contrast, the only variables that are consistently correlated with the Ibbotson
WACCs are the size proxy (Total Revenue), LEVERAGE, and stock price volatility
(VOL). Thus, the key factors related to the Ibbotson estimates are industry size, equity
risk, and financial leverage. Other factors related to growth opportunities, profitability,
and liquidity do not appear to be consistently related to the Ibbotson figures. In sum, the
Required WACC estimates are the ones most consistently correlated to financial
variables which, a priori, we would expect to be related to an industry’s cost of capital.
31
This is also consistent with our earlier finding that the Required WACC estimates are
significantly related to stock returns whereas Ibbotson’s estimates are not related to
realized stock returns. We can investigate the relation between the Required WACC,
Ibbotson’s estimates, and key financial variables on a multivariate basis by performing
some cross-sectional tests according to the framework described by Equation (4).
Table 8 displays the OLS regression results based on Equation (4) for two
dependent variables: 1) the difference between the Required WACC and Ibbotson
Average WACC estimates (DIFFMEAN) and 2) the difference between the Required
WACC and Ibbotson Median WACC estimates (DIFFMEDIAN). The columns labeled,
Test 1 and Test 2, report the regression results for DIFFMEAN. Test 1 contains all six
financial variables expected to influence the difference between the Required WACC and
Ibbotson estimates whereas Test 2 is based on the three variables that are most
significantly related to DIFFMEAN. Tests 3 and 4 contain the results of similar tests
using DIFFMEDIAN.
For both dependent variables, the two variables that are consistently significant
factors affecting the differences between our model and Ibbotson’s approach are: 1)
international sales activity (FORSALE) and 2) profitability (ROE). Also, note that for all
four tests the explanatory power of (3) is quite good, as measured by the adjusted R2
statistics (ranging from .5270 to .5390). As described earlier, FORSALE can be
interpreted as a proxy for growth opportunities because international operations imply
larger markets for the industry’s goods and services. In addition, FORSALE might also
be a proxy for greater diversification (and hence lower risk). Conceivably, one can also
argue that FORSALE might represent greater risk (due to higher currency and country
risks faced by firms with substantial international operations).
Overall, the positive parameter estimates for FORSALE in Table 8 suggest that
the growth opportunities and higher risk rationales related to this variable are the ones
best supported by our sample. A positive parameter estimate indicates that the Required
WACC is more likely to be larger (smaller) than the Ibbotson estimate when FORSALE
is relatively high (low). This suggests that our model’s WACC estimates are more
sensitive to variations in FORSALE than Ibbotson’s estimates. Thus, our model’s
32
estimates might be capturing the effect of variations in the growth opportunities and risks
associated with an industry’s international exposure.38
The results for ROE indicate that the level of profitability is also directly related
to an industry’s cost of capital. Thus, the positive parameter estimates for ROE also
suggest that the Required WACC estimates are more sensitive to these factors than the
Ibbotson figures. Interestingly, the market-to-book ratio (MB), stock volatility (VOL),
and liquidity (VOLUME) variables are not significant factors influencing the differences
between the two methods’ WACC estimates.
Lastly, Table 8 reports mixed results for LEVERAGE with statistically significant
negative parameter estimates based on DIFFMEDIAN but no significance when the
regressions are run with DIFFMEAN as the dependent variable. The consistent negative
sign for both dependent variables suggests that industries with larger amounts of financial
leverage are expected to have lower WACCs based on our method when compared to
those WACCs derived with Ibbotson’s approach. This finding is consistent with the
notion that industries with high financial leverage typically keep operating / business
risks relatively low so that they can reap debt’s tax benefits as well as take advantage of
debt’s lower overall cost (versus equity). It is not consistent, however, with the notion
that LEVERAGE might be proxying for expected financial distress costs. Thus, the
empirical results suggest that firms with high financial leverage might have lower
WACCs due to the cost advantages of debt and these firms’ relatively low operating risk.
Credit institutions such as those contained in SIC industry codes 60 and 61, as well as
public utilities found in code 49, are classic examples that illustrate the inverse relation
between debt and the firm’s cost of capital noted above. Not surprisingly, the Required
WACC estimates for all three of these industries are less than 10% (and less than the
corresponding Ibbotson estimates).
38
It should be noted that the construction of Ibbotson’s estimates might also be affecting this parameter
estimate. For example, the Ibbotson estimates are based on the costs of U.S.-financed corporate debt and
equity. Thus, if an industry with large foreign sales also borrows overseas extensively, then Ibbotson’s
estimates might be systematically different than WACC estimates based on Equation (2) because our
method does not require such data. However, confirmation of this possibility and its potential impact on
the magnitude of the parameter estimates is beyond the scope of this paper.
33
In sum, Tables 4-8 report several results that support our inference that the
restricted form of Equation (2) can generate WACC estimates that are more closely
related to financial factors such as stock returns, growth opportunities, profitability, and
risk than estimates derived from the conventional textbook approach. Since we do not
observe the “true” WACC for the industries in our sample, we cannot be certain that our
model presents a more accurate picture of real-world cost of capital figures. However,
the indirect evidence reported in Tables 4-8 indicates that Equation (2) can provide
WACC estimates that are more responsive to those financial factors that are commonly
thought to be important influences on a firm’s cost of capital.
V. Conclusion
We have presented a model that can provide estimates of an industry’s weighted
average cost of capital (WACC) in a simple, parsimonious, less-subjective (and
potentially more accurate) fashion than the conventional textbook approach. The tests
presented here indicate that our economic profit-based approach summarized by Equation
(2) provides ex post estimates of industry-level WACCs for the 1990-1999 period that are
positively correlated to conventional WACC estimates published by Ibbotson Associates.
In addition, our WACC estimates are more positively correlated with realized stock
returns and yield superior out-of-sample forecasts of an industry’s future profitability
than the Ibbotson estimates. Further, when compared to these textbook-based estimates,
our model’s estimates are more closely related to key financial variables that, a priori,
one would expect to be correlated with an industry’s cost of capital. Our estimates are
also more closely aligned with WACC estimates reported by other studies such as Fama
and French (1999) and Poterba (1998). Our WACC estimates exhibit mean-reverting
behavior over time similar to the dynamics in market betas observed by Blume (1975)
and thus provide a means for using our model to develop out-of-sample, or ex ante,
WACC estimates. In addition, the unrestricted form of Equation (2) enables an analyst to
estimate the average economic profit generated over the estimation period. We find that
the average per-industry economic profit rises from 0 to $2.37 billion during 1990-1999.
It should be noted that follow-on research related to this topic is quite feasible in
at least three areas. First, additional cross-sectional tests within an industry would be
34
helpful to develop shorter-term industry-specific WACC estimates. For example, one
can estimate our model for one industry on a cross-sectional basis at a point in time (e.g.,
during one quarter or one year). A weighted least squares approach (with the weights
equal to the relative size of each firm within the industry) might be preferable for these
tests. This approach would also enable the analyst to form a longer time series of WACC
estimates that could then be used to explore the time variation and mean-reverting
behavior of WACC in more detail.
Second, there are potentially several straightforward applications of our model to
event studies in corporate finance and market microstructure. For example, one can
study the impact of a change in capital structure or dividend policy on the firm’s cost of
capital and economic profit in a more direct way because Equation (2) provides a method
for estimating a firm’ WACC for both the pre- and post-event periods. In addition, a
change in the microstructure of a securities exchange might enhance liquidity that, in
turn, could lower the liquidity premium associated with a firm’s securities. This effect
can be measured by estimating the firm’s WACC before and after the microstructure
change (and, obviously, controlling for other potential confounding factors).
Third, asset pricing tests might also benefit from our proposed methodology
because, in theory, one could infer the cost of equity capital from our WACC estimates if
the researcher had a reasonably good estimate of the firm’s capital structure and the costs
of debt/preferred stock. This would enable the analyst to identify the cost of equity
capital without having to specify an explicit asset pricing model.
35
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37
Appendix A. (The SIC Code is followed by the Industry Title)
01
10
13
15
16
17
20
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
42
44
45
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
67
70
72
73
75
78
79
80
82
87
Agriculture Production Crops
Metal Mining
Oil and Gas Extraction
Building Construction-General Contractors and Operative Builders
Heavy Construction Other Than Building Construction-Contractors
Construction-Special Trade Contractors
Food and Kindred Spirits
Textile Mill Products
Apparel and Other Finished Products Made from Fabrics
Lumber and Wood Products, Except Furniture
Furniture and Fixtures
Paper and Allied Products
Printing, Publishing, and Allied Industries
Chemicals and Allied Products
Petroleum Refining and Related Industries
Rubber and Miscellaneous Plastic Products
Leather and Leather Products
Stone, Clay, Glass, and Concrete Products
Primarily Metal Industries
Fabricated Metal Products, Except Machinery and Transportation Equipment
Industrial and Commercial Machinery and Computer Equipment
Electronic and Other Electrical Equipment
Transportation Equipment
Measuring, Analyzing and Controlling Equipment
Miscellaneous Manufacturing Industries
Railroad Transportation
Motor Freight Transportation and Warehousing
Water Transportation
Transportation by Air
Transportation Services
Communications
Electric, Gas, and Sanitary Services
Wholesale Trade-Durable Goods
Wholesale Trade-Nondurable Goods
Building Materials, Hardware, Garden Supply and Mobile Home Dealers
General Merchandise Stores
Food Stores
Automotive Dealers and Gasoline Service Stations
Apparel and Accessories Stores
Home Furniture, Furnishings, and Equipment Stores
Eating and Drinking Places
Miscellaneous Retail
Depository Institutions
Non-depository Credit Institutions
Security and Commodity Brokers, Dealers, Exchanges, and Services
Insurance Carriers
Insurance Agents, Brokers, and Service
Real Estate
Holding and Other Investment Offices
Hotels, Rooming Houses, and Other Lodging Places
Personal Services
Business Services (including Software Development)
Automotive Repair, Services and Parking
Motion Pictures
Amusement and Recreation Services
Health Services
Educational Services
Engineering, Accounting, Research, Management, and Related Services
38
Table 1. Descriptive Statistics (1995-1999)
The following two panels display summary statistics for the 58-industry cross-section of cost of capital
estimates and selected financial variables, respectively, during 1995-1999.
Panel A.
Variable
Cost of Capital Estimates
N
Mean
Std. Dev.
Required WACC
Ex Post WACC
EVA ($Mil.)
Ibbotson Average
Ibbotson Median
Median CAPM
Median Adjusted CAPM
Median Fama-French
Median Discounted CF
Median 3-Stage DCF
Average CAPM
Average Adjusted CAPM
Average Fama-French
Average Discounted CF
Average 3-Stage DCF
Adjusted R2 - Required WACC
Adjusted R2 - Ex Post WACC
Panel B.
Variable
ROE
ROA
Assets / Book Value-Equity
Number of Firms
NOPAT ($ Mil.)
Total Assets ($ Mil.)
Total Revenue ($ Mil.)
Foreign Rev. / Total Revenue
Stock Return (Annual %)
Market-to-Book Ratio
Beta
Stock Volatility
Share Volume (000 sh.)
58
58
58
58
58
58
58
58
58
57
58
58
58
58
56
58
58
11.34
10.09
2,366.55
12.69
12.64
10.74
12.30
13.78
13.50
12.88
11.89
12.49
13.55
14.03
10.82
0.9348
0.9627
3.70
11.04
7,457.92
1.69
1.35
1.29
1.53
1.96
2.32
1.46
1.67
1.79
2.49
3.27
1.66
0.1299
0.0867
Minimum
2.83
-9.52
-17,064.95
8.56
8.38
8.17
8.99
8.95
7.62
9.02
8.06
8.32
9.28
7.71
6.95
0.1585
0.3538
Cross-Sectional Financial Variables
N
Mean
Std. Dev.
Minimum
58
58
58
58
58
58
58
56
58
58
58
58
58
11.06
3.86
4.1166
59.9069
5,233.0
51,569.2
45,445.1
0.1441
25.5965
4.4448
0.8577
0.6430
54,685.1
39
5.08
2.18
4.4165
70.4608
8,485.7
89,214.5
79,168.3
0.1457
19.6266
3.2944
0.4707
0.2205
147282
1.95
-0.15
1.1618
5.0000
12.2950
326.3
531.8
0.0000
-7.3300
1.0800
-1.8000
0.2600
616.8
Maximum
18.98
61.44
33,742.03
15.32
15.31
13.47
15.33
17.55
20.51
15.76
14.83
15.41
20.24
23.55
14.77
0.9989
0.9989
Maximum
25.11
8.66
25.9825
296.2000
37,899.8
390,244.0
361,609.0
0.4587
91.9000
19.5000
1.9800
1.4000
905755
Table 2. Industry-Specific Cost of Capital Estimates (1995 – 1999)
The column labeled, Required WACC, contains cost of capital estimates for 58 industries (referred to as SIC in the table) based on the restricted form of Equation
(2). The columns labeled, S.E. and Adj. R2, report the standard error of the corresponding WACC estimate and the regression equation’s adjusted coefficient of
determination, respectively. The column labeled, Ex Post WACC, reports cost of capital estimates based on the unrestricted form of Equation (2). The intercept
from this model’s regression is reported below in the column labeled EVA. The WACC estimates based on the average and median of Ibbotson Associates’ five cost
of capital estimation techniques are reported in the columns labeled, Ibbotson Average and Ibbotson Median. Summary statistics are presented at the bottom of the
table (Average and Std. Dev.). No. of Firms denotes the average number of firms used to estimate the Required and Ex Post WACC figures.
SIC
1
10
13
15
16
17
20
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
No. of
Firms
11
22
118
23
11
5
82
31
39
20
24
36
53
225
21
46
16
19
48
47
237
250
67
227
38
Required
WACC
11.22
3.89
7.43
8.95
10.64
6.60
18.98
8.87
14.99
10.49
13.33
11.77
14.09
18.76
9.74
15.90
10.57
18.70
10.63
16.19
14.99
15.12
11.77
15.97
16.04
S.E.
0.979
1.342
0.558
0.487
0.434
0.510
0.133
0.246
0.322
0.455
0.466
0.394
0.646
0.178
0.346
0.545
0.529
1.099
0.812
0.213
0.725
0.519
0.708
0.200
0.463
2
Adj. R
0.8854
0.1585
0.8896
0.9590
0.9742
0.8740
0.9989
0.9826
0.9877
0.9684
0.9819
0.9782
0.9571
0.9989
0.9788
0.9780
0.9609
0.9489
0.9061
0.9966
0.9721
0.9883
0.9576
0.9982
0.9779
Ex Post
WACC
-1.81
-9.52
1.55
17.32
6.63
5.07
16.11
8.44
20.43
5.82
19.92
2.29
3.83
29.08
13.81
-0.26
30.60
26.21
-8.89
14.80
5.81
8.29
2.41
13.30
10.21
S.E.
13.753
5.291
2.380
1.181
1.639
3.605
1.079
7.508
2.230
2.773
0.846
5.707
2.567
3.658
3.439
3.660
2.113
5.454
3.988
0.689
1.232
1.256
0.824
1.658
3.514
40
2
Adj. R
0.8964
0.3538
0.9194
0.9885
0.9790
0.8756
0.9988
0.9826
0.9919
0.9737
0.9955
0.9834
0.9788
0.9880
0.9744
0.9895
0.9926
0.9546
0.9646
0.9970
0.9853
0.9831
0.9921
0.9968
0.9803
Ibbotson
Average
11.85
12.51
13.19
12.52
14.67
12.03
11.97
11.93
13.17
14.50
13.56
11.25
12.83
12.72
10.58
13.95
14.71
13.37
13.48
12.45
13.08
14.56
9.44
12.81
13.35
S.E.
1.101
1.718
1.145
1.462
0.851
1.483
1.012
0.834
0.691
1.584
0.868
0.427
0.442
0.993
0.297
0.519
0.957
1.281
1.139
0.975
1.573
1.383
0.757
0.876
0.784
Ibbotson
Median
12.25
12.55
12.63
11.46
13.91
11.75
11.54
11.20
12.52
14.71
13.45
11.29
12.61
14.02
11.40
12.81
13.97
13.22
13.44
13.31
14.58
15.29
12.50
14.74
12.24
S.E.
1.073
1.542
1.106
0.863
0.854
1.358
0.580
0.545
0.834
0.873
1.054
0.464
0.593
0.671
0.670
0.639
1.291
1.056
0.889
0.677
0.781
1.097
0.888
0.830
0.714
EVA
659.11
801.01
2401.12
-889.10
183.95
3.03
1765.19
60.91
-518.63
282.07
-572.33
3368.13
3179.21
-17064.95
-6377.46
2102.42
-336.20
-579.87
5055.21
314.49
10145.12
6838.40
26771.20
989.32
343.77
S.E.
688.90
284.43
1053.35
131.37
64.29
6.99
873.81
1059.07
189.48
147.7085
78.57
2045.22
738.04
5996.76
5157.27
455.35
36.79
440.34
983.68
135.90
1338.66
1291.22
2774.89
631.85
214.98
Table 2. Industry-Specific WACC Estimates (continued)
SIC
40
42
44
45
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
67
70
72
73
No. of Required
Firms
WACC
9
7.58
24
9.13
11
6.93
22
13.56
8
9.85
66
11.08
185
7.26
101
9.40
53
10.47
10
14.53
28
12.33
29
14.79
10
10.44
33
13.90
22
11.17
64
13.09
57
9.49
296
9.29
30
8.50
46
2.83
91
10.03
19
18.06
34
7.97
82
10.70
11
7.92
7
10.77
216
18.16
S.E.
0.549
0.380
0.516
0.603
0.173
0.509
0.314
0.287
0.380
0.343
0.385
0.320
0.512
0.982
0.359
0.177
0.250
0.442
1.297
0.211
0.145
0.751
0.214
1.021
0.278
0.476
0.435
2
Adj. R
0.9241
0.9752
0.9236
0.9818
0.9916
0.9673
0.9838
0.9856
0.9779
0.9926
0.9875
0.9904
0.9639
0.9298
0.9816
0.9957
0.9867
0.9739
0.6754
0.5179
0.9965
0.9666
0.9847
0.8626
0.9747
0.9661
0.9921
Ex Post
WACC
S.E.
0.41
1.531
16.84
2.418
16.59
2.495
5.58
4.697
8.30
1.317
10.46
1.674
3.29
1.017
5.15
0.940
7.60 11.918
18.43
0.550
11.01
1.578
15.17
1.247
4.14
1.061
61.44
8.510
30.96
4.056
9.10
0.749
10.88
1.302
6.54
0.558
1.13
0.329
0.29
0.363
9.30
0.678
9.43
1.285
5.45
0.747
4.90
1.945
8.24
1.180
4.15
1.282
16.92
1.717
2
Adj. R
0.9744
0.9844
0.9544
0.9614
0.9919
0.9322
0.9921
0.9925
0.9847
0.9981
0.9958
0.9904
0.9901
0.9630
0.9932
0.9985
0.9876
0.9894
0.9461
0.9455
0.9967
0.9905
0.9881
0.9100
0.9748
0.9905
0.9869
41
Ibbotson
Average
11.57
13.24
14.00
12.22
12.46
11.36
8.69
13.32
11.92
15.32
12.32
10.40
15.12
14.06
13.63
13.23
13.47
9.68
8.56
9.24
12.32
14.39
11.21
9.67
14.53
14.37
14.66
S.E.
0.453
1.045
1.212
1.010
0.859
0.543
0.398
0.521
0.643
2.505
0.504
0.716
1.236
0.819
1.123
0.532
1.071
0.578
0.245
0.783
0.422
0.933
1.060
0.672
1.637
1.372
2.052
Ibbotson
Median
12.00
12.24
11.65
12.87
13.38
12.02
8.38
12.72
11.71
13.49
11.10
10.72
12.23
14.27
12.45
12.53
12.87
10.07
9.95
13.95
13.29
13.97
10.86
11.66
12.60
14.26
15.31
S.E.
0.631
0.888
0.800
0.987
1.094
0.800
0.346
0.632
0.640
1.306
0.498
0.532
1.056
1.099
0.846
0.814
0.784
0.683
0.431
1.186
0.725
0.952
0.993
1.241
1.537
1.030
1.441
EVA
2902.94
-353.38
-474.85
3399.99
59.07
1577.35
21472.74
1010.46
847.69
-479.52
722.19
-88.64
233.76
-6101.84
-1218.57
966.41
-357.49
17510.38
15776.30
33742.03
1172.63
106.10
220.72
1070.32
-20.58
54.67
973.79
S.E.
600.25
121.60
103.55
2014.52
47.98
4482.95
3983.74
232.64
376.66
78.81
1548.71
289.12
29.69
1073.57
259.34
160.23
305.87
2612.80
1113.97
4395.01
1081.31
14.75
3.10
280.18
74.42
9.41
991.10
Table 2. Industry-Specific WACC Estimates (continued)
SIC
75
78
79
80
82
87
No. of Required
Firms
WACC
6
10.86
23
5.33
31
8.07
71
8.55
6
10.37
55
9.86
Average
Std. Dev.
11.34
3.70
S.E.
0.517
0.638
0.615
0.491
0.834
0.529
Adj. R
0.9480
0.8214
0.9180
0.9510
0.9170
0.9573
Ex Post
WACC
9.06
-3.91
0.92
1.68
16.44
18.06
0.504
0.273
0.9348
0.1299
10.09
11.04
2
S.E.
7.280
2.536
1.078
1.321
2.083
1.652
2.67
2.67
Adj. R
0.9479
0.8645
0.9880
0.9843
0.9468
0.9866
Ibbotson
Average
10.82
12.83
15.28
12.98
14.04
14.76
0.9627
0.0867
12.69
1.69
2
42
S.E.
0.815
0.949
0.957
0.800
1.574
1.628
Ibbotson
Median
11.17
13.14
13.30
12.96
12.66
14.03
S.E.
0.822
1.135
1.090
0.706
1.393
0.922
EVA
77.01
290.30
713.98
2815.13
-14.90
-271.12
S.E.
312.68
68.89
86.00
516.32
5.35
48.55
0.98
0.45
12.64
1.35
0.90
0.28
2366.55
7457.92
933.48
1375.29
Table 3. Out-of-Sample Required WACC Estimates
The WACC estimates based on the restricted form of Equation (2) for three time periods, and related
summary statistics, are presented below. At the bottom of the table, a Blume-style (1975) cross-sectional
regression is presented using the 1995-1999 WACC estimates reported below as the dependent variable
and the 1990-1994 WACC estimates as the independent variable. Parameter estimates and t-statistics
displayed in bold face are statistically significant at the .01 level.
1990-94 1995-99 1990-99
1990-94
1995-99 1990-99
SIC
WACC
WACC
WACC
SIC
WACC
WACC
WACC
1
7.79
11.22
9.99
47
8.84
9.85
9.35
10
4.60
3.89
4.62
48
11.64
11.08
10.92
13
3.63
7.43
5.38
49
8.47
7.26
7.63
15
5.34
8.95
6.89
50
10.58
9.40
9.84
16
7.50
10.64
10.29
51
10.15
10.47
10.45
17
6.85
6.60
6.85
52
11.81
14.53
13.90
20
16.76
18.98
18.35
53
12.60
12.33
12.60
22
10.33
8.87
9.20
54
13.08
14.79
14.17
23
12.67
14.99
13.83
55
13.15
10.44
11.67
24
9.18
10.49
10.62
56
14.18
13.90
13.96
25
20.54
13.33
13.55
57
8.41
11.17
10.51
26
6.18
11.77
10.89
58
13.40
13.09
13.30
27
12.52
14.09
13.95
59
12.16
9.49
9.77
28
11.55
18.76
18.06
60
16.28
9.29
10.09
29
7.36
9.74
8.73
61
6.96
8.50
8.59
30
12.09
15.90
14.59
62
2.69
2.83
2.82
31
10.66
10.57
10.40
63
10.48
10.03
10.06
32
13.61
18.70
16.37
64
18.42
18.06
18.32
33
10.39
10.63
9.89
65
5.78
7.97
7.01
34
13.36
16.19
16.00
67
8.80
10.70
9.91
35
8.66
14.99
12.95
70
10.63
7.92
8.02
36
8.09
15.12
14.89
72
15.98
10.77
12.08
37
7.21
11.77
10.54
73
16.06
18.16
16.81
38
10.30
15.97
14.00
75
7.03
10.86
9.09
39
16.50
16.04
15.49
78
10.21
5.33
7.35
40
10.80
7.58
9.23
79
8.67
8.07
8.91
42
10.30
9.13
9.51
80
9.85
8.55
9.16
44
4.32
6.93
5.82
82
15.53
10.37
11.19
45
4.96
13.56
11.27
87
8.50
9.86
9.01
Average
10.42
11.34
11.01
Std. Deviation
3.80
3.70
3.41
Minimum
2.69
2.83
2.82
Maximum
20.54
18.98
18.35
OLS Regression: 1995-99 WACCi = a + b (1990-1994 WACCi) + ei
Parameter
S.E.
t-statistic
Constant
1.158
No. Observ.
5.274
4.55
1990-94 WACC
0.105
Adjusted R2
0.582
5.57
43
58
0.3451
Table 4. Out-of-Sample NOPAT Forecasting Ability
Using the WACC estimates based on both the restricted and unrestricted forms of Equation (2), as well as
Ibbotson Associates’ Average and Median WACC estimates, out-of-sample forecasts of NOPAT are
computed via Equation (3) for the 20-quarter period during 1995-1999. From these quarterly NOPAT
forecasts, seven measures of forecast accuracy are presented below for the restricted (Required WACC) and
unrestricted (Ex Post WACC) models, as well as for the two sets of Ibbotson estimates (Ibbotson Average
and Ibbotson Median). The seven measures are the forecasts’ Root Mean Squared Error (RMSE), and
Mean Absolute Error (MAE), as well as Theil’s R2 statistic (R2) corresponding to a regression of the actual
NOPAT values on the forecasted values of NOPAT for each industry, Theil’s U-statistic (U), and Theil’s
decomposition of the U-statistic into Bias, Variance, and Covariance. These latter three statistics sum to 1
with Covariance ideally equal to 1 and the remaining two statistics equal to zero. Panel A reports the
forecast statistics based on Equation (2) while Panel B adjusts all four sets of forecasts with a first-order
autoregressive, AR(1), function to account for potential autoregressive behavior in the quarterly NOPAT
time series for each industry. Panels C and D repeat the same rows as in Panels A and B in order to report
the percentage improvements in the forecast statistics when the Required WACC estimates are used to
forecast NOPAT.
R2
U
.6457
.5032
.4122
.3884
0.28
0.36
0.46
0.39
0.01
0.03
0.06
0.01
0.01
0.09
0.38
0.04
0.99
0.88
0.56
0.95
.9472
.9069
.9022
.9178
0.11
0.15
0.16
0.14
0.02
0.08
0.10
0.09
0.16
0.28
0.51
0.37
0.82
0.64
0.39
0.55
Forecast Method RMSE
MAE
Panel A. Conventional Forecasts
Required WACC
Ex Post WACC
Ibbotson Average
Ibbotson Median
4717.1
5819.7
6335.3
6487.3
1186.5
1667.9
1992.2
1687.3
Bias Variance Covariance
Panel B. Forecasts with AR(1) Adjustment
Required WACC
Ex Post WACC
Ibbotson Average
Ibbotson Median
1744.9
2109.4
2225.8
2073.8
442.5
783.1
808.3
762.1
Panel C. Percentage Improvement of Required WACC via Conventional Forecasts
Required WACC
Ex Post WACC
Ibbotson Average
Ibbotson Median
-18.9
25.5
27.3
-28.8
40.4
29.7
-28.3
56.7
66.3
-22.2
39.1
28.2
-66.7
83.3
0.0
-88.9
97.4
75.0
-12.3
76.8
4.2
Panel D. Percentage Improvement of Required WACC via Forecasts with AR(1)
Adjustment
Required WACC
Ex Post WACC
Ibbotson Average
Ibbotson Median
-17.3
21.6
15.9
-43.5
45.3
41.9
-4.4
5.0
3.2
44
-26.7
31.3
21.4
-75.0
80.0
77.8
-42.9
68.6
43.2
-28.1
110.3
49.1
Table 5. Non-Parametric Wilcoxon Tests of the Cost of Capital Estimates
The first two rows of the table report results of a Wilcoxon test of the differences between the
Required WACC and Ibbotson Average WACC estimates reported in Table 2. The last two rows of
the table report results of a Wilcoxon test of the differences between the Required WACC and
Ibbotson Median WACC estimates reported in Table 2. The z-statistic and corresponding p-value are
reported in the last two columns.
Variable
N
Sum of
Scores
Expected Sum
Under Null
Mean Score
Required WACC
Ibbotson Average
58
58
2,889.0
3,897.0
3,393.0
3,393.0
49.810
67.190
-2.78
-
0.0054
-
Required WACC
Ibbotson Median
58
58
2848.0
3938.0
3393.0
3393.0
49.103
67.897
-3.01
-
0.0026
-
45
z-statistic p-value
Table 6. Cross-Sectional Regressions of the Relation Between Stock Returns and
the Model’s and Ibbotson’s Estimates of the Cost of Capital
The dependent variable is the 5-year (1995-1999) value-weighted total return on the common stocks
that comprise each of the 58 industry groups in our sample. We regress the stock returns for these 58
industries on their respective WACC estimates (either from the restricted form of our model, Required
WACC, or from Ibbotson Associates’ WACC estimates). A parameter estimate and its t-statistic (in
parentheses) are printed in bold face if the estimate is significant at the .05 level.
Variable
Test 1.
Test 2.
Test 3.
Test 4.
Test 5.
Test 6.
CONSTANT
11.379
(2.57)
6.824
(1.44)
20.460
(2.43)
5.254
(0.58)
12.448
(1.49)
-0.414
(-0.05)
Required WACC
(1990-1994)
0.802
(2.01)
1.220
(2.98)
1.032
(2.50)
Required WACC
(1995-1999)
1.138
(2.87)
Ibbotson Average
WACC (1995-1999)
-0.526
(-0.82)
-0.058
(-0.09)
Ibbotson Median
WACC (1995-1999)
0.678
(0.95)
1.164
(1.62)
58
58
58
58
58
58
Adjusted R2
.0503
.1128
-.0177
.0276
.1076
.1112
F-statistic
4.02
8.25
0.08
2.62
4.44
4.57
No. Observations
46
Table 7. Correlations of Selected Financial Variables (1995-1999)
This table displays the partial correlation statistics for selected explanatory variables as well as the
dependent variables. Correlations which are significant at the .05 level are displayed in bold face.
Variable
1. Required WACC
2. Ex Post WACC
3. Ibbotson Average
4. Ibbotson Median
5. Stock Return
6. Total Revenue
7. MB
8. FORSALE
9. ROE
10. LEVERAGE
11. VOL
12. VOLUME
1
2
.43
.26 .28
.33 .22
.28 .45
.02 -.00
.39 .31
.39 .01
.60 .34
-.27 -.19
.12 .35
.31 .08
3
4
5
6
.68
.03 .28
-.49 -.27 .18
.03 .19 .26 .11
.07 .29 -.02 .14
-.11 .04 .26 .18
-.61 -.29 .17 .25
.29 .46 .73 -.20
.17 .38 .60 .12
47
7
8
.17
.28
-.05
.09
.17
.06
-.15
.11
.36
9
10
11
.29
-.04 -.01
.09 -.05 .50
12
Table 8. Cross-Sectional Tests of the Differences Between the Model’s and
Ibbotson’s Estimates of the Cost of Capital
The results are based on the model specified in Equation (4). The results for two alternative
dependent variable, DIFFMEAN and DIFFMEDIAN, are reported here. DIFFMEAN is the difference
between the Required WACC and Ibbotson Average WACC estimates reported in Table 2.
DIFFMEDIAN is the difference between the Required WACC and Ibbotson Median WACC estimates
reported in Table 2. A parameter estimate and its t-statistic (in parentheses) are printed in bold face if
the estimate is significant at the .01 level.
DIFFMEAN
Test 1.
Test 2.
DIFFMEDIAN
Test 3.
Test 4.
-6.187
(-4.21)
0.050
(1.48)
6.114
(2.37)
44.767
(6.05)
-0.119
(-1.37)
-1.497
(-0.83)
2.9E-6
(1.00)
7.391
(3.07)
48.990
(6.95)
-0.137
(-1.59)
-5.158
(-3.66)
0.034
(1.05)
4.043
(1.64)
46.099
(6.50)
-0.294
(-3.54)
-1.517
(-0.88)
2.0E-6
(0.72)
4.828
(2.13)
49.088
(7.37)
-0.307
(-3.77)
No. Observations
58
58
58
58
Adjusted R2
.5270
.5228
.5297
.5390
Variable
CONSTANT
MB
FORSALE
ROE
LEVERAGE
VOL
VOLUME
-7.283
(-8.25)
48
-6.221
(-7.46)
Figure 1. Distribution of WACC Estimates using the Restricted Form of the Model
This figure plots the distribution of WACC estimates based on the restricted form of Equation (2). The
distribution is derived from 5-year average Required WACC estimates of 58 two-digit SIC industries
during 1995-1999.
50%
Probability
40%
32.8%
30%
20%
10%
13.8%
12.1% 10.3%
17.2%
6.9% 6.9%
0%
6
8
10
12
14
WACC Estimate (%)
49
16
18
Figure 2. Distribution of WACC Estimates based on Ibbotson Data
This figure plots the distribution of WACC estimates based on the average estimates published by Ibbotson
Associates for five different estimation techniques. The distribution is derived from 5-year average
WACC estimates of 58 two-digit SIC industries during 1995-1999.
46.6%
50%
P
r
o
b
a
b
i
l
i
t
y
40%
30%
24.1%
19%
20%
10.3%
10%
%
6
8
10
12
14
WACC Estimate (%)
50
16
18
SUPPLEMENT FOR REVIEWERS:
An Algebraic and Numeric Derivation of the Independence between Firm Value and
Growth in a Constant Growth Model Framework
We can begin with the conventional Constant Growth Model (CGM) popularized
by Gordon (1961) and apply it, without loss of generality, to valuing the entire firm (VA),
not just the firm’s equity value. This model can be summarized by the following relation
and associated definitions:
VA =
CFA
KA − gA
where,
CFA = net free cash flow available to the firm’s investors (i.e., creditors as well as equity
holders). In our context, this variable can be interpreted as the portion of NOPAT that is
expected to be distributed to investors in the form of dividends, interest payments, etc.
over the course of the next period;39
KA = the required return on the investors’ investments in the firm and, in equilibrium, is
equal to the firm’s WACC; and
gA = the expected constant growth rate of the investors’ investments in the firm.
Key Assumptions:
The following assumptions can be used to simplify further the above valuation equation:
1) CFA can be defined as the portion of next year’s expected NOPAT that is
distributed to investors and equals d ⋅ NOPATt+1, where d = the percentage
of NOPAT that is paid out to all investors (i.e., not just to equity holders).
2) The variable, d, can be viewed as a “pay-out ratio” for all investors and is
assumed to remain constant in perpetuity.
39
Note that the CFA variable defined above includes both dividend and interest payments because this
variable refers to cash flow paid to all investors, not just dividends paid to equity holders. In this sense, the
above model is a generalization of the constant growth dividend discount model used for equity valuation.
In our case, we are focusing on CFA because, as noted earlier, we are interested in valuing the total firm,
not just the equity component of the firm.
51
3) The growth rate variable, gA, can be estimated via the relation: gA = (1 – d)
⋅ KA . Note that this assumption is the conventional one used in textbooks
used to estimate growth in the firm’s equity except that our relation
applies broadly to all of the firm’s investors’ investments and not only
common equity. That is, (1 – d) can be interpreted as the “retention ratio”
(i.e., the percentage of NOPAT retained by the firm on behalf of all
investors to reinvest in the firm’s operations after making dividend and
interest payments) and KA can be viewed as the expected return on those
retained net operating profits.
4) A crucial assumption is that the required return on the firm’s debt and
equity is not affected by the choice of pay-out ratio, d. That is, both
creditors and equity holders are indifferent between receiving their returns
in the form of capital gains or dividends / interest income. This is
essentially the famous “dividend irrelevance” argument of Miller and
Modigliani (1961) except that it is now extended to encompass both
creditors and equity holders. If this form of “dividend irrelevance” holds,
then the required return on the investors’ investments (KA) is not affected
by the firm’s choice of d because the firm’s cost of debt (KD) and equity
(KS), as well as the firm’s capital structure, are unaffected by d.40
5) Another implicit assumption, again consistent with Miller and Modigliani,
is that capital structure is irrelevant in terms of its effect on KA and firm
value.
6) As in Miller and Modigliani (1961), the true value of the firm is therefore
based solely on the firm’s operating cash flows (denoted here as CFA) and
the required return on the firm’s investments (defined here as KA). This
intuition is formalized by using the above valuation equation and
40
One can view the yield-to-maturity (YTM) of the firm’s debt as being comprised of a current yield
component and a capital gains component, similar to the way one views the firm’s stock return as being
comprised of a dividend yield and a capital gain/loss. Thus, M-M’s dividend irrelevance theory can apply
to the firm’s YTM as long as there are no differences in the tax rates for interest payments and capital
gains/losses related to the firm’s bonds.
52
substituting the relevant definitions of the CFA and gA variables, as
follows:
VA =
d ⋅ NOPATt +1
d ⋅ NOPATt +1
d ⋅ NOPATt +1 NOPATt +1
CFA
=
=
=
=
K A − g A K A − (1 − d ) ⋅ K A K A − K A + d ⋅ K A
d ⋅KA
KA
According to the above formula, the equilibrium value of VA can simply be
computed by dividing the firm’s expected NOPAT by the current return required by the
firm’s investors. Thus, the choice of an expected growth rate, gA, is not explicitly
required in order to estimate the firm’s overall value. Clearly, the KA term will have a
growth estimate implicitly embedded in it but the analyst does not need to explicitly
separate out this estimate of gA in order to value the firm using the CGM technique.
Once again, this result holds only when the above assumptions are all met. Deviations
from these assumptions will clearly not allow the CGM to be simplified to the above
solution.
The following numerical solution demonstrates the independence between growth
rate assumptions and firm value when the above assumptions are met.
Assume:
d = 50% (i.e., the firm pays out half of its expected NOPAT to creditors and equity
holders);
NOPATt+1 = $10.00;
KA = 20%; and therefore
gA = (1 – d) ⋅ KA = (1-.50) ⋅ 20% = 10%; and
CFA = d ⋅ NOPATt+1 = .50 ⋅ $10.00 = $5.00.
Using our valuation equation, the value of the firm can be computed as:
VA = $5.00 / (.20 - .10) = $5.00 / .10 = $50.00.
Now, if we assume a different pay-out ratio, say 80%, then we can re-compute the value
of the firm as:
VA = (.80 ⋅ $10.00) / (.20 - ((1-.80) ⋅ .20)) = $8.00 / (.20 - .04) = $50.00.
Once again, the value of the firm is $50.00 even though our current growth rate
assumption is now 4% rather than 10% assumed in the first part of this example. In fact,
53
both estimates of the firm’s value are equivalent to simply dividing the expected NOPAT
by KA. That is, we can obtain the same value for the firm as follows:
VA = $10.00 / .20 = $50.00.
This latter calculation is, in effect, the same value obtained if we were to assume a
zero growth rate. Thus, the above derivations suggest that assuming a zero growth rate
for the paper’s economic profit relation might not be that egregious for our purposes as
long as the aforementioned assumptions are relatively close to real world behavior. That
is, assuming an explicit growth rate is not necessary in our model since it gives the same
valuation estimate as long as: 1) the firm’s pay-out policy is constant (and irrelevant), 2)
growth is constant and can be estimated by the product of the firm’s required return and
retention ratio, and 3) the firm’s capital structure is irrelevant.
54