8 Equity Valuation Using Multiples

Journal of Accounting
Research Vol. 40 No. 1 March

2002 Printed in U.S.A.
Equity Valuation Using Multiples

∗ ‡
JING LIU , D O R O N N I S S I M ,† A N D J A C O B T H O M A S
Received 2 January 2000; accepted 27 July 2001
ABSTRACT
We examine the valuation performance of a comprehensive list of value

drivers and find that multiples derived from forward earnings explain stock
prices remarkably well: pricing errors are within 15 percent of stock prices
for about half our sample. In terms of relative performance, the following
general rankings are observed consistently each year: forward earnings
measures are followed by historical earnings measures, cash flow measures
and book value of equity are tied for third, and sales performs the worst.
Curiously, performance declines when we consider more complex measures
of intrinsic value based on short-cut residual income models. Contrary to the
popular view that different industries have different “best” multiples, these
overall rankings are observed consistently for almost all industries examined.
Since we require analysts’ earnings and growth forecasts and positive values
for all measures, our results may not be representative of the many firm-
years excluded from our sample.
1. Introduction
In this study we examine the proximity to stock prices of valuations
generated by multiplying a value driver (such as earnings) by the
corresponding multiple, where the multiple is obtained from the ratio of
stock price to that value driver for a group of comparable firms. While
multiples are used extensively in practice, there is little published research
in the academic literature documenting the absolute and relative
performance of different
∗
University of California at Los Angeles;
† Columbia University; Columbia University. We
thank Richard Leftwich and an anonymous referee for their many useful suggestions. We also
received helpful comments from David Aboody, Sanjay Bhagat, Ted Christensen, Glen Hansen,
Jack Hughes, Jim Ohlson, Stephen Penman, Phil Shane, Michael Williams, and seminar partici-
pants at the AAA Annual Meeting at Philadelphia, University of Colorado, Columbia University,
Copenhagen Business School, Ohio State University, and UCLA.
135
Copyright ∗C , University of Chicago on behalf of the Institute of Professional Accounting, 2002
1 J. LIU, D. NISSIM, AND J.
1
multiples. We seek to investigate the performance of a comprehensive
list of multiples, and also examine a variety of related issues, such as the
variation in performance across industries and over time and the perfor-
mance improvement obtained by using alternative approaches to compute
multiples.
Although the actual valuation process used by market participants is un-
observable, we assume that stock prices can be replicated by
comprehensive valuations that convert all available information into
detailed projections of future flows. Given this efficient markets
framework for traded stocks, what role do multiples play? Even in
situations where market valuations are absent, either because the equity is
privately-held or because the proposed publicly traded entity has not yet
been created (e.g., mergers and spinoffs), is there a role for multiples vis-
a`-vis comprehensive valuations? While the multiple approach bypasses
explicit projections and present value calculations, it relies on the same
principles underlying the more comprehensive approach: value is an
increasing function of future payoffs and a decreasing function of risk.
Therefore, multiples are used often as a substitute for comprehensive
valuations, because they communicate efficiently the essence of those
valuations. Multiples are also used to complement comprehensive val-
uations, typically to calibrate those valuations and to obtain terminal values.2
In effect, our study documents the extent to which different value drivers
serve as a summary statistic for the stream of expected payoffs, and compa-
rable firms resemble the target firm along important value attributes, such
as growth and risk. We first evaluate value drivers using the conventional
ratio representation (i.e., price doubles when the value driver doubles). To
identify the importance of incorporating the average effect of omitted vari-
ables, we extend the ratio representation to allow for an intercept in the
price/value driver relation. To study the impact of selecting comparable
firms from the same industry, we contrast our results obtained by using in-
dustry comparables (the middle category from the Sector/Industry/Group
classification provided by IBES) with results obtained when all firms avail-
able each year are used as comparables. As in prior research, we evaluate
performance by examining the distribution of pricing errors (actual price
less predicted price, scaled by actual price).
The value drivers we consider include measures of historical cash flow,
such as cash flow from operations and EBITDA (earnings before interest,
1
Studies offering descriptive evidence include Boatsman and Baskin [1981], LeClair
[1990], and Alford [1992]. Recently, a number of studies have examined the role of
multiples for firm valuation in specific contexts, such as tax and bankruptcy court cases and
initial public offerings (e.g., Beatty, Riffe, and Thompson [1999], Gilson, Hutchkiss, and
Ruback [2000], Kim and Ritter [1999], and Tasker [1998]).
2
Another very different role for multiples that has been examined in the literature is the
identification of mispriced stocks. We do not investigate that role because we assume market
efficiency. Two such market inefficiency studies are Basu [1977] and Stattman [1980], where
portfolios derived from earnings and book value multiples are shown to earn abnormal
returns.
EQUITY VALUATION USING MULTIPLES 137
taxes, depreciation, and amortization), and historical accrual-based mea-
sures, such as sales, earnings, and book value of equity. We also consider
forward-looking measures derived from analysts’ forecasts of EPS
(earnings per share) and long-term growth in EPS, such as 2-year out
consensus EPS forecasts and PEG (price-earnings-growth) ratios (e.g.,
Bradshaw [1999a; 1999b]). Since sales and EBITDA should properly be
associated with enterprise value (debt plus equity), rather than equity
alone, for those two value drivers we also consider multiples based on
enterprise value (market value of equity plus book value of debt). Finally,
we consider short-cut intrinsic value measures based on the residual
income model that have been used recently in the academic literature (e.g.,
Frankel and Lee [1998], and Gebhardt, Lee, and Swaminathan [2001]).
The following is an overview of the relative performance of different
value drivers: (1) forward earnings perform the best, and performance
improves if the forecast horizon lengthens (1-year to 2-year to 3-year out EPS
forecasts) and if earnings forecasted over different horizons are aggregated;
(2) the intrinsic value measures, based on short-cut residual income
models, perform considerably worse than forward earnings;3 (3) among
drivers derived from historical data, sales performs the worst, earnings
performs better than book value; and IBES earnings (which excludes many
one-time items) out- performs COMPUSTAT earnings; (4) cash flow
measures, defined in various forms, perform poorly; and (5) using
enterprise value, rather than equity value, for sales and EBITDA further
reduces performance.
Turning from relative performance to absolute performance, forward
earnings measures describe actual stock prices reasonably well for a majority
of firms. For example, for 2-year out forecasted earnings, approximately
half the firms have absolute pricing errors less than 16 percent. The
dispersion of pricing errors increases substantially for multiples based on
historical drivers, such as earnings and cash flows, and is especially large
for sales multiples.
Some other important findings are as follows: (1) performance improves
when multiples are computed using the harmonic mean, relative to the
mean or median ratio of price to value driver for comparable firms, (2)
performance declines substantially when all firms in the cross-section each
year are used as comparable firms, (3) allowing for an intercept improves
performance mainly for poorly-performing multiples, and (4) relative per-
formance is relatively unchanged over time and across industries.
Our findings have a number of implications for valuation research. First,
we confirm the validity of two precepts underlying the valuation role of
accounting numbers: (1) accruals improve the valuation properties of
cash flows, and (2) despite the importance of top-line revenues, its value
3
Bradshaw [1999a and 1999b] observes results that are related to ours. He finds that val-
uations based on PEG ratios (this ratio of forward P/E to forecast growth in EPS is described
later in section 3.1) explain more variation in analysts’ target prices and recommendations
than more complex intrinsic value models.
relevance is limited until it is matched with expenses. Second, we confirm

that forward earnings contain considerably more value-relevant information
than historical data, and they should be used as long as earnings forecasts
are available. Third, contrary to general perception, different industries are
not associated with different “best multiples.” Finally, our investigation of
the signal/noise tradeoff associated with the more complex intrinsic value
drivers based on the residual income model suggests that even though
these measures utilize more information than that contained in forward
earnings and impose a structure derived from valuation theory on that
information, measurement error associated with the additional variables
required, especially terminal value estimates, negatively impacts
performance.4
These findings are associated with certain caveats. Since we exclude
firms not covered by IBES, typically firms with low and medium market
capitaliza- tion, we are uncertain about the extent to which our results
extend to those firms. Even firms with IBES data are not fully represented
in our sample, since we exclude firm-years with negative values for any
value driver. In particular, our results may not be descriptive of start-up
firms reporting losses and high growth firms with negative operating cash
flows.
2. Prior Research
While textbooks on valuation (e.g., Copeland, Koller, and Murrin [1994],
Damodaran [1996], and Palepu, Healy, and Bernard [2000]) devote con-
siderable space to discussing multiples, most published papers that study
multiples examine a limited set of firm-years and consider only a subset of
multiples, such as earnings and EBITDA. Also, comparisons across different
studies are hindered by methodological differences.
Among commonly used value drivers, historical earnings and cash flows
have received most of the attention. Boatsman and Baskin [1981] compare
the valuation accuracy of P/E multiples based on two sets of comparable
firms from the same industry. They find that valuation errors are smaller
when comparable firms are chosen based on similar historical earnings
growth, relative to when they are chosen randomly. Alford [1992] inves-
tigates the effects of choosing comparables based on industry, size (risk),
and earnings growth on the precision of valuation using P/E multiples. He
finds that pricing errors decline when the industry definition used to se-
lect comparable firms is narrowed from a broad, single digit SIC code to
classifications based on two and three digits, but there is no additional im-
provement when the four-digit classification is considered. He also finds
that controlling for size and earnings growth, over and above industry
controls, does not reduce valuation errors.
4
Given our efficient markets framework, we do not investigate here whether the relatively
poor performance of the intrinsic value measures is due to an inefficient market that values
stocks using multiples of forward earnings. We find evidence inconsistent with that
explanation in a separate paper (Liu, Nissim, and Thomas [2001]).
Kaplan and Ruback [1995] examine the valuation properties of the dis-
counted cash flow (DCF) approach for highly leveraged transactions. While
they conclude that DCF valuations approximate transacted values reason-
ably well, they find that simple EBITDA multiples result in similar valuation
accuracy. Beatty, Riffe, and Thompson [1999] examine different linear com-
binations of value drivers derived from earnings, book value, dividends,
and total assets. They derive and document the benefits of using the
harmonic mean, and introduce the price-scaled regressions we use. They
find the best performance is achieved by using (1) weights derived from
harmonic mean book and earnings multiples and (2) coefficients from
price-scaled regressions on earnings and book value.
In a recent study, Baker and Ruback [1999] examine econometric prob-
lems associated with different ways of computing industry multiples, and
compare the relative performance of multiples based on EBITDA, EBIT (or
earnings before interest and taxes), and sales. They provide theoretical and
empirical evidence that absolute valuation errors are proportional to value.
They also show that industry multiples estimated using the harmonic mean
are close to minimum-variance estimates based on Monte Carlo
simulations. Using the minimum-variance estimator as a benchmark, they
find that the harmonic mean dominates alternative simple estimators such
as the simple mean, median, and value-weighted mean. Finally, they use the
harmonic mean estimator to calculate multiples based on EBITDA, EBIT,
and sales, and find that industry-adjusted EBITDA performs better than
EBIT and sales.
Instead of focusing only on historical accounting numbers, Kim and
Ritter [1999], in their investigation of how initial public offering prices
are set using multiples, add forecasted earnings to a conventional list of
value drivers, which includes book value, earnings, cash flows, and sales.
Consistent with our results, they find that forward P/E multiples (based
on forecasted earnings) dominate all other multiples in valuation accuracy,
and that the EPS forecast for next year dominates the current year EPS
forecast.
Using large data sets could diminish the performance of multiples,
since the researcher selects comparable firms in a mechanical way. In con-
trast, market participants may select comparable firms more carefully and
take into account situation-specific factors not considered by researchers.
Tasker [1998] examines across-industry patterns in the selection of com-
parable firms by investment bankers and analysts in acquisition transac-
tions. She finds the systematic use of industry-specific multiples, which is
consistent with different multiples being more appropriate in different
industries.5
5
Since it is not clear whether the objective of investment bankers/analysts is to achieve the
most accurate valuation in terms of smallest dispersion in pricing errors, our results may not
be directly comparable with those in Tasker [1998].
3. Methodology
3.1 VALUE DRIVERS
We group the value drivers based on whether they refer to cash flows
or accruals, whether they relate to stocks or flows, and whether they are
based on historical or forward-looking information. 6 We provide a brief
description here for some variables that readers may not be familiar with
(details for all variables are provided in Appendix A) and then describe
the links drawn in the prior literature between different value drivers
and equity value. (1) Accrual flows: sales, actual earnings from COMPUS-
TAT (CACT) and actual earnings from IBES (IACT). (2) Accrual stocks:
book value of equity (BV). (3) Cash flows: cash flow from operations
(CFO), free cash flow to debt and equity holders (FCF), maintenance cash
flow (MCF), equal to free cash flows for the case when capital expendi-
tures equal depreciation expense, and earnings before interest, taxes, de-
preciation and amortization (EBITDA). (4) Forward looking information:
consensus (mean) one year and two year out earnings forecasts
(EPS1, and EPS2), and two forecasted earnings-growth combinations
(EG1 =EPS2∗(1 +g) and EG2 EPS2 ∗g), which are derived from EPS2
and g (the mean= long-term EPS growth forecast provided by analysts).
(5) Intrinsic value measures (P1∗, P2∗, and P3∗): These measures are based
on the residual income (or abnormal earnings) valuation approach, where
equity value equals the book value today plus the present value of fu-
ture abnormal earnings. Abnormal earnings for years+ 1 to 5, projected
from explicit or implied earnings forecasts for those years, are the same
for the first two measures. We assume that after year+5, abnormal earn-
ings remain constant for P1∗ and equal zero for P2∗. For P3∗, we as-
sume the level of profitability (measured by ROE) trends linearly from
the level implied by earnings forecasted for year + 3 to the industry me-
dian by year + 12, and abnormal earnings remains constant thereafter.
(6) Sum of forward earnings (ES1 and ES2) : These measures aggregate the
separate forward earnings forecasts. ES1 is the sum of the EPS forecasts for
years +1 to 5, and ES2 is the sum of the present value of those forecasts. 7
As explained later, these two measures are designed to provide evidence on
the poor performance of the intrinsic value measures.
Value drivers based on accruals, which distinguish accounting numbers
from their cash flow counterparts, have been used extensively in multiple
valuations. Book value and earnings, which are often assumed to repre-
sent “fundamentals,” have been linked formally to firm value (e.g., Ohlson
[1995] and Feltham and Ohlson [1995]). Although the use of sales as a
value driver has less theoretical basis, relative to earnings and cash flows,
6
Some value drivers are not easily classified. For example, Sales, which we categorize as an
accrual flow, could contain fewer accruals than EBITDA, which we categorize as a cash flow
measure.
7
We thank Jim Ohlson for suggesting ES1.
we consider it because of its wide use in certain emerging industries where
earnings and cash flow are perceived to be uninformative.
At an intuitive level, accounting earnings could be more value-relevant
than reported cash flows because some cash flows do not reflect value crea-
tion (e.g., asset purchases/sales), and accruals allow managers to reflect
their judgment about future prospects. The COMPUSTAT EPS measure we
consider is reported primary EPS excluding extraordinary items and
discon- tinued operation and the IBES EPS measure is derived from
reported EPS by deleting some one-time items, such as write-offs and
restructuring charges. To the extent that the IBES measure is a better proxy
for “permanent” or “core” earnings expected to persist in the future, it
should exhibit superior performance.
The use of cash flow multiples in practice appears to be motivated by
the implicit assumption that reported cash flow is the best available proxy
for the future cash flows that underlie stock prices, and by the feeling that
they are less susceptible to manipulation by management. The four cash
flow measures we consider remove the impact of accruals to different ex-
tents. EBITDA adjusts pre-tax earnings to debt and equity holders for the
effects of depreciation and amortization only. CFO deducts interest and
taxes from EBITDA and also deducts the net investment in working capital.
FCF deducts from CFO net investments in all long-term assets, whereas
MCF only deducts from CFO an investment equal to the depreciation
expense for that year.
The potential for analysts’ EPS forecasts to reflect value-relevant data not
captured by historical earnings has long been recognized in the literature.
For example, Liu and Thomas [2000] find that revisions in analysts’
earnings forecasts along with changes in interest rates explain a
substantially larger portion of contemporaneous stock returns than do
earnings surprises based on reported earnings. Consensus estimates are
often available for forecasted earnings for the current year (EPS1) and the
following year (EPS2). Consen- sus estimates are also frequently available
for the long-term growth forecast (g ) for earnings over the next business
cycle (commonly interpreted to re-
present the next 5 years). The measure EG1 =( EPS2∗(1 g)), which is an
estimate of three-year out earnings, should reflect value better than EPS2,
if three-year out earnings reflect long-term profitability better than two-
year out earnings.
While the second earnings-growth measure EG2 (=EPS2∗g) also com-
bines the information contained in EPS2 and g , it imposes a different
struc-
ture. Recently, analysts have justified valuations using the following rule of
thumb: forward P/E ratios (current price divided by EPS2) should equal g .
If, for example, EPS is expected to grow at 30 percent over the next
business cycle, forward P/E should equal 30. Stated differently, the ratio of
forward P/E to g (referred to as the PEG ratio) should equal 1. For certain
sectors, such as technology, analysts have suggested that even higher PEG
ratios are appropriate. Using EG2 as a value driver is equivalent to using a
PEG ratio obtained from the PEG ratios of comparable firms.
Several recent studies provide evidence that the intrinsic values derived
using the residual income model explain stock prices (e.g., Abarbanell and
Bernard [2000], Claus and Thomas [2000]) and returns (e.g., Liu and
Thomas [2000], Liu [1999]). The three generic patterns we use to project
abnormal earnings past a horizon date have been considered in Frankel
and Lee [1998] (P1∗), Palepu, Healy, and Bernard [2000] (P2∗), and
Gebhardt,
Lee, and Swaminathan [2001] (P3∗). Although these generic approaches
do not allow for firm-specific growth patterns for abnormal earnings past a
terminal date, they offer a convenient alternative to comprehensive valua-
tions as long as observed long-term growth patterns tend to converge to
the generic patterns assumed by these measures.
While the two final earnings sum measures we consider (ES1 and ES2)
have not been discussed in the literature, we examine them to understand
better the poor performance observed for the intrinsic value measures. ES1
simply sums the earnings forecasted for years + 1 to 5, and ES2 attempts
to control heuristically for the timing and risk of the different earnings
numbers by discounting those forecasted earnings before summing them.
If both ES1 and ES2 perform poorly, relative to simple forward earnings
multiple (e.g., EPS2) the earnings projected for years+ 3 to 5 probably
contain considerable error. If ES1 performs well, but ES2 does not, esti-
mation errors in the firm-specific discount rates used to discount flows at
different horizons are responsible for the poor performance of the intrinsic
value measures. If both ES1 and ES2 perform well, the poor performance
of intrinsic value measures is probably because the assumed terminal
values in each case diverge substantially from the market’s estimates of
terminal values.
We also consider the impact of using enterprise value (TP), rather than
equity value, for sales and EBITDA multiples, since both value drivers
reflect an investment base that includes debt and equity. We measure TP as
the market value of equity plus the book value of debt. To obtain predicted
share prices, we estimate the relation between TP and the value driver for
comparable firms, generate predicted TP for target firms, and then subtract
the book value of their debt.
3.2 TRADITIONAL MULTIPLE VALUATION
In the first stage of our analysis, we follow the traditional ratio represen-
tation and require that the price of firm i (from the comparable group) in
year t ( pit ) is directly proportional to the value driver:
pit = βt xit + εit (1)
where xit is the value driver for firm i in year t , βt is the multiple on the value
driver and εt is the pricing error. To improve efficiency, we divide equation
(1) by price:
xit εit
1 = βt + . (2)
pit pit
Baker and Ruback [1999] and Beatty, Riffe, and Thompson [1999] demon-
strate that estimating the slope using equation (2) rather than equation (1)
is likely to produce more precise estimates because the valuation error (the
residual in equation (1)) is approximately proportional to price.
When estimating βt , we elected to impose the restriction that expected
pricing errors (E[ε/p]) be zero, even though an unrestricted estimate for
βt from equation (2) offers a lower value of mean squared pricing error.
(Throughout the paper, the term “pricing error” refers to proportional
pricing error, or the pricing error scaled by share price.) Empirically, we
find that our approach generates lower pricing errors for most firms,
relative to an unrestricted estimate, but it generates substantially higher
errors in the tails of the distribution. 8 By restricting ourselves to unbiased
pricing errors, we are in effect assigning lower weight to extreme pricing
errors, relative to the unrestricted approach. We are also maintaining
consistency with the tradition in econometrics that strongly prefers
unbiasedness over reduced dispersion.
βt is the only parameter to be estimated in equation (2), and it is deter-
mined by the restriction we impose that pricing errors be zero on average,
i.e., E [ pεitit ]=0. Rearranging terms in equation (2) and applying the ex-
pected value operator, we obtain the harmonic mean of pit /xit as an
estimate for βt :
εit
E βx it 1
pit = 1−
pit = 0 ⇒ βt = xit (3)
E E pit
We multiply this harmonic mean estimate for βt by the target firm’s value
driver to obtain a prediction for the target firm’s equity value, and calculate
the pricing error as follows:9
εit
− βˆt xi t
pit = pi t . (4)
pit
To evaluate the performance of multiples, we examine measures of disper-
sion, such as the interquartile range, for the pooled distribution of εit / pit .
8
We estimated equation (2) for comparable firms from the cross-section without imposing
the unbiasedness restriction. (When using comparable firms from the same industry, the esti-
mated multiples for this unrestricted case generated substantial pricing errors.) We find that
the pricing error distributions for all multiples are shifted to the right substantially, relative to
the distributions for the restricted case reported in the paper (our distributions tend to peak
around zero pricing error). This shift to the right indicates that the multiples and predicted
valuations for the unrestricted case are on average lower than ours. We find that the bias cre-
ated by this shift causes greater pricing errors for the bulk of the firms not in the tails of the
distribution, relative to our restricted case.
9
While some studies measure pricing error as predicted value minus price (e.g., Alford
[1992]) we measure pricing error as price minus predicted value.
3.3 INTERCEPT ADJUSTED MULTIPLES
For the second stage of our analysis, we relax the direct proportionality
requirement and allow for an intercept:
pit = αt + βt xit + εit . (5)
Many factors, besides the value driver under investigation, affect price, and
the average effect of such omitted factors is unlikely to be zero.10 Since
the intercept in equation (5) captures the average effect of omitted factors,
allowing for an intercept should improve the precision of out of sample
predictions.
As with the simple multiple approach, we divide equation (5) by price to
improve estimation efficiency:
1 xit εit
1 = αt + βt + , (6)
pit pit pit
Estimating equation (6) with no restrictions minimizes the square of
pricing errors, but the expected value of those errors is nonzero. 11 For the
reasons mentioned in section 3.2, we again impose the restriction that
pricing errors be unbiased.12 That is, we seek to estimate the parameters αt
and βt that minimize the variance of εit / pit , subject to the restriction that
the expected value of εit / pit is zero:
min var(εit / pit ) = var[( pit − αt − βt · xit )/ pit ]
α,β
1 xit
= var 1 − α + βt (7a)
t
pit pit
εit
s.t. E = 0. (7b)
pit
It can be shown that the estimates for αt and βt that satisfy (7a) and (7b)
are as follows
xt
E 1
1 xt 1
pt
β =
var pt — cov pt , pt
E pt (8)
1 xt
t
1 2 xt 2 xt 1 1 xt ,
pt pt
E pt var pt
+E pt var pt − 2E pt E pt cov
x
1−β E t
αt = t pt (9)
1
E pt
10
If the relation between price and the value driver is non-linear, the omitted factors
include higher powers of the value driver.
11
In general, this bias could be removed by allowing for an intercept. That avenue is not
available, however, when the dependent variable is a constant (=1), since the intercept cap-
tures all the variation in the dependent variable, thereby making the independent variables
redundant.
12
As with equation (2), pricing errors from the unrestricted approach for equation (6) are
higher for most firms (in the middle of the distribution) but there are fewer firms in the tails
of the distribution. (See footnote 8.)
where the different Et [.], var(.), and cov(.) represent the means, variances,
and covariances of those expressions for the population, and are estimated
using the corresponding sample moments for the comparable group. We
compute prediction errors, defined by equation (10), and examine their
distribution to determine performance.
εit
ˆ
pit = pi t − αˆ t − β t xi t . (10)
pit
4. Sample and Data

To construct our sample, we merge data from three sources: accounting
numbers from COMPUSTAT; price, analyst forecasts, and actual earnings
per share from IBES; and stock returns from CRSP. As of April of each year
(labeled year t +1), we select firm-years that satisfy the following criteria:
(1) COMPUSTAT data items 4, 5, 12, 13, 25, 27, 58, and 60 are non-missing
for the previous fiscal year (year t); (2) at least 30 monthly returns (not
nec- essarily contiguous) are available on CRSP from the prior 60 month
period;
(3) price, actual EPS, forecasted EPS for years t+ 1 and t 2, and the long
term growth forecast are available in the IBES summary file; and (4) all
price to value-driver ratios for the simple multiples (excluding the three P ∗
and two ES measures) lie within the 1st and 99th percentiles of the pooled
distribution. The resulting sample, which includes 26,613 observations
between
1982 and 1999, is used for the descriptive statistics reported in table 1.
For the results reported after table 1, we impose three additional
requirements: (1) share price on the day IBES publishes summary
forecasts in April is greater than or equal to $2; (2) all multiples are
positive; and (3) each industry-year combination has at least five
observations. The first condition avoids large pricing errors in the second
stage analysis (where an intercept is allowed) due to firms with low share
prices. The second condition avoids negative predicted prices, and the third
condition ensures that the comparable group is not unreasonably small.
Regarding the second condition, we discovered that many firm-years were
eliminated because of negative values for two cash flow measures: free cash
flow and maintenance cash flow. More important, preliminary analysis
indicated that both measures exhi- bited larger pricing errors than the
other measures. As a result, we felt that these two measures were
unsuitable for large sample multiples analyses and dropped them from the
remainder of our study. The final sample has 19,879 firm-years.
Our sample represents a small fraction of the NYSE + AMAX NASDAQ
population that it is drawn from: the fraction included varies between 11
percent earlier in the sample period to 18 percent later in our sample
period. The fraction of market value of the population represented,
however, is considerably larger because the firms deleted for lack of
analyst data are on average much smaller than our sample firms. Also,
firm-years excluded because they have negative value drivers are
potentially different from our
TABLE 1
Distribution of Ratio of Value Driver to Price
Summary descriptions of the variables are as follows (all amounts are on per share basis): P is
stock price; BV is book value of equity; MCF is maintenance cash flow (equivalent to free cash
flow when depreciation expense equals capital expenditure); FCF is free cash flow to debt and
equity holders; CFO is cash flow from operations; EBITDA is earnings before interest, taxes,
depreciation and amortization; CACT is COMPUSTAT earnings before extraordinary items;
IACT is IBES actual earnings; EPS1 and EPS2 are one year out and two year out EPS forecasts;
EG1 = EPS2 ∗(1 + g), EG2 = EPS2 ∗g, where g is the growth forecast; and TP is enterprise
value (market value of equity + book value of debt).
5
Et (EPSt s − kt BVt s 1) Et (EPSt s − kt BVt 4)
P 1∗t = BVt + + − + +
+ s + s
,
s (1 + kt ) kt (1 + kt )
=1
Et (EPSt s − kt BVt s 1 )
5
+ +−
P 2∗t = BVt
s (1 + kt )s
+ =1
2
Et (EPSt s − kt BVt s )
1
[Et (ROEt s ) − kt ]BVt s 1
11
∗
P3 t = BVt + s +− + s +−
+
s =1 (1 + kt (1 + kl )
s =3
+
)
[Et (ROEt+12) − kt ]BVt+11
+ ,
kt (1 + kt )11
where Et (ROEt+s ) for s =4, 5, . . . , 12 is forecasted using a linear interpolation to the industry
median ROE. The industry median ROE is calculated as a moving median of the past ten years’
ROE of all firms in the industry. To eliminate outliers, industry median ROEs are Winsorized
at the risk free rate and 20%.
5 5
Et (EPSt s )
ES 1t = Et (EPSt+s ), and ES 2t +
= s .
s =1 s =1
( 1 + kt )
Sample firms are collected in April each year between 1982 and 1999, and we require non-
missing values for a set of core financial variables from COMPUSTAT, 30 non-missing monthly
returns from the prior 60 months from CRSP, and non-missing share price, 1 and 2-year out
EPS forecasts and long-term growth forecasts from IBES. The sample is trimmed at 1% and
99% for each value driver using the pooled distribution, resulting in a sample of 26,613 firm-
years.
Mean Median SD 1% 5% 10% 25% 75% 90% 95% 99%
BV/P 0.549 0.489 0.336 0.050 0.131 0.184 0.308 0.717 0.985 1.180 1.620
MCF/P 0.035 0.035 0.183 —0.566 − 0.171 − 0.076 − 0.002 0.074 0.145 0.238 0.626
FCF/P —0.025 0.002 0.252 − 1.008 − 0.379 − 0.218 − 0.069 0.050 0.131 0.234 0.648
CFO/P 0.093 0.079 0.190 —0.516 − 0.100 − 0.019 0.034 0.146 0.239 0.328 0.693
CACT/P 0.050 0.056 0.073 —0.249 − 0.043 0.005 0.033 0.080 0.108 0.130 0.178
IACT/P 0.057 0.059 0.060 —0.184 − 0.013 0.018 0.040 0.082 0.109 0.130 0.175
Ebitda/P 0.173 0.148 0.128 − 0.051 0.032 0.055 0.095 0.224 0.320 0.397 0.617
Sales/P 1.419 0.988 1.416 0.098 0.215 0.313 0.552 1.773 2.991 4.080 7.112
EPS1/P 0.073 0.070 0.037 − 0.026 0.024 0.036 0.052 0.092 0.117 0.137 0.178
EPS2/P 0.091 0.085 0.036 0.027 0.043 0.052 0.067 0.108 0.138 0.160 0.205
EG1/P 0.105 0.097 0.040 0.034 0.052 0.062 0.077 0.124 0.159 0.183 0.235
EG2/P 0.013 0.011 0.007 0.002 0.004 0.005 0.008 0.016 0.021 0.026 0.036
P1∗/P 0.708 0.658 0.296 0.222 0.318 0.383 0.500 0.863 1.086 1.264 1.660
P2∗/P 0.587 0.553 0.241 0.186 0.258 0.308 0.407 0.732 0.910 1.029 1.304
P3∗/P 0.652 0.577 0.366 0.125 0.203 0.266 0.393 0.834 1.120 1.330 1.918
ES1/P 0.525 0.489 0.202 0.164 0.259 0.310 0.389 0.624 0.794 0.912 1.168
ES2/P 0.350 0.334 0.125 0.111 0.173 0.209 0.265 0.417 0.517 0.588 0.723
Ebitda/TP 0.113 0.110 0.060 − 0.031 0.026 0.044 0.075 0.147 0.187 0.215 0.276
Sales/TP 0.939 0.708 0.788 0.086 0.169 0.234 0.396 1.234 1.925 2.495 3.981
sample, because they are more likely to be young firms and/or technology
firms. For these reasons, our results may not be descriptive of the general
population.
We adjust all per share numbers for stock splits and stock dividends
using IBES adjustment factors. If IBES indicates that the consensus forecast
for that firm-year is on a fully diluted basis, we use IBES dilution factors to
convert those numbers to a primary basis. We use a discount rate (kt ) equal
to the risk-free rate plus beta times the equity risk premium. The risk-free rate
is the 10-year Treasury bond yield on April 1 of year + t 1 and we assume the
equity premium is 5 percent. We estimate betas using monthly stock
returns and value-weighted CRSP returns over the 60 month period ending
in March+of year t 1. Since individual firm betas are measured with
considerable error, we set firm beta equal to the median beta of all firms in
the same beta decile.
For a subgroup of firm-years (less than 5 percent), we were able to
obtain mean IBES forecasts for all years in the five-year horizon. For all
other firms, with less than complete forecasts available between years 3
and 5, we generate forecasts by applying the mean long-term growth forecast
(g ) to the mean forecast for the prior year in the horizon; = i.e., epst+s
∗
epst+s−1 (1 g ).
We obtain book values for future years by assuming the “ex-ante clean
surplus relation” (ending book value in each future period equals beginning
book value plus forecasted earnings less forecasted dividends). Since
analyst forecasts of future dividends are not available on IBES, we assume
that the current dividend payout ratio will be maintained in the future. We
measure the current dividend payout as the ratio of the indicated annual
cash dividends to the earnings forecast for year + t 1 (both obtained from
the IBES summary file).13 To minimize biases that could be induced by
extreme dividend payout ratios (caused by forecast+ t 1 earnings that are
close to zero), we Winsorize payout ratios to lie between 10% and 50%.
The results are relatively insensitive to assumed payout ratios, since
altering the payout has only a small effect on future book values and an
even smaller effect on computed future abnormal earnings.
5. Results
We report results separately for two sets of comparable firms with data
available that year: all firms from the same industry and all firms in the
cross-section. In either case, our analysis is always conducted out of
sample; i.e., the target firm is removed from the group of comparable firms.
Since the traditional approach involves the no-intercept relation and the
selection of comparable firms from the same industry, much of our
discussion focuses
13
Indicated annual dividends are four times the most recent quarter’s declared dividends.
We use EPS1 as the deflator because it varies less than current year’s earnings and is less
likely to be close to zero or negative.
on that combination, and most of our ancillary investigations relate only to

this combination.
To conduct the analysis using comparable firms from the same industry,
we considered alternative industry classifications. Because of the evidence
that SIC codes frequently misclassify firms (Kim and Ritter [1999]), we use
the industry classification provided by IBES, which is indicated to be based
loosely on SIC codes, but is also subject to detailed adjustments. 14 The IBES
industry classification has three levels (in increasing fineness): sector, in-
dustry, and group. We use the intermediate (industry) classification level
because visual examination of firms included in the same sector suggested
it was too broad a classification to allow the selection of homogeneous
firms, and tabulation of the number of firms in different groups suggested it
was too narrow to allow the inclusion of sufficient comparable firms (given
the loss of observations due to our data requirements).
Because of the volume of results generated, we report only some represen-
tative results and describe briefly some interesting extensions. In
particular, we do not report on tests of statistical significance we conducted
to compare differences in performance across value drivers. Our statistical
significance tests focus on the interquartile range as the primary measure
of dispersion that is relevant to us, and we conduct a bootstrap-type
analysis for each pair of value drivers for all sets of results reported in
tables 2 and 3. We generate “samples” of 19,879 firm-years by drawing
observations randomly from our sample, with replacement. For each trial
we compute the inter-quartile range for each multiple, and then compute
the difference between all pairs of inter-quartile ranges. This process is
repeated 100 times and a distribution is obtained for each pairwise
difference. (Increasing the number of trials beyond 100 has little impact on
the t-statistics generated.) We compute a t-statistic by dividing the mean
by the standard deviation for each of these distributions. Those t-statistics
(available from the authors) indicate that almost every pairwise difference
for the different interquartile ranges reported in our tables is statistically
significant (t-statistic greater than 2). In essence, readers can safely assume
that if differences in performance across value drivers are economically
significant, they are also statistically significant.
In section 5.4, we provide a summary of our results on variation in
performance of different value drivers across different industries and
years in our sample. Appendix B contains more details of the across-
industry variation in performance.
5.1 DESCRIPTIVE STATISTICS
Table 1 reports the pooled distribution of different value drivers, scaled

by price. While most distributions contain very few negative values, the
14
The IBES classification resembles the industry groupings suggested by Morgan Stanley.
TABLE 2
Distribution of Pricing Errors for Simple Multiples
Value and value drivers are assumed to be proportional: pit = βt xit +εit . Multiples are estimated
using harmonic means: βt = 1/Et ( xit ) in panels A& B, and medians are used in panel C.
pi t pit
εi t
Pricing error is pit =
Summary descriptions of the variables are as follows (all
−βˆ x pit
it amounts
are on per share basis): P is stock price; BV is book value of equity; CFO is cash flow from
operations; EBITDA is earnings before interest, taxes, depreciation and amortization; CACT is
COMPUSTAT earnings before extraordinary items; IACT is IBES actual earnings; EPS1, EPS2
are one year out and two year out EPS forecasts; EG1= EPS2 ∗(1 ∗
+ g), EG2 EPS2 g, where g
is =
growth forecast. TP is enterprise value (market value of equity plus book value of debt). When
TP multiples are used, predicted equity value is calculated by subtracting the book value of debt.
5
∗
Et (EPSt s − kt BVt 4)
P1 t = BVt + +− + +
+ s s
,
s (1 + kt ) kt (1 + kt )
=1
Et (EPSt s − kt BVt s 1)
5
∗
P2 t = BVt + +−
+ s
s (1 + kt )
=1
Et (EPSt s − kt BVt s 1 ) [Et (ROEt s ) − kt ]BVt s 1
11
2 +
∗
P3 t = BVt + s +− + s +−
+
s =1 (1 + kt (1 + kl )
s =3
)
+ ,
kt (1 + k1)11
where Et (ROEt+s )for s =4, 5, .. . , 12 is forecasted using a linear interpolation to the industry
5 5
Et (EPSt s )
ES1t = Et (EPSt+s ), and ES2t = +
.
s =1 s =1 (1 + kt )s
returns from the prior 60 months from CRSP, and non-missing share price, 1- and 2-year out
99% for each value driver. We then require a minimum $2 share price, that all value drivers be
positive, and that each industry-year combination have at least five observations. The final
sample contains 19,879 firm-years.
Mean Median SD 75%-25% 90%-10% 95%-5%

Panel A: Multiples based on harmonic means of firms from the same industry
BV/P −0.016 0.066 0.560 0.602 1.266 1.710
CFO/P −0.042 0.150 0.989 0.777 1.652 2.355
CACT/P −0.012 0.012 0.490 0.518 1.119 1.549
IACT/P −0.009 0.023 0.421 0.442 0.941 1.317
Ebitda/P −0.017 0.066 0.573 0.553 1.163 1.631
Sales/P −0.032 0.163 0.859 0.738 1.645 2.357
EPS1/P −0.005 0.015 0.321 0.348 0.744 1.037
EPS2/P −0.004 0.021 0.290 0.317 0.677 0.935
EG1/P −0.004 0.027 0.290 0.313 0.671 0.936
EG2/P −0.009 0.071 0.435 0.424 0.907 1.280
P1∗/P −0.006 0.037 0.351 0.377 0.807 1.118
P2∗/P −0.006 0.033 0.352 0.410 0.835 1.124
P3∗/P −0.009 0.055 0.443 0.469 0.983 1.377
ES1/P −0.004 0.026 0.285 0.307 0.661 0.915
T A B L E 2—continued
Mean Median SD 75%-25% 90%-10% 95%-5%

ES2/P −0.004 0.023 0.283 0.311 0.664 0.919
Ebitda/TP −0.013 0.024 0.645 0.619 1.266 1.753
Sales/TP −0.057 0.156 1.067 0.901 1.919 2.763
Panel B: Multiples based on harmonic means of firms from the entire cross-section
BV/P 0.000 0.080 0.565 0.744 1.343 1.732
CFO/P − 0.001 0.261 1.086 0.812 1.682 2.460
CACT/P 0.000 0.045 0.512 0.625 1.228 1.627
IACT/P 0.000 0.048 0.453 0.551 1.077 1.431
Ebitda/P 0.000 0.127 0.613 0.692 1.343 1.778
Sales/P − 0.001 0.265 0.943 0.801 1.766 2.531
EPS1/P 0.000 0.028 0.361 0.452 0.880 1.166
EPS2/P 0.000 0.030 0.320 0.388 0.781 1.038
EG1/P 0.000 0.041 0.317 0.368 0.754 1.024
EG2/P 0.000 0.077 0.500 0.526 1.168 1.608
P1∗/P 0.000 0.053 0.378 0.479 0.923 1.211
P2∗/P 0.000 0.052 0.396 0.549 0.986 1.250
P3∗/P 0.000 0.098 0.511 0.652 1.257 1.587
ES1/P 0.000 0.040 0.312 0.362 0.740 1.008
ES2/P 0.000 0.030 0.312 0.379 0.760 1.011
Ebitda/TP − 0.008 0.029 0.734 0.704 1.415 1.939
Sales/TP 0.026 0.284 1.337 1.097 2.374 3.648
Panel C: Multiples based on median of comparable firms from the same industry
BV/P − 0.110 0.000 0.638 0.649 1.407 1.962
CFO/P − 0.263 0.000 1.235 0.903 2.020 2.944
CACT/P − 0.041 0.000 0.527 0.513 1.164 1.640
IACT/P − 0.046 0.000 0.457 0.450 0.985 1.394
Ebitda/P − 0.111 0.000 0.676 0.581 1.283 1.814
Sales/P − 0.287 0.001 1.157 0.887 2.062 3.020
EPS1/P —0.028 − 0.001 0.351 0.350 0.761 1.074
EPS2/P − 0.033 0.000 0.314 0.320 0.696 0.980
EG1/P − 0.039 0.000 0.318 0.318 0.702 0.982
EG2/P —0.099 − 0.003 0.490 0.444 0.988 1.419
P1∗/P 0.014 0.029 0.441 0.425 0.982 1.604
P2∗/P −0.051 0.000 0.378 0.421 0.882 1.205
P3∗/P −0.087 0.000 0.497 0.499 1.070 1.522
ES1/P −0.039 0.000 0.312 0.312 0.691 0.967
ES2/P −0.035 0.000 0.306 0.319 0.691 0.961
Ebitda/TP −0.054 0.000 0.678 0.629 1.321 1.842
Sales/TP −0.290 0.000 1.312 1.038 2.279 3.361
incidence of negative values is higher for cash flow measures. In particular,

free cash flow and maintenance cash flow are often negative
(approximately 30% and 20% of the sample, respectively). Moreover, the
mean of FCF/P is negative, and the mean of MCF/P is close to zero,
despite the dele- tion of observations with extreme values (top and
bottom 1%). Including these two value drivers would result in a drastic
reduction in sample size. Since we discovered that they perform
considerably worse than other value
TABLE3
Distribution of Pricing Errors for Intercept Adjusted Multiples
Value and value drivers are assumed to be linear: pit = αt + βt xit εit . Multiple is estimated ex-
cluding the firm under valuation, by solving the following+constrained minimization problem:
min var(εit / pit ) = var[( pit − αt − βt · xit )/ pit ]]; s.t. εit
Eα,β = 0.
pit
εit
Pricing error is
it p −α −β x
= it pt it t it Summary descriptions of the variables are as follows (all
p
amounts are on per share basis): P is stock price; BV is book value of equity; CFO is cash
flow from operations; EBITDA is earnings before interest, taxes, depreciation and amor-
tization; CACT is COMPUSTAT earnings before extraordinary items; IACT is IBES actual
earnings; EPS1, EPS2 are one year out and two year out EPS forecasts; EG1 = EPS2 ∗(1 g),
EG2 = EPS2 ∗g, where g is growth forecast. TP is enterprise value (market value of equity plus
book value of debt). When TP multiples are used, predicted equity value is calculated by sub-
tracting the book value of debt.
5
∗
P1 t = BVt + +− + +
+ s s
,
s (1 + kt ) kt (1 + kt )
=1
5
∗
P2 t = BVt + +−
+ s
s (1 + kt )
=1
Et (EPSt s − kt BVt s 1 ) [Et (ROEt s ) − kt ]BVt s 1
11
2 +
P 3∗t = BVt + s +− + s +−
+
s =1 (1 + kt (1 + kl )
s =3
)
[Et (ROEt+12) − kt ]BVt−11
+ ,
kt (1 + k1)11
where Et (RO Et+s )for s =4, 5, .. . , 12 is forecasted using a linear interpolation to the industry
5
Et (EPSt s )
.5
ES1t = Et (EPSt+s ),and ES 2t +
.
s s (1 + kt )s
=1
= =1
returns from the prior 60 months from CRSP, and non-missing share price, 1- and 2-year out
99% for each value driver. We then require a minimum $2 share price, that all value drivers
be positive, and that each industry-year combination have at least five observations. The final
sample contains 19,879 firm-years.
Mean Median SD 75%-25% 90%-10% 95%-5%

Panel A: Comparable firms from the same industry
BV/P −0.027 0.058 0.538 0.538 1.153 1.599
CFO/P −0.037 0.091 0.621 0.577 1.237 1.765
CACT/P −0.018 0.027 0.439 0.433 0.953 1.352
IACT/P −0.015 0.029 0.387 0.390 0.843 1.179
Ebitda/P −0.025 0.052 0.488 0.482 1.041 1.459
Sales/P −0.039 0.101 0.646 0.614 1.312 1.841
EPS1/P −0.010 0.018 0.310 0.323 0.704 0.982
EPS2/P −0.008 0.019 0.290 0.305 0.656 0.917
EG1/P −0.007 0.023
EQUITY VALUATION USING MULTIPLES
0.291 0.306 0.654
153
0.912
EG2/P −0.012 0.055 0.400 0.402 0.855 1.195
T A B L E 3—continued
Mean Median SD 75%-25% 90%-10% 95%-5%
P1∗/P −0.013 0.034 0.348 0.365 0.775 1.078
P2∗/P −0.014 0.028 0.360 0.392 0.819 1.120
P3∗/P −0.020 0.045 0.428 0.433 0.919 1.276
ES1/P −0.007 0.022 0.285 0.301 0.648 0.888
ES2/P −0.007 0.021 0.283 0.302 0.649 0.891
Ebitda/TP −0.008 0.025 0.626 0.538 1.121 1.576
Sales/TP −0.038 0.094 0.838 0.730 1.532 2.154
Panel B: Comparable firms from the entire cross-section
BV/P 0.008 0.084 0.518 0.610 1.171 1.581
CFO/P 0.013 0.175 0.654 0.582 1.279 1.833
CACT/P − 0.002 0.053 0.447 0.513 1.006 1.385
IACT/P − 0.005 0.050 0.405 0.475 0.923 1.252
Ebitda/P 0.012 0.111 0.517 0.560 1.090 1.513
Sales/P 0.038 0.206 0.646 0.595 1.293 1.849
EPS1/P − 0.009 0.025 0.339 0.415 0.811 1.092
EPS2/P − 0.007 0.023 0.315 0.376 0.759 1.024
EG1/P − 0.003 0.040 0.314 0.361 0.743 1.016
EG2/P 0.031 0.120 0.459 0.495 1.060 1.459
P1∗/P − 0.007 0.049 0.359 0.445 0.855 1.141
P2∗/P − 0.007 0.042 0.385 0.517 0.934 1.200
P3∗/P − 0.010 0.078 0.455 0.556 1.047 1.380
ES1/P − 0.002 0.040 0.308 0.355 0.732 0.993
ES2/P − 0.006 0.028 0.307 0.366 0.739 0.994
Ebitda/TP 0.044 0.059 0.686 0.587 1.207 1.710
Sales/TP 0.143 0.246 1.010 0.835 1.860 2.805
drivers, we decided to remove them from the set of value drivers

considered hereafter.
Examination of correlations for different pairs of value drivers, scaled
by price, indicates that most value drivers are positively correlated, which
suggests that they share considerable common information. (These results,
which are available from the authors, show that Pearson correlations are
very similar to Spearman correlations.) The correlations among different
forward earnings and earnings-growth measures are especially high, gener-
ally around 90%. Interestingly, the correlations between the different for-
ward earnings measures and the three intrinsic value measures (P1 ∗, P2∗,
and P3∗) are much lower (only about 50 percent).
5.2 NO-INTERCEPT RELATION BETWEEN PRICE AND VALUE DRIVERS
The results of the first stage analysis, based on the ratio representation
(no intercept), are reported in table 2. Our primary results are those
reported in panel A, where comparable firms are selected from the same
industry. The results reported in panel B are based on comparable firms
including all firms in the cross-section. We report the following statistics
that describe the distribution of the pricing errors: two measures of
central tendency
(mean and median) and four measures of dispersion (the standard devia-
tion and three non-parametric dispersion measures: interquartile range,
90th percentile less 10th percentile, and 95th percentile less 5th
percentile). We separate our results into four categories: historical value
drivers, forward earnings measures, intrinsic value and earnings sum
measures, and multiples based on enterprise value.
To offer a visual picture of the relative and absolute performance of
different categories of multiples, we provide in figure 1, Panel A, the his-
tograms for pricing errors for the following selected multiples: EPS2, P1 ∗,
IACT, EBITDA, BV, and Sales. The histograms report the percentage of
the sample that lies within ranges of pricing error that are of width equal
to 10% of price (e.g. −0.1 to 0, 0 to 0.1, and so on). To reduce clutter,
we draw a smooth line through the middle of the top of each histogram
column, rather than provide the histograms for each of the multiples. We
consider a multiple superior if it has a more peaked distribution. The differ-
ences in performance across the different value drivers are clearly visible in
figure 1.
In general, the valuation errors we report are skewed to the left,
indicated by medians that are greater than means.15 While the skewness is
less noticeable for multiples based on forward earnings, it is quite
prominent for multiples based on sales and cash flows. Since predicted
values are bounded from below at zero, while they are not bounded above,
the right side of the pricing error +distribution cannot exceed 1, whereas
the left side is unbounded. One way to make the error distribution more
symmetrical is to take the log of the ratio of predicted price to observed
price (Kaplan and Ruback [1995]). Although we find that the distributions
are indeed more symmetric for the log pricing error metric, we report the
results using the pricing error metric because it is easier to interpret
absolute performance using that metric. We did, however, recalculate the
dispersion metrics reported here using the log pricing error metric to
confirm that all our inferences regarding relative performance remain
unchanged.
Examination of the standard deviation and the three non-parametric dis-
persion measures in panel A suggests the following ranking of multiples.
Forecasted earnings, as a group, exhibit the lowest dispersion of pricing
errors. This result is intuitively appealing because earnings forecasts
should reflect future profitability better than historical measures.
Consistent with this reasoning, performance increases with forecast
horizon. The dispersion measures for two-year out forward earnings
(EPS2) are lower than those for one-year out earnings (EPS1), and they are
lower still for three-year out forward earnings (EG1). The multiple derived
from PEG ratios (EG2) does not perform as well, however, suggesting that
the specific relation between
15
Means are close to zero because we require pricing errors to be unbiased, on average. Of
course, the observed means would deviate slightly from zero by chance, since the valuations
are done out of sample.
forward earnings and growth implied by the PEG ratio is not supported for
our sample of firm-years.
Multiples generated from the three intrinsic value measures (P1 ∗, P2∗,
and P3∗) also do not perform as well as the simple forward earnings
multiples. This result is consistent with measurement error in the esti-
mated discount rates, forecasted forward abnormal earnings, or assumed
terminal values for these three measures. The larger pricing errors asso-
ciated with P2∗ relative to P1∗ suggests that the terminal value assump-
tion of zero abnormal earnings past year +5 (for P2∗) is less appropriate
than the assumption of zero growth in abnormal earnings past year+5
(for P1∗). The very high pricing errors associated with P3∗ suggest that
the more complex structure of profitability trends imposed for this mea-
sure and/or the assumption that abnormal earnings remain constant past
year +12 at the level determined by current industry profitability are inap-
propriate.
The sharp improvement in performance observed for ES1 and ES2 sup-
ports the view that the poor performance of the intrinsic value measures is
caused by the generic terminal value assumptions. Recall that ES1 simply
aggregates the same five years’ earnings forecasts that are used for P1∗ and
P2∗, and ES2 discounts those forecasts using firm-specific discount rates (kt )
before summing them. The fact that the performance of ES2 is only slightly
worse than that of ES1 suggests that the estimated values of kt in the de-
nominators of the intrinsic value terms (used to discount future abnormal
earnings) are unlikely to be responsible for the poor performance of those
measures. The improvement in performance observed for ES1 over the
one-, two-, and three-year earnings forecasts suggests that despite the high
corre- lation observed among these forecasts for different horizons, they
contain independent value relevant information.
Comparing book value and earnings, the two popular accounting value
drivers, we find that earnings measures clearly outperform book value.
Pric- ing errors for book value (BV) exhibit greater dispersion than those
for COMPUSTAT earnings (CACT). The performance of historical earnings is
further enhanced by the removal of one-time transitory components. Con-
sistent with the results in Liu and Thomas [2000], pricing errors for IBES
earnings (IACT) exhibit lower dispersion than those for CACT. The sales
multiple performs quite poorly, suggesting that sales do not reflect prof-
itability until expenses have been considered.
Contrary to the belief voiced by some that cash flow measures are bet-
ter than accrual measures at representing future cash flows, our results
show that cash flows perform significantly worse than accounting earn-
ings. Between the two cash flow measures, CFO fares considerably worse
than EBITDA; in fact it is consistently the worst performer in all our
analyses.
The last two rows in panel A of table 2 relate to valuations for sales
and EBITDA multiples based on enterprise value. Even though enterprise
value is more appropriate for these two value drivers, the performance
for both multiples is even worse than that reported for the same mul-
tiples based on equity value. For example, the interquartile range of
pricing errors for sales increases from 0.738 to 0.901 when the base
is changed from equity value (P) to enterprise value (TP). We find
this result surprising and are unable to provide any rationale for why
such a result might be observed. (Similar results are reported in Alford
[1992].)
A frequent reason for using sales as a value driver is because earnings
and cash flows are negative. Since we restrict our sample to firms with pos-
itive earnings and cash flows, our sample is less likely to contain firms for
which the sales multiple is more likely to be used in practice. In partic-
ular, our sample is unlikely to contain emerging technology firms such
as Internet stocks. While some early research, such as Hand [1999] and
Trueman, Wong, and Zhang [2000], suggests that traditional value drivers
are inappropriate for such stocks, Hand [2000] finds that economic funda-
mentals, especially forward earnings forecasts, explain valuations for such
firms.
To provide some evidence on the impact of deleting firms with negative
values for earnings and cash flow measures, we examine the pricing errors
for sales and forward earnings multiples for a larger sample of 44,563 firm-
years with positive values for sales, EPS1, and EPS2. Although this sample
is obtained by applying the same conditions used to generate our primary
sample it is more than twice as large because we do not require positive
values for all the other value drivers. We find that even though the rel-
ative performance differences reported in table 2, panel A, are observed
again in this larger sample, the dispersion of pricing errors increases for all
three multiples. For example, the interquartile ranges for sales, EPS1, and
EPS2 increase to 0.805, 0.448, and 0.396, respectively, from 0.738, 0.348, and
0.317 in table 2, panel A. These results emphasize our earlier caution that
the results reported for our main sample may not be descriptive of other
samples.
In addition to ranking the relative performance of different multiples,
the results in table 2, panel A, and the histograms in figure 1 can also be
used to infer absolute performance. Our main finding is that industry mul-
tiples based on simple forward EPS forecasts provide reasonably accurate
valuations for a large fraction of firms. Consider, for example, the percent-
ages of the sample covered by the two intervals on either side of zero
for EPS2 in figure 1. The sum of those four percentages (13 percent
between
—0.2 and − 0.1, 18 percent between − 0.1 and 0, 16.5 percent between 0
and 0.1, and 12 percent between 0.1 and 0.2) suggests that multiples based
on industry harmonic means for EPS2 generate valuations within 20 per-
cent of observed prices for almost 60 percent of firm years. Alternatively,
halving the interquartile range of 0.348 for EPS2 in panel A suggests that
absolute pricing errors below 17.4 percent are observed for approximately
50 percent of the sample. 16 The lower interquartile ranges for other value
drivers, such as 0.313 for EG1 and 0.307 for ES1, indicate the potential
for further improvement with other value drivers derived from forward
earnings.
The pricing error distributions in panel B of table 2, when the com-
parable group includes all firms in the cross-section, are systematically
more dispersed for all multiples, relative to those reported in panel A. The
superior performance observed when the comparable group is selected
from the same industry, is consistent with the joint hypothesis that (1)
increased homogeneity in the value-relevant factors omitted from the
multiples results in better valuation, and (2) the IBES industry classification
identifies relatively homogeneous groups of firms. 17 Overall, we find that
the frequency of small (medium) pricing errors increases (decreases),
when comparable firms are selected from the same industry. (The
frequency of large valuation error remains relatively unchanged.)
The multiples used in calculating the pricing errors in panels A and
B are estimated using the harmonic mean. To allow comparison with re-
sults in previous studies (e.g., Alford [1992]), we repeat the panel A anal-
ysis using the median instead of the harmonic mean. Those results are
reported in panel C. Consistent with the evidence in Baker and Ruback
[1999] and Beatty, Riffe, and Thompson [1999], we find that the absolute
16
This statement assumes the distribution is symmetric around zero. Since that
assumption is only approximately true, and only for better-performing multiples (e.g. forward
earnings), this description is intended primarily for illustrative purposes.
17
Even if these conditions are satisfied, it is not clear that there should be an improvement.
Moving from the cross-section to each industry results in a substantial decrease in sample size,
and consequently the estimation is less precise. This fact is also reflected in the increase in the
deviation of the sample mean of the valuation errors from zero.
FIG. 1.—Distribution of Pricing Errors Using Simple Industry Multiples. Value for firm i
in year t ( pit ) and value drivers (xit ) are assumed to be proportional: pit = it βi xit + εit . The
multiple, βt , is estimated using the industry harmonic mean: βt = 1/E( x ), and pricing
pi t −βˆ t pit
εi t
errors are computed as pit = . The variables are defined as follows (all amounts are
pit
xi t
on a per share basis): P is stock price; BV is book value of equity; EBITDA is earnings before
interest, taxes, depreciation and amortization; IACT is ∗IBES actual earnings; EPS2 is two year
.
out5 earnings forecast and g is growth forecast, and P 1 = BV +
E (EPSt+s −kt BVt+s −1 )
( t )+
t t s =1 (1+kt )s
Et (EPSt+s −kt BVt+4 )
kt (1+kt
. All multiples are calculated using the harmonic means
for comparable firms
within)s each industry (based on IBES industry classification), and the firm being valued is
excluded when computing industry multiples. Sample firms are collected in April each year
between 1982 and 1999, and we require non-missing values for a set of core financial
variables from COMPUSTAT, 30 non-missing monthly returns from the prior 60 months from
CRSP, and non-missing share price, 1- and 2-year out EPS forecasts and long-term growth
forecasts from IBES. The sample is trimmed at 1% and 99% for each value driver. We then
require a minimum
$2 share price, that all value drivers be positive, and that each industry-year combination have
at least five observations. The final sample contains 19,879 firm-years.
FIG. 1.—continued
FIG. 1.—continued
performance of median multiples is worse than that for harmonic mean

multiples. To be sure, the mean pricing error is no longer close to zero,
whereas the median pricing error is now close to zero. Note that the
improvement observed for harmonic means, relative to median multi-
ples, is inversely related to the absolute performance of that multiple,
and the improvement for forward earnings multiples is quite small. Im-
portantly, the relative performance of the different multiples remains un-
changed.
We also examined the impact of using the industry mean of price-to-
value driver ratios as the multiple, rather than the harmonic mean (results
available from authors). We find that the pricing error distributions for
different value drivers exhibit much greater dispersion, and mean values
that are substantially negative. Similar to the results reported for medians,
the decline in performance is greater for multiples that perform poorly in
table 2, panel A.
While it is inappropriate to include the target firm in the group of
comparable firms, we investigated the bias caused by doing so. The bias
(in terms of the impact on the distribution of pricing errors for mul-
tiples computed in sample versus out of sample) is negligible when
the group of comparable firms includes all firms in the cross-section
(corresponding to panel B results), since the addition of one firm
has almost no effect on the multiple. When firms are selected from
the same industry, however, there is a decrease in the dispersion of
pricing errors when we use in-sample harmonic means (e.g. the in-
terquartile range for EPS2 declines from 0.317 in table 2, panel A,
to 0.301). The decline in dispersion is even larger for in-sample median
multiples (e.g., interquartile range for EPS2 declines from 0.320 in table 2,
panel C, to 0.290).
We considered two other extensions to the multiple approach (results
available upon request). First, we combined two or more value drivers (e.g.,
Cheng and McNamara [1996]). Our results, based on a regression approach
that is related to the intercept adjusted multiple approach discussed in
section 3.3 (e.g., Beatty, Riffe, and Thompson [1999]) indicate only small
improvements in performance over that obtained for forward earnings.
Second, we investigated conditional earnings and book value multiples.
That is, rather than using the harmonic mean P/E and P/B values of
comparable firms, we use a P/E (P/B) that is appropriate given the forecast
earnings growth (forecast book profitability) for that firm. We first
estimate the relation between forward P/E ratios and forecast earnings
growth (P/B ratios and forecast return on common equity) for each
industry-year, and then read off from that relation the P/E (P/B)
corresponding to the earnings growth forecast (forecast ROCE) for the firm
being valued. Despite the intuitive appeal of conditioning the multiple on
relevant information, little or no improvement in performance was
observed over the unconditional P/E and P/B multiples.
5.3 INTERCEPT ALLOWED IN PRICE-VALUE DRIVER RELATION
In this subsection, we report results based on the second stage analysis,

where we allow for an intercept in the relation between price and value
drivers. Again, the analysis is conducted separately for comparable firms
from the same industry (table 3, panel A) and for comparable firms from
the entire cross-section (panel B).
As predicted, relaxing the no-intercept restriction improves the perfor-
mance of all multiples. The best performance is achieved when we allow for
an intercept and select comparable firms from the same industry (table 3,
panel A). Comparison of these results with those in table 2, panel B,
provides the joint improvement created by limiting comparable firms to be
from the same industry and allowing for an intercept. Generally, the
improvement generated by selecting comparable firms from the same
industry (panel B to panel A in each table) is relatively uniform across value
drivers. In contrast, the improvement generated by allowing an intercept
(table 2 to table 3 for each panel) is inversely related to that value driver’s
performance in table 2. Value drivers that perform poorly in table 2
improve more than those that do well in that table. Contrast, for example,
the improvement observed for Sales (interquartile range of 0.738 in table 2,
panel A, to 0.614 in table 3, panel A) with the improvement observed for
EG1 (interquartile range of
0.313 in table 2, panel A, to 0.306 in table 3, panel A). Although the im-
provement in absolute performance of the value drivers is not uniform, the
rank order of different value drivers remains unchanged from table 2 to
table 3.
5.4 VARIATION IN PERFORMANCE ACROSS INDUSTRIES AND YEARS
Given our focus on understanding the underlying information content

of the different multiples, our results so far relate to pooled data. We con-
sider next variation in the performance of different value drivers across
years and industries to determine if the overall results are observed con-
sistently in different years and industries. Arguments have been made be-
fore for different value drivers to perform better in certain industries than
in others. For example, Tasker [1998] reports that investment bankers
and analysts appear to use different preferred multiples in different in-
dustries. Although we recognize that our search is unlikely to offer con-
clusive results, since we do not pick comparable firms with the same skill
and attention as is done in other contexts, we offer some preliminary
findings.
Since investment professionals use simple multiples (no intercept) and
select comparable firms from the same industry, we conduct the analysis
only for that combination (corresponding to table 2, panel A). We pool the
valuation results for each industry across years, and rank multiples based
on the interquartile range of pricing errors within each industry. The re-
sults for the 81 industries we analyze are reported in Appendix B. The
rankings range between 1 (best) and 17 (worst). We also report summary

statistics of the rankings at the bottom of the table. The rankings reported
in our pooled results are observed with remarkable consistency across all
industries.
To illustrate graphically the essence of these rankings, we focus only on
the six representative value drivers considered in figure 1, panel A,
compute rankings again for each industry, and tabulate the number of
times each value driver was ranked first, second, and so on in an industry.
The results of that tabulation are reported in figure 1, panel B, and the
consistency of the rankings across industries is clearly evident. EPS2 is
ranked first in 66 of 81 industries, ranked second in 11 industries and
ranked third and fourth in two industries each. It is never ranked fifth or
sixth. The modal rank for
P1∗ is second, is third for IACT, is fourth for EBITDA, is fifth for BV, and
sixth for Sales. These modal ranks are observed in more than half the 81
industries in each case. Removing P1 ∗ from the analysis only strengthens
further the performance of EPS2 (it is ranked first 77 times out of 81).
This pattern of superior relative performance for forward earnings mul-
tiples, which is consistent with the results in Kim and Ritter [1999], sug-
gests that the information contained in forward looking value drivers cap-
tures a considerable fraction of value, and this feature is common to
all industries. The absence of a significant number of industries where
EBITDA performs better than other value drivers is inconsistent with
the conventional wisdom that this cash flow measure is particularly use-
ful in low growth industries or industries with considerable amortiza-
tion of goodwill. The absence of superior performance for Sales in
any industry (it is never ranked first or second in figure 1, panel B)
is also inconsistent with Sales multiples being useful in certain indu-
stries.
Our evidence on the consistency of these rankings across different years
is reported in figure 1, panel C. We focus only on the six representative
value drivers and report the interquartile range of pricing errors each
year for the six value drivers. The absolute and relative levels of those
interquartile ranges appear fairly consistent over time. One noticeable
deviation from that overall description is that although the performance of
P1∗ is similar to that
of EPS2 during the 1980s, it declines during the 1990s (interquartile range
for EPS2 increases from about 0.35 in 1991 to 0.46 by 1999). Notwithstanding
this deviation, these results suggest that our overall results are robust and
observed consistently throughout the 18-year sample period.
6. Conclusions
In this study we examine the valuation properties of a comprehensive list
of value drivers. Although our primary focus is on the traditional approach,
which assumes direct proportionality between price and value driver and
selects comparable firms from the same industry, we also consider a less
restrictive approach that allows for an intercept and examine the effect of
expanding the group of comparable firms to include all firms in the cross-
section.
We find that multiples based on forward earnings explain stock prices
reasonably well for a majority of our sample. In terms of relative per-
formance, our results show historical earnings measures are ranked sec-
ond after forward earnings measures, cash flow measures and book value
are tied for third, and sales performs the worst. This ranking is robust
to the use of different statistical methods and, more importantly, simi-
lar results are obtained across different industries and sample years. We
find that the common practice of selecting firms from the same indus-
try improves performance for all value drivers. Although we find that the
improvement in performance obtained by allowing for an intercept in the
price/value driver relation is quite large for value drivers that perform
poorly, it is minimal for value drivers that perform well (such as forward
earnings). We speculate that multiples are used primarily because they
are simple to comprehend and communicate and the additional complex-
ity associated with including an intercept may exceed the benefits of im-
proved fit.
Our results regarding the information in different value drivers are
consistent with intuition. For example, forward-looking earnings fore-
casts reflect value better than historical accounting information, account-
ing accruals add value-relevant information to cash flows, and profitabil-
ity can be better measured when revenue is matched with expenses.
Some results in this paper are surprising, however. For example, multi-
ples based on the residual income model, which explicitly forecasts ter-
minal value and adjusts for risk, perform worse than simple multiples
based on earnings forecasts. And adjusting for leverage does not improve
the valuation properties of EBITDA and Sales. We investigate these re-
sults further and feel that these results indicate the trade-off that exists
between signal and noise when more complex but theoretically correct
structures are imposed. As a caveat, we recognize that our study is de-
signed to provide an overview of aggregate patterns, and thus may have
missed more subtle relationships that are apparent only in small sample
studies.
APPENDIX A
This appendix describes how the variables are constructed. The #s in
parentheses refer to data items from COMPUSTAT. Number of shares
and per share data from COMPUSTAT are adjusted for subsequent
splits and stock dividends to allow comparability with IBES per share
data.
P: Share price from IBES, as of April each year.

TP: Enterprise value per share=book value of debt, deflated by
shares outstanding (#25), plus share price (P), where book
value of debt=long term debt (#9) debt in current liabili-
ties (#34)+preferred stock (#130) −preferred treasury stock
(#227) +preferred dividends in arrears (#242).
BV: Per share book value of equity = book equity (#60) deflated
by shares outstanding (#25).
SALES: Per share sales sales
= (#12) deflated by shares outstanding
(#25).
CACT: COMPUSTAT actual earnings per share = EPS excluding ex-
traordinary items (#58).
IACT: IBES actual earnings per share (per share earnings adjusted
for one-time items).
EBITDA: Per share earnings before interest, taxes, depreciation and
amortization = EBITDA (#13), deflated by shares outstand-
ing (#25).
CFO: Per share cash flow from operations= EBITDA minus the to-
tal of interest expense (#15), tax expense (#16) and the net
change in working capital, deflated by shares outstanding
(#25), where net change in working capital is change in cur-
rent assets (#4) minus change in cash and cash equivalents
(#1) minus change in current liabilities (#5) plus change in
debt included in current liabilities (#34).
Data items 15, 16, 1 or 34 are set to zero if missing.
FCF: Per share free cash flow=CFO minus net investment, where
net investment is capital expenditures (#128) plus acquisi-
tions (#129) plus increase in investment (#113) minus sale
of PP&E (#107) minus sale of investment (#109), deflated
by shares outstanding (#25).
Data items 128, 129, 113, 107 or 109 are set to zero if missing.
MCF: Per share maintenance cash flow = CFO minus depreciation
expense (#125), deflated by shares outstanding (#25).
EPS1: mean IBES one year out earnings per share forecast
EPS2: mean IBES two year out earnings per share forecast
EG1: IBES three year out earnings per share forecast, measured
as EPS2∗(1+g), where g is mean IBES long term growth
forecast
EG2: EPS2∗g, where g is mean IBES long term EPS growth
forecast
The three P∗ measures are defined as follows:
5
+ +− + +
P 1∗t = BVt s
s =1 (1 + kt ) kt (1 + kt )s
+
5
Et (EPSt s − kt BVt s 1)
+ +−
P 2∗t = BVt
s =1 (1 + kt )s
+
2
∗
1
P3 t = BVt + s +−
+
s =1 (1 + kt )
11 [Et (ROEt+5) − kt ]BVt+s−1) [Et (ROEt+12) − kt ]BVt+11
+ +
(1 + kt )s Kt (1 + kt )11
s
=3
The variables used in the P∗ calculations are obtained as follows: The dis-
count rate (kt ) is calculated as the risk-free rate plus beta times the eq-
uity risk premium. We use the 10-year Treasury bond yield on April 1
of year t +1 as the risk-free rate and assume a constant 5% equity risk
premium. We measure beta as the median beta of all firms in the same
beta decile in year t. We estimate betas using monthly stock returns and
value-weighted CRSP returns for the five years ending in March of year
t +1 (we require a minimum of 30 non-missing monthly returns in those
5 years).
For a subgroup of firm-years (less than 5 percent), we were able to
obtain mean IBES forecasts for all years in the five-year horizon. For all
other firms, with less than complete forecasts available between years 3
and 5, we generated forecasts by applying the mean long-term growth
forecast (g) to the mean forecast for the prior year in the horizon; i.e.,
EPSt+s =EPSt+s−1∗(1 g ).
The book values for future years, corresponding to the earnings forecasts,
are determined by assuming the “ex-ante clean surplus” relation (ending
book value in each future period equals beginning book value plus fore-
casted earnings less forecasted dividends). Since analyst forecasts of future
dividends are not available on IBES, we assume that the current dividend
payout ratio will be maintained in the future. We measure the current divi-
dend payout as the ratio of the indicated annual cash dividends to the earn-
ings forecast for year + t 1 (both obtained from the IBES summary file).
To minimize biases that could be induced by extreme dividend payout ra-
tios (caused by forecast t+1 earnings that are close to zero), we Winsorize
payout ratios at 10% and 50%.
∗
In the calculation of P 3t , we forecast Et (ROEt+5) for s =4, 5, . . . , 12 using a
linear interpolation to the industry median ROE. The industry median ROE
is calculated as a moving median of the past ten years’ ROE of all firms in
the industry. To eliminate outliers, industry median ROEs are Winsorized
The earnings forecasts for years+1 to 5 are summed to obtain the two
earnings sum measures.
ES1t =
5 Et (EPSt+s ) and ES 2t 5
Et (EPS+t s )
=
s s (1 + kt )s
=1 =1
166
APPENDIX B
INDUSTRY RANKINGS OF MULTIPLES
Pricing errors (scaled by share price) are computed for each firm-year using harmonic means of firms in each industry. Multiples are ranked for each
J. LIU, D. NISSIM, AND J. THOMAS

industry according to the inter-quartile range of pricing errors. Lower ranks indicate better performance. Industry classification is from the IBES sec-
tor/industry group classification code. Years covered are 1981 through 1999. Sample size is 19,879. Summary descriptions of the variables are as fol-
lows (all amounts are on per share basis): P is stock price; BV is book value of equity; CFO is cash flow from operations; EBITDA is earnings be-
fore interest, taxes, depreciation and amortization; CACT is COMPUSTAT earnings before extraordinary items; IACT is IBES actual earnings; EPS1,
EPS2 are one year out and two year out earnings forecasts; EG1= EPS2∗(1 +g), EG2 EPS2∗g, where g is growth forecast. TP is enterprise value
(market value of equity plus book value of debt). When TP multiples are used,= predicted equity value is calculated by subtracting the book value of
debt.
5
P 1∗t = BVt + + +− + +
s s
,
s (1 + kt ) kt (1 + kt )
=1
1
5
P 2∗t = BVt + + +−
s s
(1 + kt )
=1
1 [Et(ROEt s ) − kt ]BVt s 1
11
2 +
∗
P3 t = BVt + + s +− + s +−
s =1 (1 + kt (1 + kt )
s =3
)
+ ,
kt (1 + kt )11
where Et (RO Et+s ) for s = 4, 5, .. . , 12 is forecasted using a linear interpolation to the industry median ROE. The industry median ROE is calculated
as a moving median of the past ten years’ ROE of all firms in the industry. To eliminate outliers, industry median ROEs are Winsorized at the risk free rate and
20%.
5 5 Et (EPSt s )
ES 1t = Et (EPSt+s ), and ES 2t +
.
s s (1 + kt )s
=1
= =1
Years covered are 1982 through 1999. Sample size is 19,879.

Ebitda/ Sales/
Sector Industry BV CFO CACT IACT Ebitda Sales EPS1 EPS2 EG1 EG2 P1∗ P2∗ P3∗ ES1 ES2 TP TP
Basic Ind. Building & Related 17 15 10 11 12 16 8 6 7 2 1 9 3 5 4 13 14
Basic Ind. Chemicals 14 16 11 8 13 15 5 4 3 7 6 9 10 1 2 12 17
Basic Ind. Containers 14 17 15 10 11 16 6 3 2 7 5 9 8 4 1 12 13
Basic Ind. EAFE Metals-Nonfer 8 17 16 15 6 7 13 4 1 11 12 3 9 2 5 10 14
Basic Ind. Forest Products 13 14 15 11 10 16 8 2 4 9 6 5 7 3 1 12 17
Basic Ind. Metal Fab & Dist 14 15 9 10 13 16 4 5 3 2 8 7 12 1 6 11 17

Basic Ind. Multi-Ind Basic 11 16 10 9 12 14 3 1 4 15 7 6 8 5 2 13 17
Basic Ind. Nonfer Base Met 13 15 11 12 10 16 7 1 8 6 9 5 2 3 4 14 17
Basic Ind. Paper 13 16 11 10 12 15 7 6 2 9 3 8 5 4 1 14 17
Basic Ind. Precious Metals 13 12 14 8 10 16 11 6 4 15 2 7 1 5 3 9 17
Basic Ind. Steel 5 16 14 11 12 15 8 2 3 10 7 1 9 6 4 13 17
Basic Ind. Textiles 14 17 10 9 13 15 5 2 4 8 6 7 11 1 3 12 16
Cap. Goods Aerospace 14 15 11 9 13 16 6 1 3 5 7 10 8 2 4 12 17
Cap. Goods Auto OEMS 10 17 11 12 13 14 6 1 2 8 7 5 9 3 4 15 16
Cap. Goods Bldg Materials 14 16 11 10 13 15 5 2 3 7 6 9 8 1 4 12 17
Cap. Goods Defense 12 17 11 10 13 15 6 3 5 8 4 7 9 1 2 14 16
Cap. Goods Electrical 14 16 11 10 12 15 3 7 5 9 1 6 8 2 4 13 17
Cap. Goods Machinery 12 16 13 9 11 15 5 3 1 8 6 7 10 2 4 14 17
Cap. Goods Multi-Ind Cap Good 17 16 8 9 10 12 2 3 4 1 7 14 13 5 6 11 15
Cap. Goods Office Products 16 14 9 7 13 15 3 1 2 8 6 12 11 4 5 10 17
Cap. Goods Undesig Capital 15 14 11 13 8 16 5 1 2 12 6 10 9 4 3 7 17
167
168
APPENDIX B—continued

Ebitda/ Sales/
∗ ∗ ∗
Sector Industry BV CFO CACT IACT Ebitda Sales EPS1 EPS2 EG1 EG2 P1 P2 P3 ES1 ES2 TP TP
Consumer Dur. Auto Part Mfg 14 17 11 7 12 15 4 1 3 8 9 6 10 2 5 13 16
Consumer Dur. Automotive Mfg 3 8 15 14 16 7 13 11 12 6 4 1 2 10 9 17 5
Consumer Dur. Home Bldg 13 17 11 10 12 15 5 1 3 6 7 8 9 2 4 14 16
Consumer Dur. Home Furnish 14 17 12 8 11 15 5 3 4 10 6 7 13 2 1 9 16
Consumer Dur. Leisure Prods 14 15 7 4 11 16 1 2 3 6 9 10 13 5 8 12 17
Consumer Dur. Rec Vehicles 14 16 10 7 13 17 1 3 5 6 8 9 12 2 4 11 15
Consumer Dur. Rubber 16 17 13 9 10 15 7 5 4 8 3 11 6 2 1 12 14
Consumer Dur. Tools & Hardware 12 15 3 4 16 17 7 2 5 13 10 9 11 6 1 8 14
Cons. Non-Dur. Beverages 15 14 10 8 12 16 7 5 2 6 4 11 9 1 3 13 17
Cons. Non-Dur. Clothing 14 16 12 10 9 15 4 1 5 6 7 8 13 3 2 11 17
Cons. Non-Dur. Consumer Containers 13 15 12 10 9 16 2 4 5 11 6 7 8 3 1 14 17
Cons. Non-Dur. Cosmetics 17 14 8 6 13 15 5 3 2 11 7 12 9 1 4 10 16
Cons. Non-Dur. Food Processors 15 14 9 8 13 16 1 3 5 6 7 12 11 2 4 10 17
Cons. Non-Dur. Home Prods 14 15 12 8 13 16 6 5 1 3 7 9 10 2 4 11 17
Cons. Non-Dur. Leisure Time 16 17 14 12 10 13 5 4 3 9 8 6 11 1 2 7 15
Cons. Non-Dur. Leisure Times 12 14 11 9 15 16 7 4 1 8 6 5 10 2 3 13 17
Cons. Non-Dur. Paint & Rel Mats 13 16 10 8 12 15 6 4 5 2 7 11 9 3 1 14 17
Cons. Non-Dur. Tobacco 16 15 13 7 11 14 6 1 3 8 5 10 9 4 2 12 17
Cons. Services Communications 15 14 13 8 12 16 7 3 5 4 6 10 9 1 2 11 17
Cons. Services Ind Svcs 13 16 10 6 14 15 4 7 3 8 1 9 11 5 2 12 17
Cons. Services Retail—Foods 14 15 10 8 12 16 5 4 2 7 6 9 11 1 3 13 17
Cons. Services Retail—Goods 14 16 10 9 12 15 6 4 2 3 7 8 11 1 5 13 17
Cons. Services Undesig Conr Svc 12 16 10 8 14 15 4 3 2 7 6 9 11 1 5 13 17
Ebitda/ Sales/
∗ ∗ ∗
Sector Industry BV CFO CACT IACT Ebitda Sales EPS1 EPS2 EG1 EG2 P1 P2 P3 ES1 ES2 TP TP
Energy Canadian Energy 14 16 10 8 11 15 5 1 6 13 7 9 2 3 4 12 17
Energy Coal 12 16 7 10 14 17 6 5 2 8 4 11 9 3 1 13 15
Energy EAFE Energy Srcs 2 13 16 15 1 12 11 8 4 9 10 6 14 3 5 7 17
Energy Gas 7 14 8 12 10 16 3 4 6 15 11 1 9 5 2 13 17
Energy Oil 9 13 15 12 11 16 8 5 2 10 6 1 7 3 4 14 17
Finance Banking 11 16 9 6 12 13 5 3 4 8 10 7 14 2 1 17 15

Finance Finan & Loan 8 17 7 4 11 10 6 1 2 13 12 9 14 3 5 15 16
Finance Finan Svcs 17 16 12 6 13 11 9 5 3 8 1 7 10 4 2 14 15
Finance Insurance 15 16 12 8 10 14 5 2 3 7 6 11 9 4 1 13 17
Finance Investments 14 15 11 9 12 17 6 2 5 10 4 8 7 3 1 13 16
Finance S&L 11 15 12 7 9 14 1 4 2 10 8 5 13 3 6 17 16
Finance Undesignated Finance 10 14 6 7 12 16 15 11 9 2 1 4 3 8 5 13 17
Health Care Biotech 14 17 13 11 9 15 10 1 4 2 7 8 3 6 5 16 12
Health Care Drugs 15 17 13 10 11 14 5 4 2 9 7 6 8 1 3 12 16
Health Care Hosp Supplies 14 17 11 9 12 15 7 6 2 4 5 8 10 1 3 13 16
Health Care Hospitals 14 15 12 10 13 16 6 1 5 9 4 8 7 2 3 11 17
Health Care Med Supplies 15 17 10 9 13 14 5 4 2 6 7 8 12 1 3 11 16
Health Care Svc to Med Prof 14 15 12 9 11 16 7 5 4 1 8 6 13 2 3 10 17
Misc. Undesig. Unclassified 12 13 11 10 14 16 5 3 4 7 6 9 8 2 1 15 17
Public Utilities Electrical Util 11 14 10 9 12 15 5 2 4 13 6 7 8 3 1 16 17
Public Utilities Gas Util 8 16 11 9 10 15 5 1 2˚ 14 7˚ 6˚ 12 3˚ 4˚ 13 17
Public Utilities Phone Util 15 16 13 8 12 11 5 4 2˚ 10 7˚ 6˚ 9˚ 1˚ 3˚ 17 14
Public Utilities Water Util 9 12 8 4 5 13 1 3˚ 2˚ 15 11 10 14 6˚ 7˚ 16 17
169
170
Ebitda/ Sales/
Sector Industry BV CFO CACT IACT Ebitda Sales EPS1 EPS2 EG1 EG2 P1∗ P2∗ P3∗ ES1 ES2 TP TP
Technology Computers 14 17 11 10 12 15 6 4 2 5 7 8 9 1 3 13 16
Technology Electronics Sys/Dev 14 15 10 8 11 16 6 4 3 5 7 9 12 1 2 13 17
Technology Electronics 13 15 14 11 12 16 6 3 4 7 5 8 9 2 1 10 17
Technology Office/Comm Equip 13 17 15 9 14 12 5 3 1 7 6 8 10 2 4 11 16
Technology Other Computers 15 14 11 9 13 16 4 6 3 5 7 8 10 1 2 12 17
Technology Photo-Optic Equip 14 17 11 10 15 13 5 4 2 7 6 8 9 3 1 16 12
Technology Semicond/Comp 14 15 12 9 11 16 6 4 3 8 7 5 13 1 2 10 17
Technology Software EDP 17 15 14 8 12 13 5 4 1 6 9 7 10 3 2 11 16
Technology Undesignated 12 14 7 9 15 16 1 3 4 10 8 6 11 2 5 13 17
Tech
Technology Undesignated 15 17 12 11 10 13 7 2 6 14 8 5 9 3 4 1 16
Technology
Transportation Airlines 11 15 13 10 12 16 8 7 5 1 6 3 9 2 4 14 17
Transportation Maritime 9 16 13 8 12 17 7 4 2 11 3 1 14 6 5 10 15
Transportation Railroads 12 13 11 7 15 16 5 2 4 8 6 9 10 3 1 14 17
Transportation Trucking 12 14 8 10 16 15 4 3 5 9 7 6 11 1 2 13 17
Mean Rank 12.9 15.3 11.1 9.0 11.7 14.8 5.7 3.5 3.5 7.5 6.4 7.5 9.4 2.8 3.2 12.3 16.1
Median Rank 14 16 11 9 12 15 5 3 3 8 7 8 9 2 3 13 17
Standard Deviation of Rank 2.90 1.53 2.37 2.18 2.30 1.90 2.61 2.08 1.87 3.44 2.35 2.68 2.95 1.79 1.76 2.55 1.72
REFERENCES
ABARBANELL, J., AND V. L. BERNARD. “Is the U.S. Stock Market Myopic?” Journal of Accounting
Research (Autumn, 2000): 221–42.
ALFORD, A. “The Effect of the Set of Comparable Firms on the Accuracy of the Price-earnings
Valuation Method.” Journal of Accounting Research 30 (1992): 94–108.
BAKER, M., AND R. RUBACK. “Estimating Industry Multiples.” Working paper, Harvard University,
Cambridge, MA, 1999.
BASU, S. “Investment Performance of Common Stocks in Relation to Their Price-
earnings Ratios: A Test of the Efficient Markets Hypothesis.” Journal of Finance (1977): 663–
82.
BEATTY, R. P.; S. M. R IFFE; AND R. THOMPSON. “The Method of Comparables and Tax Court
Valuations of Private Firms: An Empirical Investigation.” Accounting Horizons 13 (1999):
177–99.
BOATSMAN, J., AND E. BASKIN. “Asset Valuation with Incomplete Markets.” The Accounting Review
56 (1981): 38–53.
BRADSHAW, M. T. “How Do Analysts Use Their Earning Forecasts in Generating Stock Recom-
mendations?” Working paper, University of Michigan, Ann Arbor, MI, 1999a.
BRADSHAW, M. T. “Analysts Reports, Target Prices, and Stock Recommendations.” Working
paper, University of Michigan, Ann Arbor, MI, 1999b.
CHENG, C. S. A., AND R. MCNAMARA. “The Valuation Accuracy of the Price-Earnings and Price-
Book Benchmark Valuation Methods.” Working paper, University of Houston, Houston, TX,
1996.
CLAUS, J. J., AND J. K. THOMAS. “Equity Premia as Low as Three Percent? Empirical Evidence
from Analysts’ Earnings Forecasts for Domestic and International Stock Markets.” Working
paper, Columbia University, New York, NY, 2000.
COPELAND, T.; T. KOLLER; AND J. MURRIN. Valuation. New York: Wiley, 1994.
DAMODARAN, A. Damodaran on Valuation. New York: Wiley, 1996.
FELTHAM, G., AND J. A. OHLSON. “Valuation and Clean Surplus Accounting for Operating and
Financial Activities.” Contemporary Accounting Research (Spring 1995): 689–731.
FRANKEL, R., AND C. M. C. LEE. “Accounting Valuation, Market Expectation, and Cross-Sectional
Stock Returns.” Journal of Accounting and Economics 25 (1998): 283–319.
GEBHARDT, W. R.; C. M. C. LEE; AND B. SWAMINATHAN. “Toward an Implied Cost-of-Capital.”
Journal of Accounting Research 39 ( June 2001): 135–176.
GILSON, S. C.; E. S. HOTCHKISS; AND R. S. RUBACK. “Valuation of Bankrupt Firms.” Review of
Financial Studies 13 (2000): 43–74.
HAND, J. R. M. “Profits, Losses, and the Stock of Internet Firms.” Working paper, University
of North Carolina, Chapel Hill, NC, 1999.
HAND, J. R. M. “The Role of Economic Fundamentals, Web Traffic, and Supply and Demand
in the Pricing of US Internet Stocks.” Working paper, University of North Carolina,
Chapel Hill, NC, 2000.
KAPLAN, S. N., AND R. S. RUBACK. “The Valuation of Cash Flow Forecasts: An Empirical Analysis.”
The Journal of Finance 50 (1995): 1059–93.
KIM, M., AND J. RITTER. “Valuing IPOs.” Journal of Financial Economics 53 (1999): 409–37.
LECLAIR, M. S. “Valuing the Closely-held Corporation: The Validity and Performance of
Esta-
blished Valuation Procedures.” Accounting Horizons 4 (September, 1990) 31–42.
LIU, J. 1999. “Post-earnings-announcement Drift and Analyst Forecasts.” Working paper, UCLA,
Los Angeles, CA, 1999.
LIU, J., AND J. THOMAS. “Stock Returns and Accounting Earnings.” Journal of Accounting Research
38 (Spring 2000): 71–101.
LIU, J.; D. NISSIM; AND J. THOMAS . “Valuations Based on Multiples and Future Stock Returns.”
Working paper, Columbia University, New York, NY, 2001.
OHLSON, J. “Earnings, Book Values, and Dividends in Equity Valuation.” Contemporary Account-
ing Research (Spring 1995): 661–87.
172 J. LIU, D. NISSIM, AND J. THOMAS
PALEPU, K.; P. HEALY; AND V. BERNARD. “Business Analysis and Valuation.” 2nd Edition. Cincin-
nati, Ohio: South-Western College Publishing, 2000.
PENMAN, S. H. “Financial Statement Analysis and Security Valuation.” Irwin: McGraw-Hill, 2001.
STATTMAN, D. “Book Value and Stock Returns.” The Chicago MBA: A Journal of Selected Papers,
Chicago: University of Chicago, 1980, pp. 25–45.
TASKER, S. C. “Industry Preferred Multiples in Acquisition Valuation.” Working paper,
Cornell University, Ithaca, NY, 1998.
TRUEMAN, B.; M. H. F. WONG; AND X. ZHANG. “The Eyeballs Have It: Searching for the Value
in Internet Stocks.” Journal of Accounting Research 38 (2000): 137–62.

8 Equity Valuation Using Multiples

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Journal of Accounting

Research Vol. 40 No. 1 March

Equity Valuation Using Multiples

Received 2 January 2000; accepted 27 July 2001

We examine the valuation performance of a comprehensive list of value

relevance is limited until it is matched with expenses. Second, we confirm

3.2 TRADITIONAL MULTIPLE VALUATION

3.3 INTERCEPT ADJUSTED MULTIPLES

4. Sample and Data

on that combination, and most of our ancillary investigations relate only to

5.1 DESCRIPTIVE STATISTICS

Table 1 reports the pooled distribution of different value drivers, scaled

Mean Median SD 75%-25% 90%-10% 95%-5%

Mean Median SD 75%-25% 90%-10% 95%-5%

incidence of negative values is higher for cash flow measures. In particular,

Mean Median SD 75%-25% 90%-10% 95%-5%

drivers, we decided to remove them from the set of value drivers

5.2 NO-INTERCEPT RELATION BETWEEN PRICE AND VALUE DRIVERS

performance of median multiples is worse than that for harmonic mean

In this subsection, we report results based on the second stage analysis,

5.4 VARIATION IN PERFORMANCE ACROSS INDUSTRIES AND YEARS

Given our focus on understanding the underlying information content

rankings range between 1 (best) and 17 (worst). We also report summary

P: Share price from IBES, as of April each year.

J. LIU, D. NISSIM, AND J. THOMAS

Years covered are 1982 through 1999. Sample size is 19,879.

EQUITY VALUATION USING MULTIPLES

J. LIU, D. NISSIM, AND J. THOMAS

EQUITY VALUATION USING MULTIPLES

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