Preliminary. Comments welcome. Equity Valuation Using Multiples Jing Liu Anderson Graduate School of Management University of California at Los Angeles (310) 206-5861 [email protected]Doron Nissim Columbia University Graduate School of Business (212) 854-4249 [email protected]and Jacob Thomas Columbia University Graduate School of Business (212) 854-3492 [email protected]August, 2000 We received helpful comments from David Aboody, Sanjay Bhagat, Ted Christensen, Glen Hansen, Jack Hughes, Jim Ohlson, Stephen Penman, Phil Shane, Michael Williams, and seminar participants at AAA Annual Meeting at Philadelphia, University of Colorado, Columbia University, Copenhagen Business School, Ohio State University, and UCLA.
Transcript
Preliminary. Comments welcome.
Equity Valuation Using Multiples
Jing LiuAnderson Graduate School of Management
University of California at Los Angeles(310) 206-5861
We received helpful comments from David Aboody, Sanjay Bhagat, Ted Christensen, GlenHansen, Jack Hughes, Jim Ohlson, Stephen Penman, Phil Shane, Michael Williams, and seminarparticipants at AAA Annual Meeting at Philadelphia, University of Colorado, ColumbiaUniversity, Copenhagen Business School, Ohio State University, and UCLA.
1
Equity Valuation Using Multiples
Abstract
We examine the valuation performance of a comprehensive list of pricing multiples. We find thatmultiples derived from forward earnings explain stock prices remarkably well for most firms:pricing errors are within 15 percent of stock prices for about half of our sample. In terms ofrelative performance, the following general rankings are observed: 1) forward earningsmeasures, 2) historical earnings measures, 3) cash flow measures and book value of equity (tied),and 4) sales. Contrary to the popular view that different industries have different “best”multiples, we find that these overall rankings are observed consistently for almost all industriesexamined. Adjusting the ratio formulation typically followed in practice to allow for an interceptoffers some improvement, especially for multiples that perform poorly. No improvement isobserved, however, when we consider more complex measures of intrinsic value based on short-cut residual income models (where forward earnings are combined with book values, estimateddiscount rates, and generic terminal value estimates).
1
Equity Valuation Using Multiples1. 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 multiples.1 In addition
to investigating the performance of a comprehensive list of multiples, we also seek to examine a
variety of related issues, such as the variation in relative performance across industries.
Although the actual valuation process used by market participants is unobservable, we
assume that the stock prices resulting from that process are efficient. Comprehensive valuations,
which convert all available information into detailed projections of future flows, can be
conducted to replicate these market valuations for traded stocks. Comprehensive valuations can
also be used for privately-held equities (e.g., valuations for estate and gift tax purposes) as well
as for cases where a new entity will be publicly held (e.g., mergers and acquisitions, spinoffs,
and initial public offerings). Multiples are used often as a substitute for comprehensive
valuations in these and other contexts, because they communicate efficiently the essence of those
valuations. They are also used to complement comprehensive valuations, typically to calibrate
those valuations and to obtain terminal values. Given our efficient markets framework, our focus
is on explaining current prices, not on the ability of multiples to identify mispriced stocks.2
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, suchas 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 Many market inefficiency studies use multiples to identify mispriced stocks. For example, Basu [1977] andStattman [1980]) document abnormal returns to portfolios derived from earnings and book value multiples.
2
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, the
performance of multiples should be determined by the extent to which a) value drivers reflect
future profitability and b) the comparable firms selected resemble the firm being valued along
important value attributes, such as growth and risk.
The multiples we consider include three measures of accrual flows (sales, COMPUSTAT
earnings and IBES earnings), one accrual stock measure (book value), four measures of cash
flows (cash flow from operations, free cash flow, maintenance cash flow, and EBITDA or
earnings before interest, taxes, depreciation, and amortization), and two measures of forward
earnings (EPS1 and EPS2: 1 and 2-year out consensus analysts’ earnings forecasts). Since sales
and EBITDA should properly be associated with enterprise value (debt plus equity), rather than
equity alone, we also consider multiples for those two value drivers based on enterprise value
(market value of equity plus book value of debt).
We investigate two ways to supplement forward earnings information. First, we combine
EPS2 with estimates of forecasted earnings growth (g) to generate two “earnings-growth”
measures: EG1 and EG2, equal to EPS2*(1+g) and EPS2*g, respectively. EG1 is in effect a 3-
year out forecast, and EG2 is related to the PEG ratio used by analysts to value technology and
other high growth stocks, where forward price-earnings ratios are assumed to equal a multiple of
g (see Bradshaw, 1999a and b). Second, we construct variants of the 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]). In
essence, forward earnings forecasts are converted to forward residual income (also known as
3
abnormal earnings) using estimated discount rates and forecasted book values, and terminal
values are estimated by assuming generic patterns for long-term profitability.
Even though these intrinsic value measures utilize more information than that contained
in simple forward earnings multiples and impose a structure derived from valuation theory on
that information, we find that they perform much worse than simple multiples based on forward
earnings.3 To understand better the reasons for this poor performance, we construct two
“earnings sum” measures that also use multi-year earnings forecasts but do not convert them to
forecasted abnormal earnings: ES1, which is the sum of forecasted earnings for years +1 to +5,
and ES2 which is the sum of discounted values of those forecasts.
As in most prior research, we evaluate multiples by examining the distribution of percent
pricing errors: actual price less price predicted by the multiple, scaled by actual price. To
eliminate in-sample bias and to control for differences in the degrees of freedom across tests, we
evaluate all multiples based on out of sample prediction. That is, when calculating multiples
from comparable firms we exclude the firm being valued. To study the impact of selecting
comparable firms from the same industry, we contrast our results obtained by using industry
comparables (the middle category from the Sector/Industry/Group classification provided by
IBES) with results obtained when all firms in the cross-section are used as comparables.
Our analysis consists of two stages. In the first stage, we use the conventional ratio
representation (i.e., price doubles when the value driver doubles). In the second stage, we relax
the requirement that value is directly proportional to value drivers, while retaining the
assumption that the relation is linear. In effect, the second stage analysis allows for an intercept,
whereas the first stage does not.
4
In the first stage, multiples are calculated using the harmonic mean of the ratio of price to
value driver (the reciprocal of the mean of the value driver-to-price ratio) for comparable firms.
Although this estimator is rarely used in practice (see Beatty, Riffe, and Thompson [1999]), it
offers the desirable property that the percent pricing error is zero, on average. It is also
recommended by Baker and Ruback [1999], based on detailed econometric analyses of
alternative estimators. While the harmonic mean estimator results in lower pricing errors than the
simple mean or median, our ranking of the relative performance of different multiples remains
unchanged when the mean or median is used instead of the harmonic mean.
The following is an overview of the relative performance of different multiples in the first
stage of our analysis (no intercept):
• forward earnings perform the best, and accuracy improves with the forecast horizon;
• performance is improved if earnings forecasted over different horizons are aggregated;
• the intrinsic value measures perform considerably worse than forward earnings;
• among drivers derived from historical data, earnings performs better than book value; and
IBES earnings (which exclude some one-time items) performs better than COMPUSTAT
earnings;
• cash flow measures, defined in various forms, perform poorly;
• sales performs the worst; and
• using enterprise value, rather than equity value, for sales and EBITDA further reduces
performance.
3 Bradshaw [1999a and 1999b] observes results that are related to ours. He finds that valuations based on PEG
ratios (corresponding to our EG2) explain more variation in analysts’ target prices and recommendations thanmore rigorous valuation models.
5
• When comparable firms are restricted to be from the same industry, performance improves
for all multiples.
An important finding is that the relative performance of the multiples we consider does
not vary across industries. That is, contrary to general perception, we do not find that different
industries are associated with different “best multiples.” This finding suggests that our results are
driven by the intrinsic information content of the different value drivers, rather than their ability
to capture industry-specific value-relevant factors.
Turning from relative performance to absolute performance, the forward earnings
multiples describe actual stock prices reasonably well. For example, for 2-year out forecasted
earnings or EPS2, the standard deviation of pricing error is about 29 percent, and the
interquartile range is 31.7 percent (approximately half the firms have absolute pricing errors less
than 16 percent). While there are some firms with very large pricing errors, stock prices for a
majority of firms are explained relatively well by simple multiples based on forward earnings.
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. For example, the
interquartile range increases to 51.8 percent, 55.3 percent, and 73.8 percent for Compustat actual
earnings, EBITDA, and sales, respectively.
For the second stage, we estimate the intercept and slope of the price/value driver relation
by minimizing the sample variance of percent valuation errors, subject again to the constraint
that the valuation is on average unbiased. The procedure we follow is related to that proposed by
Beatty, Riffe, and Thompson [1999]. As might be expected, allowing for an intercept reduces the
dispersion of valuation errors for all multiples, but the improvement observed is considerably
smaller for multiples that perform well in the first stage (no intercept). These results suggest that
6
the traditional ratio formulation should be replaced by a relation that allows for an intercept,
especially for multiples that perform poorly in the traditional ratio formulation. We recognize,
however, that if simplicity is the primary motivation to use multiples, the reduction in pricing
errors may not be sufficient to compensate for the additional complexity introduced by adding an
intercept. As in the first stage, we find that pricing errors are lower when using comparable firms
from the same industry, relative to using all firms in the cross-section as comparables.
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: a) accruals
improve the valuation properties of cash flows, and b) despite the importance of top-line
revenues, its value relevance is limited until it is matched with expenses. Second, we confirm
that forward earnings contain considerably more value-relevant information than historical data.
Third, we provide evidence on the signal/noise tradeoff associated with developing more
complex valuation drivers based on the residual income model. Finally, our results suggest that
forward earnings multiples should be used as long as earnings forecasts are available, since they
outperform other multiples in almost all industries we examine.
The rest of the paper is organized as follows: section 2 contains a literature review; our
methodology is described in section 3; the sample selection process is provided in section 4; the
results and implications are discussed in section 5; and section 6 concludes the paper.
2. Literature Review
While textbooks on valuation (e.g., Copeland, Koller, and Murrin [1994], Damodaran
[1996] and Palepu, Healy, and Bernard [2000]) devote considerable space to discussing
multiples, most published papers that study multiples examine a limited set of firm-years and
7
consider only a subset of multiples, such as earnings and EBITDA. Also, comparisons across
different studies are hindered by differences in the methodology used.
Among commonly used value drivers, 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] investigates 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 valuation errors decline when the industry definition used to
select comparable firms is narrowed from a broad, single digit SIC code to classifications based
on two and three digits, but there is no additional improvement 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.
Kaplan and Ruback [1995] examine the valuation properties of the discounted cash flow
(DCF) approach for highly leveraged transactions. While they conclude that DCF valuations
approximate transacted values reasonably well, they find that simple EBITDA multiples result in
similar valuation accuracy. Beatty, Riffe, and Thompson [1999] examine different linear
combinations 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 a) weights
derived from harmonic mean book and earnings multiples and b) coefficients from price-scaled
regressions on earnings and book value.
8
In a recent study, Baker and Ruback [1999] examine econometric problems 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] add
forecasted earnings to the conventional list of value drivers, which includes book value, earnings,
cash flows, and sales. They investigate how initial public offering prices are set using multiples.
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
(EPS2) dominates the current year EPS forecast (EPS1).
It has been recognized that the use of large data sets could diminish the performance of
multiples, since the researcher selects comparable firms in a mechanical way. In contrast, 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 comparable firms by investment bankers and analysts in acquisition transactions.
9
She finds the systematic use of industry-specific multiples, which is consistent with different
multiples being more appropriate in different industries.4
3. Methodology
In this section we describe the different value drivers considered, and the methodology
used in the two stages of our analyses: estimating the price/value driver relation without and with
an intercept.
3.1 Value Drivers
The following is a list of value drivers examined in this paper. We have grouped them
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. 5 We provide only a brief
description of the variables here (additional details are provided in the Appendix) and then
describe the links that have been drawn in the prior literature between these variables and equity
value.
• Accrual stocks: book value of equity (BV).
• Accrual flows: sales, actual earnings from COMPUSTAT (CACT) and actual earnings from
IBES (IACT).
• 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
expenditures equal depreciation expense), and earnings before interest, taxes, depreciation
and amortization (EBITDA).
4 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 percent pricing errors, our results may not be directly comparablewith those in Tasker [1998].
5 Some value drivers are not easily classified. For example, Sales, which is categorized as an accrual flow, couldcontain less accruals than EBITDA, which is categorized as a cash flow measure.
10
• 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).
• 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 future abnormal earnings. Forward earnings are converted to
forward abnormal earnings, based on projected book values and assumed discount rates.
Each measure is based on different assumptions regarding future profitability and patterns of
future abnormal earnings. Specifically, abnormal earnings are assumed to remain constant
after year +5 for P1*, whereas they are assumed to be zero after year +5 for P2*. For P3*, the
level of profitability (measured by ROE) is assumed to trend linearly from the level implied
by earnings forecasted for year +3 to the industry median by year +12, and abnormal
earnings are assumed to remain constant thereafter.
( )( )
( )( )∑
=
++−++∗
+−
+
+−
+=5
15
451
1E
1E
1s tt
tttts
t
sttstttt
kkbkeps
kbkeps
bPνν
ν
( )( )∑
=
−++∗
+−
+=5
1
1
1E
2s
st
sttstttt
kbkeps
bPν
ν
[ ] [ ]2 11* 1 12 111
111 3
( ) ( )( )3
(1 ) (1 ) (1 )t t s t t s t t t tt t s t t s
t t s ss st t t t
ROE k bv ROE k bveps kbvP bv
k k k k+ + − + ++ + −
= =
Ε − Ε − Ε −= + + + + + +
∑ ∑
where
bv t+s = book value per share at time t+s (the end of year t+s),
epst+s = forecasted earnings per share in year t+s,
ROEt+s = forecasted return on equity in year t+s,
11
kt = the discount rate for equity at time t.
• Sum of forward earnings: To understand better the poor performance of the three intrinsic
value measures, we consider two other measures (ES1 and ES2) that use forward earnings
but do not rely on the residual income model. 6
( )∑=
+=5
1E1
ssttt epsES and
( )( )∑
=
+
+=
5
1 1
E2
ss
t
sttt
k
epsES
All the value drivers listed above, except for ES1 and ES2, have been linked before to
value. Accruals distinguish accounting numbers from cash flows, and accounting book value and
earnings, which are assumed to represent “fundamentals,” are used extensively for valuation
purposes. At an intuitive level, accounting earnings could be more value-relevant than current
cash flows for at least two reasons: a) cash flows do not reflect value creation in some cases
(e.g., asset purchases), and b) accruals allow managers to reflect their judgment about future
prospects. More formally, Ohlson [1995] and Feltham and Ohlson [1995] build valuation models
in which earnings and book value play instrumental roles.
For earnings-based multiples, we consider reported earnings excluding extraordinary
items and discontinued operation from COMPUSTAT, and actual earnings as defined by IBES.
The second measure is derived from the first earnings measure 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 that are expected to persist in the future, it will be
linked more directly to price. Although the use of sales as a value driver has less theoretical
basis, relative to earnings and cash flows, we consider it because of its wide use in certain
emerging industries where earnings and cash flow are perceived to be uninformative.
6 We thank Jim Ohlson for suggesting ES1.
12
The flexibility allowed within GAAP creates the potential for accounting numbers to be
distorted, thereby reducing their value relevance. This potential for earnings management, in
combination with the truism that price reflects the present value of future cash flows, has caused
some to prefer cash flow multiples over multiples based on accounting numbers. To provide
some empirical evidence on this debate, we consider four cash flow measures, and contrast their
value-relevance with two multiples based on accounting earnings. Each measure removes the
impact of accruals to a different extent. 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 historical data, such as reported earnings and cash flows, to not capture
fully the forward-looking information reflected in prices has long been recognized in the
literature. Analysts’ forecasts of forward earnings offer a possible solution to this mismatch. Liu
and Thomas [2000] find that revisions in analysts’ earnings forecasts and changes in interest
rates explain a large portion of contemporaneous stock returns. Consensus estimates are often
available for forecasted earnings for the current year (EPS1) and the following year (EPS2).
Consensus estimates are also frequently available for the long-term growth forecast (g) for
earnings over the next business cycle (commonly interpreted to represent 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 combines the
information contained in EPS2 and g, it imposes a different structure. To justify the valuation of
13
high-growth firms, analysts have introduced the concept of PEG ratios, which is the ratio of P/E
to g. Initially, PEG ratios were assumed to equal one. Subsequently, as technology stock
valuations soared during the late 1990s, PEG ratios higher than one have been proposed by
analysts.
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 they incorporate more information than any of the simple multiples, these
generic approaches are not as detailed as a comprehensive valuation based on projections that
allow for firm-specific growth in abnormal earnings beyond the horizon date.
While the two final earnings sum measures we consider (ES1 and ES2) have not been
discussed in the literature, our motivation to introduce these two value drivers is to understand
better the poor performance observed for the intrinsic value measures. Whereas the first measure
simply sums the earnings forecasted for years +1 to +5, the second measure 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, then the estimation errors in
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, relative to
14
the intrinsic value measures, assumed terminal values and the process of converting earnings
forecasts to forecasted abnormal earnings cause measurement error.
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, TP is measured by the market value of equity plus the book value of debt.
Multiples are generated based on the ratio of value driver to TP for comparable firms, those
multiples are then used to predict TP for target firms, and finally the book value of debt is
subtracted from predicted TP obtain predicted equity values.
3.2 Traditional Multiple Valuation
In the first stage of our analysis, we follow the traditional ratio representation and require
that the price of firm i (from the comparable group) in year t (pit) is directly proportional to the
value driver:
itittit xp εβ += (1)
where itx is the value driver for firm i in year t, tβ is the multiple on the value driver and tε is
the pricing error. To improve efficiency, we divide equation (1) by price:
it
it
it
itt pp
x εβ +=1 . (2)
Baker and Ruback [1999] and Beatty, Riffe, and Thompson [1999] demonstrate 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 β t, we elected to impose the restriction that expected percent pricing
errors (ε/p) be zero, even though an unrestricted estimate for β t from equation (2) offers a lower
value of mean squared percent pricing error. Empirically, we find that our approach generates
lower pricing errors for most firms, relative to an unrestricted estimate, but it generates
15
substantially higher errors in the tails of the distribution. 7 By restricting ourselves to unbiased
percent 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 determined by the
restriction we impose that percent pricing errors be zero on average, i.e., 0=
it
it
pE
ε.
Rearranging terms in equation (2) and applying the expected value operator, we obtain the
harmonic mean of /it itp x as an estimate for β t:
01 =
−=
it
it
it
it
px
Ep
Eβε
=⇒
it
it
px
E
1tβ (3)
This harmonic mean estimate for β t is used to obtain a prediction for the target firm’s
equity value by multiplying the β t estimate by the firm’s value driver, and the percent pricing
error is calculated as follows:8
it
ittit
it
it
pxp
p
^βε −
= . (4)
The performance of multiples is evaluated by examining the dispersion of the pooled distribution
of itit p/ε (lower dispersion indicates better performance).
7 To investigate the tradeoff between bias and dispersion of pricing errors associated with our choice of a
restricted regression, we investigated the distribution of percent pricing errors for the unrestricted case. Weestimated equation (2) for comparable firms from the cross-section. (When using comparable firms from thesame industry, the estimated multiples generated substantial pricing errors.) We find that the percent pricingerror distributions for all multiples are shifted to the right substantially, relative to the distributions for therestricted case reported in the paper (our distributions tend to peak around zero pricing error). This shift to theright indicates that the multiples and predicted valuations for the unrestricted case are on average lower thanours. We find that the bias created by this shift causes greater pricing errors for the bulk of the firms not in thetails of the distribution, relative to our restricted case.
16
3.3 Intercept Adjusted Multiples
For the second stage of our analysis, we relax the direct proportionality requirement and
allow for an intercept:
ititttit xp εβα ++= . (5)
There are many factors, besides the value driver under investigation, that affect price.9 The
average effect on price of such omitted factors is not likely to be zero. The intercept in equation
(5) captures the average effect of omitted factors and thus its inclusion 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:
it
it
it
itt
itt pp
xp
εβα ++=
11 , (6)
Estimating equation (6) with no restrictions minimizes the square of percent pricing errors, but
the expected value of those errors is non-zero.10 For the reasons mentioned in section 3.2, we
again impose the restriction that percent pricing errors be unbiased.11 That is, we seek to estimate
the parameters αt and β t that minimize the variance of itit p/ε , subject to the restriction that the
expected value of itit p/ε is zero:
)]1
(1var[]/)var[()/( varmin,
it
itt
ittititttititit p
xp
pxpp βαβαεβα
+−=⋅−−=(7a)
8 Note that some studies measure the pricing error as the difference between the predicted value and price (e.g.,
Alford [1992]) while we measure the pricing error as the difference between price and the predicted value.9 If the relation between price and the value driver is non-linear, the omitted factors include higher powers of the
value driver.10 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 captures all the variation in the dependent variable,thereby making the independent variables redundant.
11 As with equation (2), percent pricing errors from the unrestricted approach for equation (6) are higher for mostfirms (in the middle of the distribution) but there are fewer firms in the tails of the distribution. (See footnote 7.)
17
.0E .. =
it
it
pts
ε
(7b)
It can be shown that the estimates for αt and β t that satisfy (7a) and (7b) are as follows
−
+
−
=
t
t
tt
t
ttt
t
t
t
t
tt
t
ttt
t
t
px
ppx
Ep
Epp
xE
px
pE
pE
px
pppx
E
,1
cov1
21
varvar1
1,
1cov
1var
22β
(8)
−
=
t
t
tt
t
pE
px
E
1
1 β
α (9)
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. Prediction errors, defined by equation (10), are then computed for the
different multiples and their distribution examined to determine performance.
it
itttit
it
it
pxp
p
^^βαε −−
= . (10)
4. Sample and Data
To construct the 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, 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; (2) at least 30 monthly returns are available from the prior 60 month period;
(3) price, actual EPS, forecasted EPS for years +1 and +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
18
the pooled distribution. The resulting sample includes 26,613 observations between 1982 and
1999. This sample is used for the descriptive statistics reported in Table 1. For the results
reported after Table 1, we impose three additional requirements: (5) share price on the day IBES
publishes summary forecasts in April is greater than or equal to $2;12 (6) all multiples (except for
maintenance cash flow and free cash flow) are positive;13 and (7) each industry-year combination
has at least five observations. These additional requirements reduce the sample to 19,879
observations.
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.
The discount rate (kt) is calculated as the risk-free rate plus beta times the equity 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.14 We estimate betas using monthly stock returns and value-
weighted CRSP returns for the five years that end in March of year t+1.
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.,
)1(*1 gepseps stst += −++ .
12 Since our valuation model in the second stage analysis includes an intercept, valuation errors would be
abnormally large for stocks with very low share prices.13 Given the substantial fraction of the sample with negative values for these two value drivers, we elected to
exclude them from the remainder of the analysis.14 We use decile median betas, since firm-specific betas are estimated with considerable error.
19
The book values for future years are determined 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).15 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 at 10% and 50%.16
It is important to recognize that our sample only 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 are on average much smaller than our sample firms. In particular, firm-years excluded
because they lack analyst coverage typically have low market capitalization. Also, firm-years
excluded because they have negative value drivers are potentially different from our sample,
because they are more likely to be young firms and/or technology firms. Overall, our results
should be extrapolated with caution. For example, the performance we document for the sales
multiple may not be representative of that multiple for all firms with positive sales, because our
results are based on a relatively small subset of those firms.
15 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.16 The impact of altering the dividend payout assumptions on the results is negligible, because it has a very small
impact on future book value and an even smaller impact on the computed abnormal earnings.
20
5. Results
5.1 Descriptive Statistics
Table 1 reports the pooled distribution of ratios of value drivers to price. While most
distributions contain very few negative values, the incidence of negative values is higher for cash
flow multiples. 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 deletion of observations with
extreme values (top and bottom 1%). Given the difficulty of mapping negative value drivers to
positive share prices, we conclude that these two value drivers are not suitable for multiple
valuation purposes in large-sample analyses such as ours and drop them hereafter.
Table 2 reports the Pearson and Spearman correlations among the ratios of value drivers
to price. In general, the two sets of correlations are similar. Most of the ratios are positively
correlated with each other, which suggests that they share considerable common information.
The correlations among different forward earnings and earnings-growth ratios are especially
high, generally around 90%. Interestingly, the correlations between the different forward
earnings multiples and the three intrinsic value measures (P1*, P2*, and P3*) are much lower
(only about 50 percent). The lower correlations suggest that converting forward earnings to
forward abnormal earnings alters substantially the information represented by the two sets of
value drivers.
5.2 Traditional Multiples
The results of the first stage analysis, based on the traditional ratio representation (no
intercept), are reported in Table 3. The results reported in Panel A use the entire cross-section of
firms as comparables for computing multiples, and the results in Panel B are based on
21
comparables selected from the same IBES industry group. Out-of-sample value predictions are
made each year, and percentage valuation errors (price less predicted price, scaled by price) are
pooled across firm-years. We report the following statistics that describe the distribution of the
percent pricing errors: two measures of central tendency (mean and median) and five measures
of dispersion (the standard deviation and four non-parametric dispersion measures: (i) 75%-25%,
(ii) 90%-10%, (iii) 95%-5% and (iv) 99%-1%). The different multiples are separated into four
categories: historical value drivers, forward earnings meaures, intrinsic value and earnings sum
measures, and drivers based on enterprise value.
In general, the valuation errors we report are skewed to the left, indicated by medians that
are greater than means.17 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 elected to report the results using the percent
pricing error metric because it is easier to interpret absolute performance using that metric. We
did, however, recalculate the dispersion metrics reported in this paper using the log pricing error
metric to confirm that all our inferences regarding relative performance remain unchanged.
Examination of the standard deviation and the four non-parametric dispersion measures
in Panel A suggests the following ranking of multiples. Forecasted earnings, as a group, exhibit
the lowest dispersion of percent pricing errors. This result is intuitively appealing because
17 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.
22
earnings forecasts 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 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 estimated discount rates, forecasted forward abnormal earnings, or
assumed terminal values for these three measures. The larger percent pricing errors associated
with P2* relative to P1* suggests that the terminal value assumption of zero abnormal earnings
past year +5 for is less appropriate than the assumption of zero growth in abnormal earnings past
year +5. The very high pricing errors associated with P3* suggest that the more complex
structure of profitability trends imposed for this measure and/or the assumption that abnormal
earnings remain constant past year +12 at the level determined by current industry profitability
are inappropriate.
The sharp improvement in performance observed for ES1 and ES2 supports the view that
the poor performance of P1* and P2* is caused by the generic terminal value assumptions and/or
the conversion of forward earnings forecasts to abnormal earnings.18 Recall that ES1 simply
aggregates the same five years’ earnings forecasts that are used for P1* and P2*, and ES2
18 While not immediately obvious, it can be shown that P1* is also equal to a function of earnings projected for
years +1, +2, and +3. Specifically,2
32
21*
)1()1()1(1
k
keps
k
dk
dP ttt
t+
++
++
= +++ [Penman, 2000]. Note that dividends for
+1 and +2 are derived from earnings forecasts for those two years. In effect, P1* is similar to ES2, except that itignores forecasted earnings for years +4 and +5, and it capitalizes earnings for year +3 (= epst+3/k ).
23
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 denominators 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 correlation 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. Percent pricing errors for book value
(BV) have a standard deviation of 0.565 and inter-quartile range of 0.744, compared to a
standard deviation of 0.512 and inter-quartile range of 0.625 for COMPUSTAT earnings
(CACT). The performance of historical earnings is further enhanced by the removal of one-time
transitory components. Consistent with the results in Liu and Thomas [2000], pricing errors for
IBES earnings (IACT) have an even lower standard deviation of 0.453 and inter-quartile range of
0.551. The inferior performance of book value relative to earnings and the improvement
observed when one-time items are removed are both consistent with “street wisdom.”
Contrary to the belief that “Cash is King” in valuation, our results show cash flows
perform significantly worse than accounting earnings. For example, the valuation error of
EBITDA has a standard deviation of 0.613 and inter-quartile range of 0.697 (both of which
indicate higher dispersion than that for the earnings measures). Between the two cash flow
measures, CFO fares considerably worse than EBITDA; in fact it is consistently the worst
performer in all our analyses.19
19 The free cash flow and maintenance free cash flow measures, which are excluded from this analysis because of
the large proportion of negative values, exhibit even worse performance.
24
The sales multiple performs quite poorly, only slightly better than CFO. Its valuation
error has a standard deviation of 0.943, and inter-quartile range of 0.801. This result suggests
that sales do not reflect profitability until expenses have been considered.
The last two rows in Panel A of Table 3 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 multiples based on equity value. For example, the interquartile range of pricing errors for
sales increases from 0.801 to 1.097 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].) It is possible that our
measure of debt (the book value of long-term debt) measures the true value of total debt with
considerable error.
To conduct the analysis using comparable firms from the same industry, we searched for
a reasonable industry classification scheme. Because of the evidence that SIC codes frequently
misclassify firms (Kim and Ritter [1999]), we use the industry classification provided by IBES.
IBES indicate that their classification is based loosely on SIC codes, but it is also subject to
detailed adjustments.20 The IBES industry classification has three levels (in increasing fineness):
sector, industry, and group. We use the intermediate (industry) classification level because
sectors are too broad to allow the selection of homogenous firms, and groups are too narrow to
allow the inclusion of sufficient comparable firms (given the loss of observations due to our data
requirements).
20 The IBES classification resembles the industry groupings suggested by Morgan Stanley.
25
The results reported in Panel B of Table 3, which are based on comparable firms from the
same IBES industry classification, represent our primary results because the procedures used are
most closely related to practice. Consequently, much of the sensitivity analysis we conduct later
relates to this set of results.
The pricing error distributions in this panel exhibit improved performance over those
reported in Panel A for all multiples. The improvement 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.21 Generally, the improvement is larger at the center of the distributions; that is,
small valuation errors became much smaller while large valuation errors do not change much.
To offer a visual picture of the relative and absolute performance of different categories
of multiples, we provide in Figure 1 the histograms for percent pricing errors for the following
selected multiples: EPS2, P1*, IACT, EBITDA, BV and Sales. The histograms report the
fraction 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. A multiple is considered better if it has a more peaked distribution. The differences in
performance across the different categories are clearly visible in Figure 1. The figure also offers
a better view of the shapes of the different distributions and enables readers to find the fraction
of firms within different pricing error ranges for each distribution.
21 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 isless precise. This fact is also reflected in the increase in the deviation of the sample mean of the valuation errorsfrom zero.
26
The performance of sales multiples continues to lag behind all others, except CFO. A
frequent reason for using sales as a value driver is when earnings and cash flows are negative.
Since we restrict our sample to firms with positive 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
particular, 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],
indicate that traditional value drivers are inappropriate for such stocks, Hand [2000] finds that
economic fundamentals, especially forward earnings forecasts, explain valuations for such firms.
To provide some sense of the impact of deleting firms with negative values for earnings
and cash flow measures, we examined 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. The
dispersion of pricing errors increases for all three multiples, relative to those reported in Table 3,
Panel B. 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 Panel B. These results emphasize
our earlier caution that the results reported here may not be descriptive of other samples.
In addition to ranking the relative performance of different multiples, the results in Table
3, Panel B, (as well as the histograms in Figure 1) can also be used to infer absolute pricing
errors. Specifically, halving the four non-parametric dispersion measures provides an estimate of
the range of absolute pricing error within which a certain fraction of the sample lies. For
example, the inter-quartile range of 0.313 for EG1 in Panel B, indicates that approximately half
the sample has an absolute pricing error less than 15.65 percent for that multiple.22
22 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 only used forillustrative purposes.
27
The multiples used in calculating the percent pricing errors in Panels A and B were
estimated using the harmonic mean. To allow comparison with results in previous studies (e.g.,
Alford [1992]), we repeat the Panel B analysis 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 performance of median
multiples is worse than that for harmonic mean multiples. Of course, 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 multiples, is inversely related to
the absolute performance of that multiple, and the improvement for forward earnings multiples is
quite small. Importantly, the relative performance of the different multiples remains
unchanged.23
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) is negligible when all firms in the cross-section are included as comparable firms,
since the addition of one firm has almost no effect on the multiple. There is a decrease in the
dispersion of pricing errors when we use in-sample harmonic means from the same industry (e.g.
the interquartile range for EPS2 declines from 0.317 in Table 3, Panel B, to 0.301), and an even
larger decline in dispersion is observed for in-sample median multiples (e.g., interquartile range
for EPS2 declines from 0.320 in Table 3, Panel C, to 0.290).
23 We also examined the impact of using the industry mean of price-to-value driver ratios as the multiple, rather
than the harmonic mean. We find a considerable increase in the dispersion of pricing errors as well as meanvalues that are substantially negative. Similar to the results reported for medians, the decline in performance isgreater for multiples that perform poorly in Table 3, Panel B.
28
5.3 Intercept Adjusted Multiples
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
for comparable firms from the entire cross-section (Table 4, Panel A) and then for firms from the
same industry (Panel B).
As predicted, relaxing the no-intercept restriction improves the performance of all
multiples. The degree of improvement is not uniform, however. Multiples that perform poorly in
Panel A of Table 3 improve more than those that do well in that panel. For example, valuation
errors for sales exhibit a decline in standard deviation (inter-quartile range): from 0.943 (0.801)
to 0.646 (0.595) whereas valuation errors for EG1 exhibit only a small decrease in standard
deviation (inter-quartile range): from 0.317 (0.368) to 0.314 (0.361). Although the improvement
in absolute performance of the multiples is not uniform, the rank order of multiples remains
unchanged from Table 3 to Table 4.
The best performance is achieved when we allow for an intercept and select comparable
firms from the same industry (Table 4, Panel B). Comparison of these results with those in Table
3, Panel A, 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 A to Panel B in both Tables) is relatively
uniform across multiples. In contrast, the improvement generated by allowing an intercept (Table
3 to Table 4 for each Panel) is inversely related to that multiple’s performance.
5.4 Statistical significance of performance differences across multiples
Although our results suggest that many of the performance differences across different
multiples are economically significant, we have not provided any evidence regarding the
29
statistical significance of those differences. In other words, is the dispersion in pricing errors
observed for one multiple significantly different from that for another multiple? We focus on the
interquartile range as the primary measure of dispersion that is relevant to us, and conduct a
bootstrap-type analysis to provide tests of significance. We only report (in Table 5) the results
for the valuation procedures corresponding to our primary results reported in Table 3, Panel B
(no intercept and harmonic means of comparable firms from the same industry). Similar results
are observed when we considered other multiple valuation procedures.
We generated “samples” of 19,879 firm-years by drawing observations randomly from
our sample, with replacement. For each trial we computed the inter-quartile range for each
multiple, and then computed the difference between all pairs of inter-quartile ranges. This
process is repeated 100 times and a distribution is obtained for each pairwise difference.24 A t-
statistic is computed as the mean divided by the standard deviation for each of these
distributions. Those t-statistics, reported in Table 5, suggest that almost every pairwise difference
is statistically significant (t-statistic greater than 2). As expected, the performance of the different
multiples in Table 5 is consistent with that in Table 3, Panel B. For example, ES1 the multiple
with the lowest inter-quartile range in Table 3, Panel B, has all positive (negative) t-statistics in
the column (row) corresponding to that multiple.
5.5 Ranking Multiples in Each Industry
Given our focus on understanding the underlying information content of the different
multiples, we investigated overall patterns for firms pooled across industries. It has been
suggested, however, that different multiples work best in different industries. For example,
Tasker [1998] reports that investment bankers and analysts appear to use preferred multiples in
24 Given the large sample size considered in each trial, the statistics asymptote as the number of trials approaches
100, and increasing the number of trials beyond 100 provided almost no additional benefit.
30
each industry. Therefore, we determine the extent to which the relative performance of different
multiples varies across different industries, based on the dispersion of valuation errors within that
industry. Although we recognize that our search is unlikely to offer conclusive results, since we
do not pick comparable firms with the same skill and attention as others do in different contexts,
we wish to offer some general results.
Since investment professionals use simple multiples (no intercept) and select comparable
firms from the same industry, we only conduct the analysis for that combination (corresponding
to Table 3, Panel B). The valuation results for each industry are pooled across years, and
multiples are ranked by the interquartile range of pricing errors within each industry. Table 6
reports the results for the 81 industries we analyze. 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 overall results are observed with remarkable consistency
across all industries. In almost all industries, forecasted earnings perform the best. While the
specific forward earnings multiple that is ranked 1 varies from industry to industry, the general
dominance of those multiples is clearly evident. In terms of the mean and median ranks across all
industries, ES1 is ranked the highest (mean rank of 2.83 and median rank of 2), followed by ES2,
EG1, and EPS2 (all three have a median rank of 3). This pattern of superior relative performance
for forward earnings multiples, which is consistent with the results in Kim and Ritter [1999],
suggests that the information contained in forward looking value drivers captures a considerable
fraction of value, and this feature is common to all industries. At the other extreme, CFO and
sales multiples (especially the sales multiple based on enterprise value) consistently perform near
the bottom for most industries. Turning to the other value drivers (book values, historical
earnings and EBITDA), while the overall ranks are consistent with those reported in Table 3,
31
Panel B, there is more heterogeneity across industries. We were unable to find, however, any
systematic patterns of performance across the different sectors for these value drivers.
6. Conclusions
In this study we have examined the valuation properties of a comprehensive list of
multiples. We consider both the commonly used multiple approach, which assumes direct
proportionality between price and value driver, and a less restrictive approach that allows for an
intercept. To identify the importance of selecting comparable firms from the same industry, we
also report results based on the comparable group including 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 performance, our results show historical earnings
measures are ranked second 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, similar results are obtained across different industries.
We show that both the industry adjustment (selecting comparables from the same industry) and
the intercept adjustment (allowing for an intercept in the price/value driver relation) improve the
valuation properties of all multiples. While the industry adjustment is commonly used, the
intercept adjustment is not. We speculate that multiples are used primarily because they are
simple to comprehend and communicate and the additional complexity associated with including
an intercept may exceed the benefits of improved fit.
Our results regarding the information in different value drivers are consistent with
intuition. For example, forward-looking earnings forecasts reflect value better than historical
accounting information, accounting accruals add value-relevant information to cash flows, and
profitability can be better measured when revenue is matched with expenses. Some results in this
32
paper are surprising, however. For example, multiples based on the residual income model,
which explicitly forecasts terminal 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 results 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. We recognize that our study is designed to provide an overview
of aggregate patterns, and thus we may have missed more subtle relationships that are only
apparent in small sample studies.
We also 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 (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 use 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.
We note in conclusion that our analysis assumes that market prices are efficient, and we
evaluate multiples based on their ability to mimic current market valuations. The poor
performance we observe for intrinsic value measures could be due to an inefficient market that
33
prices stocks using simple forward earnings multiples and ignores the additional information
captured by intrinsic value measures. If so, portfolios formed using valuation errors from
intrinsic value measures should predict future returns, and portfolios formed using forward
earnings multiples should not. We investigated this possibility and estimated hedge portfolio
returns (invest long in deciles with the highest pricing error and invest short in deciles with the
most negative pricing error) over one, two, and three years following the April when portfolios
are formed. Although we find evidence of abnormal returns for certain portfolios, they are
observed for most forward earnings measures and for some intrinsic value measures (e.g., P1*).
In particular, there is no evidence to suggest that P3*, the most complex intrinsic value measure,
predicts abnormal returns better than simple forward earnings multiples. These findings suggest
that any mispricing that may occur is probably due to the market not fully incorporating
information in forward earnings forecasts, rather than due to the intrinsic value measures
identifying fundamental value with more accuracy than the market does.
34
APPENDIX
This appendix describes how the variables are constructed. All the value drivers are
adjusted for changes in number of shares. (#s refer to data items from COMPUSTAT).
IACT: IBES actual earnings (per share earnings adjusted for one-time items)
EBITDA: Earnings before interest, taxes, depreciation and amortization, #13
CFO: cash flow from operations, measured as EBITDA minus the total of interest expense
(#15), tax expense (#16) and the net change in working capital. We calculated the
change in working capital as: ∆CA - ∆CL - ∆Cash + ∆STD, where
∆CA = change in current assets (#4)
∆CL = change in current liabilities (#5)
∆Cash = change in cash and cash equivalents (#1)
∆STD = change in debt included in current liabilities (#34)
When data items 15, 16, 1 or 34 were missing, we set their value to zero.
FCF: free cash flow, measured as CFO minus net investment. We measure net investment
as capital expenditures (#128) plus acquisitions (#129) plus increase in investment
(#113) minus sale of PP&E (#107) minus sale of investment (#109).
When data items 128, 129, 113, 107 or 109 were missing, we set their value to zero.
MCF: maintenance cash flow, measured as CFO minus depreciation expense (#125)
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
35
EG2: EPS2*g, where g is mean IBES long term growth forecast
The three P* measures:
( )( )
( )( )s
tt
ttstt
ss
t
sttstttt
kkbkeps
kbkeps
bP+−
+
+−
+= ++
=
−++∗ ∑1
E1
E1 4
5
1
1 ννν
( )( )∑
=
−++∗
+−
+=5
1
1
1E
2s
st
sttstttt
kbkeps
bPν
ν
[ ] [ ]2 11* 1 12 111
111 3
( ) ( )( )3
(1 ) (1 ) (1 )t t s t t s t t t tt t s t t s
t t s ss st t t t
ROE k bv ROE k bveps kbvP bv
k k k k+ + − + ++ + −
= =
Ε − Ε − Ε −= + + + + + +
∑ ∑
The variables used in the P* calculations are obtained as follows:
The discount rate (kt) is calculated as the risk-free rate plus beta times the equity 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 that end in March of year t+1 (at least 30 observations are
required).
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.,
)1(*1 gepseps stst += −++ .
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 forecasted earnings less forecasted dividends). Since analyst forecasts
of future dividends are not available on IBES, we assume that the current dividend payout ratio
36
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). 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 at 10%
and 50%.
In the calculation of *3tP , ( )5E +tt ROE for s = 4, 5, …, 12 are 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%.
The earnings forecasts for years +1 to +5 are summed to obtain the two earnings sum
measures.
( )∑=
+=5
1E1
ssttt epsES
( )( )∑
=
+
+=
5
1 1
E2
ss
t
sttt
k
epsES
37
Table 1Distribution of value driver to price ratios
Summary descriptions of the variables are as follows: P is stock price; BV is book value of equity; MCF ismaintenance cash flow (equivalent to free cash flow when depreciation expense equals capital expenditure); FCF isfree 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 IBESactual earnings; EPS1 and EPS2 are one year out and two year out earnings 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 ofdebt). All totals are deflated by the number of shares outstanding at the end of the year.
( )( )
( )( )s
tt
ttstt
ss
t
sttstttt
kk
bkeps
k
bkepsbP
+
−+
+
−+= ++
=
−++∗ ∑1
E
1
E1 4
5
1
1 ννν ,
( )( )∑
=
−++∗
+
−+=
5
1
1
1
E2
ss
t
sttstttt
k
bkepsbP
νν ,
( )( )
( )[ ]( )
( )[ ]( )11
111211
3
12
1
1
111
E3
tt
tttt
ss
t
sttstt
ss
t
sttstttt
kk
bvkROEE
k
bvkROEE
k
bkepsbvP
+
−+
+
−+
+
−+= ++
=
−++
=
−++∗ ∑∑ ν, where
( )stt ROEE + for s = 4, 5, …, 12 is forecasted using a linear interpolation to the industry median ROE. The industrymedian ROE is calculated as a moving median of the past ten years’ ROE of all firms in the industry. To eliminateoutliers, industry median ROEs are Winsorized at the risk free rate and 20%.
( )∑=
+=5
1
E1s
sttt epsES , and( )
( )∑=
+
+=
5
1 1
E2
ss
t
sttt
k
epsES .
Sample is trimmed at 1% and 99% for each simple multiple using the pooled distribution. Years covered are 1982through 1999. Sample size is 26,613.
Table 2Correlations among value drivers (scaled by stock price)
Pearson (Spearman) correlations above (below) the main diagonalSummary descriptions of the variables are as follows: P is stock price; BV is book value of equity; MCF is maintenance cash flow (equivalent to free cash flowwhen depreciation expense equals capital expenditure); FCF is free cash flow to debt and equity holders; CFO is cash flow from operations; EBITDA is earningsbefore interest, taxes, depreciation and amortization; CACT is COMPUSTAT earnings before extraordinary items; IACT is IBES actual earnings; EPS1 andEPS2 are one year out and two year out earnings forecasts; EG1=EPS2*(1+g), EG2=EPS2*g, where g is the growth forecast; and TP is enterprise value (marketvalue of equity + book value of debt). All totals are deflated by the number of shares outstanding at the end of the year.
( )( )
( )( )s
tt
ttstt
ss
t
sttstttt
kk
bkeps
k
bkepsbP
+
−+
+
−+= ++
=
−++∗ ∑1
E
1
E1 4
5
1
1 ννν ,
( )( )∑
=
−++∗
+
−+=
5
1
1
1
E2
ss
t
sttstttt
k
bkepsbP
νν ,
( )( )
( )[ ]( )
( )[ ]( )11
111211
3
12
1
1
111
E3
tt
tttt
ss
t
sttstt
ss
t
sttstttt
kk
bvkROEE
k
bvkROEE
k
bkepsbvP
+
−+
+
−+
+
−+= ++
=
−++
=
−++∗ ∑∑ ν, where ( )stt ROEE + 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 theindustry. To eliminate outliers, industry median ROEs are Winsorized at the risk free rate and 20%.
( )∑=
+=5
1
E1s
sttt epsES , and( )
( )∑=
+
+=
5
1 1
E2
ss
t
sttt
k
epsES . Sample is trimmed at 1% and 99% for each simple multiple using the pooled distribution. Years
covered are 1982 through 1999. Sample size is 19,879.
Table 3Distribution of pricing errors for simple multiples
Value and value drivers are assumed to be proportional: itittit xp εβ += . Multiples are estimated using harmonic
means:
=
it
ittt p
xE1β in Panels A&B, and medians are used in Panel C. Pricing error is
it
itit
it
it
pxp
p
^βε −
=
Summary descriptions of the variables are as follows: P is stock price; BV is book value of equity; CFO is cash flowfrom operations; EBITDA is earnings before interest, taxes, depreciation and amortization; CACT is COMPUSTATearnings before extraordinary items; IACT is IBES actual earnings; EPS1, EPS2 are one year out and two year outearnings forecasts; EG1=EPS2*(1+g), EG2=EPS2*g, where g is growth forecast. All totals are deflated by thenumber of shares outstanding at the end of the year. TP is enterprise value (market value of equity plus book valueof debt). When TP multiples are used, predicted equity value is calculated by subtracting the book value of debt.
( )( )
( )( )s
tt
ttstt
ss
t
sttstttt
kk
bkeps
k
bkepsbP
+
−+
+
−+= ++
=
−++∗ ∑1
E
1
E1 4
5
1
1 ννν ,
( )( )∑
=
−++∗
+
−+=
5
1
1
1
E2
ss
t
sttstttt
k
bkepsbP
νν ,
( )( )
( )[ ]( )
( )[ ]( )11
111211
3
12
1
1
111
E3
tt
tttt
ss
t
sttstt
ss
t
sttstttt
kk
bvkROEE
k
bvkROEE
k
bkepsbvP
+
−+
+
−+
+
−+= ++
=
−++
=
−++∗ ∑∑ ν, where
( )stt ROEE + 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 eliminateoutliers, industry median ROEs are Winsorized at the risk free rate and 20%.
( )∑=
+=5
1
E1s
sttt epsES , and( )
( )∑=
+
+=
5
1 1
E2
ss
t
sttt
k
epsES .
Multiples are based on all firms in the cross-section in Panel A, and firms from the same Industry (based on IBESindustry classification) for panels B & C. Years covered are 1982 through 1999. Sample size is 19,879.
Panel A: Valuation using harmonic mean cross-sectional multiplesMean Median SD 75%-25% 90%-10% 95%-5% 99%-1%
Table 4Distribution of pricing errors for intercept adjusted multiples
Value and value drivers are assumed to be linear: ititttit xp εβα ++= . Multiple is estimated excluding the firmunder valuation, by solving the following constrained minimization problem:
]]/)var[()/( varmin,
ititttititit pxpp ⋅−−= βαεβα
; .0E .. =
it
it
pts
ε Pricing error is it
itttit
it
it
pxp
p
^^βαε −−
=
Summary descriptions of the variables are as follows: P is stock price; BV is book value of equity; CFO is cash flowfrom operations; EBITDA is earnings before interest, taxes, depreciation and amortization; CACT is COMPUSTATearnings before extraordinary items; IACT is IBES actual earnings; EPS1, EPS2 are one year out and two year outearnings forecasts; EG1=EPS2*(1+g), EG2=EPS2*g, where g is growth forecast. All totals are deflated by thenumber of shares outstanding at the end of the year. TP is enterprise value (market value of equity plus book valueof debt). When TP multiples are used, predicted equity value is calculated by subtracting the book value of debt.
( )( )
( )( )s
tt
ttstt
ss
t
sttstttt
kk
bkeps
k
bkepsbP
+
−+
+
−+= ++
=
−++∗ ∑1
E
1
E1 4
5
1
1 ννν ,
( )( )∑
=
−++∗
+
−+=
5
1
1
1
E2
ss
t
sttstttt
k
bkepsbP
νν ,
( )( )
( )[ ]( )
( )[ ]( )11
111211
3
12
1
1
111
E3
tt
tttt
ss
t
sttstt
ss
t
sttstttt
kk
bvkROEE
k
bvkROEE
k
bkepsbvP
+
−+
+
−+
+
−+= ++
=
−++
=
−++∗ ∑∑ ν, where
( )stt ROEE + for s = 4, 5, …, 12 is forecasted using a linear interpolation to the industry median ROE. The industrymedian ROE is calculated as a moving median of the past ten years’ ROE of all firms in the industry. To eliminateoutliers, industry median ROEs are Winsorized at the risk free rate and 20%.
( )∑=
+=5
1
E1s
sttt epsES , and( )
( )∑=
+
+=
5
1 1
E2
ss
t
sttt
k
epsES .
Multiples are based on all firms in the cross-section in Panel A, and firms from the same Industry (based on IBESindustry classification) in panel B. Years covered are 1982 through 1999. Sample size is 19,879.
Panel A: Valuation using intercept adjusted cross-sectional multiplesMean Median SD 75%-25% 90%-10% 95%-5% 99%-1%
Table 5t-statistics associated with pairwise comparisons of inter-quartile ranges for pricing errors from different multiples
Random samples of 19,879 firm-years are drawn with replacement from our sample, and the inter-quartile range computed for all multiples, using harmonicmeans for firms in the same IBES industry. Differences in these interquartile ranges are computed for all pairs of multiples. This process is repeated 100 times,and a distribution is obtained for each pairwise difference. The t-statistics equal the mean divided by the standard deviation of these distributions. A positive(negative) t-statistic indicates that the row multiple performs worse (better) than the column multiple. Summary descriptions of the variables are as follows: P isstock price; BV is book value of equity; CFO is cash flow from operations; EBITDA is earnings before interest, taxes, depreciation and amortization; CACT isCOMPUSTAT 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. All totals are deflated by the number of shares outstanding at the end of the year. TP is enterprisevalue (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.
( )( )
( )( )s
tt
ttstt
ss
t
sttstttt
kk
bkeps
k
bkepsbP
+
−+
+
−+= ++
=
−++∗ ∑1
E
1
E1 4
5
1
1 ννν ,
( )( )∑
=
−++∗
+
−+=
5
1
1
1
E2
ss
t
sttstttt
k
bkepsbP
νν ,
( )( )
( )[ ]( )
( )[ ]( )11
111211
3
12
1
1
111
E3
tt
tttt
ss
t
sttstt
ss
t
sttstttt
kk
bvkROEE
k
bvkROEE
k
bkepsbvP
+
−+
+
−+
+
−+= ++
=
−++
=
−++∗ ∑∑ ν, where ( )stt ROEE + 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 theindustry. To eliminate outliers, industry median ROEs are Winsorized at the risk free rate and 20%.
( )∑=
+=5
1
E1s
sttt epsES , and( )
( )∑=
+
+=
5
1 1
E2
ss
t
sttt
k
epsES . Years covered are 1982 through 1999. Sample size is 19,879.
Pricing errors are computed for each firm-year using harmonic means of firms in each industry. Multiples are ranked for each industry according to the inter-quartile range of percent pricing errors. Lower ranks indicate better performance. Industry classification is from the IBES sector/industrygroup classificationcode. Years covered are 1981 through 1999. Sample size is 19,879. Summary descriptions of the variables are as follows: P is stock price; BV is book value ofequity; CFO is cash flow from operations; EBITDA is earnings before interest, taxes, depreciation and amortization; CACT is COMPUSTAT earnings beforeextraordinary 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 gis growth forecast. All totals are deflated by the number of shares outstanding at the end of the year. TP is enterprise value (market value of equity plus bookvalue of debt). When TP multiples are used, predicted equity value is calculated by subtracting the book value of debt.
( )( )
( )( )s
tt
ttstt
ss
t
sttstttt
kk
bkeps
k
bkepsbP
+
−+
+
−+= ++
=
−++∗ ∑1
E
1
E1 4
5
1
1 ννν ,
( )( )∑
=
−++∗
+
−+=
5
1
1
1
E2
ss
t
sttstttt
k
bkepsbP
νν ,
( )( )
( )[ ]( )
( )[ ]( )11
111211
3
12
1
1
111
E3
tt
tttt
ss
t
sttstt
ss
t
sttstttt
kk
bvkROEE
k
bvkROEE
k
bkepsbvP
+
−+
+
−+
+
−+= ++
=
−++
=
−++∗ ∑∑ ν, where ( )stt ROEE + 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 theindustry. To eliminate outliers, industry median ROEs are Winsorized at the risk free rate and 20%.
( )∑=
+=5
1
E1s
sttt epsES , and( )
( )∑=
+
+=
5
1 1
E2
ss
t
sttt
k
epsES . Years covered are 1982 through 1999. Sample size is 19,879.
Figure 1Distribution of Pricing Errors Using Simple Industry Multiples
Value and value drivers are assumed to be proportional: ititiit xp εβ += . The multiple, βt, is estimated using the
industry harmonic mean:
=
it
itt p
x/E1β , and the distribution of percent pricing error,
it
ittit
it
it
pxp
pβε ˆ−
= , is plotted
below. The variables are defined as follows (all amounts are on a per share basis): P is stock price; BV is book valueof equity; EBITDA is earnings before interest, taxes, depreciation and amortization; IACT is IBES actual earnings;EPS2 is two year out earnings forecast and g is growth forecast, and
( )( )
( )( )∑
=
++−++∗
+
−+
+
−+=
5
15
451
1
E
1
E1
s tt
tttts
t
sttstttt
kk
bkeps
k
bkepsbP
ννν
All multiples are calculated using comparable firms within each industry (based on IBES industry classification),and the firm being valued is excluded when computing industry multiples. Years covered are 1982 through 1999.Sample size is 19,879.The chart below is derived from a histogram with columns of width=0.1 (or 10% of price).For example, for EPS2, the fraction of the sample with pricing error between 0 and -0.1 is about 18%.
0
2
4
6
8
10
12
14
16
18
20
-2.1
-2.0
-1.9
-1.8
-1.7
-1.6
-1.5
-1.4
-1.3
-1.2
-1.1
-1.0
-0.9
-0.8
-0.7
-0.6
-0.5
-0.4
-0.3
-0.2
-0.1 0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
pricing error (scaled by price)
freq
uen
cy (i
n %
)
BV
EPS2
IACT
SALES
EBITDA
P1*
48
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