gains to valuation accuracy of direct valuation over...
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Gains to Valuation Accuracy of Direct Valuation Over Industry Multiplier Approaches
by
Lucie Courteaua
Jennifer L. Kaob
Terry O�Keefec
and
Gordon D. Richardsond
April 4, 2003
a. Department of Business Administration, Eastern Mediterranean University, Gazimağusa, TRNC, Mersin
10, Turkey; Tel: 90-392-630-1405; Fax: 90-392-365-1017; Email: [email protected] b. Department of AMIS, University of Alberta, Edmonton, Alberta, Canada, T6G 2R6.
Tel: (780) 492-7972; Fax: (780) 492-3325; Email: [email protected] c. Department of Accounting, University of Oregon and Commerce Department, the University of
Queensland; Tel: (541) 346-3317 and + 61 7 3365 6588; Fax: + 61 7 3365 6788; Email: [email protected]; [email protected]
d. Joseph L. Rotman School of Management, University of Toronto, 105 St. George St., Toronto, Ontario M5S 3E6. Tel: (416) 946-8601; Fax: (416) 971-3048; Email: [email protected]
Acknowledgments We would like to thank workshop participants at The Chinese University of Hong Kong, Ohio State University, University of Queensland, and University of Toronto for their comments. Special thanks are extended to Jeffrey Callen, Tom Scott, and especially Peter Easton for their helpful comments and suggestions on an earlier version of the paper; Phil Gray for help in solving a technical question, Kendrick Fiorito and Mort Siegel at Value Line for their advice on the project; David Bellamy and Flora Niu for their excellent research assistance. This research project is supported by the Social Sciences and Humanities Research Council of Canada and the University of Queensland. Jennifer Kao also receives financial support from Faculty of Business-Muir Funds. Terry O�Keefe thanks Ehrman V. Giustina for financial support. All remaining errors are the authors� sole responsibilities.
Gains to Valuation Accuracy of Direct Valuation Over Industry Multiplier Approaches
Abstract
The primary objective of this paper is to assess the gain in valuation accuracy when the analyst performs an exhaustive pro-forma about the target firm beyond the four-year forecast horizon under the direct method, compared to the alternative of using heuristic industry multiples to compute continuing values if she is uncertain about the firm�s post-horizon prospects. We also examine the determinants of the edge to direct valuation vis-à-vis industry multiplier approaches. Three industry-multiplier approaches are considered, the ETSS, IHP and PE4 models. Given variations in size and growth prospects across firms within an industry, we expect to achieve greater valuation accuracy under the direct method than any of the multiplier models that we explore in the study. Results from the study are consistent with this prediction. In particular, the direct method generates the lowest mean squared errors, tightest inter-percentile ranges and highest regression 2R , when data are either un-scaled or deflated by current book value per share. The direct method loses some of its edge over the other models, however, when current stock price per share is used as a deflator. Results also indicate that the valuation gains to directly forecasting firm-specific continuing values are greatest for small and fast growing target firms from highly heterogeneous industries. We contribute to the academic literature in three ways: first, we present a benchmark model against which the efficacy of various multiplier approaches may be evaluated; second, we identify firm characteristics and industries under which gains to direct forecasts of continuing value is greatest; third, we show the analyst and students of financial statement analysis how to use reverse engineering techniques to extract from comparable firms inferences about industry average growth prospects at the horizon. Keywords: Direct Valuation; Industry Multiplier Approaches; Valuation Accuracy; Valuation
Determinants
1
1. Introduction We consider a setting where an analyst has forecasted, for a target firm, the fundamentals out to
a horizon four years hence, but faces the dilemma of obtaining an appropriate continuing value at
the horizon. To come up with an intrinsic value for the firm, the analyst can perform a
comprehensive pro-forma analysis about that firm beyond the four-year forecast horizon
(hereafter, termed the direct method). Alternatively, she may choose to adopt a simpler valuation
heuristic using industry multiples to compute intrinsic values, perhaps because she is uncertain
about the post-horizon prospects of the firm in question (hereafter, termed the industry multiplier
approach). The objective of this study is to assess the gain in valuation accuracy when the direct
method is used to obtain continuing values, compared to industry multiplier approaches. In order
to draw inferences about bias and accuracy across measures of intrinsic value obtained from
these two general approaches, we focus on pricing errors assuming that the market is efficient.
We employ Value Line�s (hereafter VL) forecasts as a proxy for how well the
representative analyst could do using the direct method. We assume that the VL analyst has
prepared a complete pro-forma statement allowing her to make horizon price and price minus
book premium forecasts, summarizing her forecasted fundamentals about the target firm beyond
the horizon. Discounting these horizon premium forecasts and VL's forecasted abnormal
earnings to the horizon using an exogenous (CAPM) industry cost of capital yields the intrinsic
value for the target firm. The difference between intrinsic value and actual stock price is referred
to as benchmark errors. We interpret such errors as a measure of valuation accuracy under the
direct method, and assume that any analyst would do as well as the VL analyst when they too
apply this method for a target firm.
2
To implement the industry multiplier approach, we adopt a holdout procedure under
which industry multiples for the target firm are estimated using the applicable VL forecasted
valuation attributes of all the firms within the industry, except for the firm in question. This
procedure avoids the problem of circularity caused by using the target firm�s current stock price
as an input when computing its intrinsic value.1
The first industry multiplier approach that we compare to our benchmark pricing errors is
adapted from Easton, Taylor, Shroff and Sougiannis (2002, hereafter ETSS). ETSS develop a
reverse-engineering procedure to simultaneously solve for estimates of the industry cost of
equity capital and the market�s expected growth in residual earnings using I/B/E/S forecast data
from 1981 to 1998. Their procedure requires, in addition to current book value, annual forecasts
of residual income out to a horizon four years hence. We apply ETSS�s approach to value the
holdout firm by solving for the industry multiple (hereafter, termed ETSS multiple) that
reconciles forecasted fundamentals to the current observed price minus book premiums for firms
other than the target firm. The target firm�s intrinsic value is computed as the product of the
ETSS multiple and the corresponding VL forecasted fundamentals for the target firm.
The second industry multiplier approach is based on a reverse-engineering procedure that
we introduce into the literature. Using all estimation firms in the industry, we solve for the
industry horizon premium-to-book multiple (hereafter, termed IHP multiple) that minimizes the
squared price-deflated differences between current stock price and intrinsic value. In order to
obtain a continuing value for the holdout firm, we apply the estimated IHP multiple to horizon
book value forecasted by the VL analyst. Intrinsic value for the holdout firm is the sum of the
present value of this continuing value and VL forecasted abnormal earnings to the horizon.
1 A recent study by Liu, Nissim and Thomas (2002a) employs a similar holdout procedure.
3
The third multiplier approach that we examine is forward earnings-to-price multiple
where earnings are summed over a four-year forecast horizon (hereafter, termed PE4 multiple).
We focus on the harmonic mean version of PE4, calculated excluding the holdout firm, as a
recent study by Liu, Nissim and Thomas (2002a) shows that it yields the tightest distribution of
percentage pricing errors for the target firm.2 Forward earnings-to-price multiples are important
models to explore because, according to Liu et al, they outperform several residual income-based
multiples whose continuing values are estimated under ad hoc growth assumptions about the
post-horizon residual income.3
We hypothesize that the target firm�s benchmark pricing errors are lower than the
analogously defined pricing errors under any of the three industry-multiplier approaches
considered in the study. Our prediction is based on the notion that no two firms are alike. Given
heterogeneity across firms within an industry, greater valuation accuracy can be expected when
the continuing value is computed by drawing on the analyst�s detailed knowledge about the
target firm (i.e., the direct method), as opposed to relying on inferences made from information
about comparables within the same industry (i.e., industry-multiplier approaches). Consistent
with this prediction, we find that the direct method generates the lowest mean squared errors,
tightest inter-percentile ranges and highest 2R from regressing current stock price on intrinsic
value, compared to the ETSS, IHP and PE4 models. These results hold whether data are reported
on a per share basis or are deflated by current book value per share. The direct method loses
some of its edge over the other models, however, when current stock price per share is used as a
deflator instead.
2 Beatty, Riffe and Thompson (1999) also show that the harmonic mean model outperforms multipliers calculated as the median one period ahead earnings-to-price ratios. 3 These assumptions include: post-horizon residual income equals zero, is constant and equals horizon residual income, or fades to the industry median book return on equity.
4
The benefit from incurring additional forecasting costs to improve accuracy in continuing
value estimates may vary with industry heterogeneity, proxied by the within-industry dispersion
in horizon premiums. We explore this issue and, more generally, the determinants of relative
valuation accuracy in a multivariate setting. Results indicate that, after controlling for the effects
of covariates, the edge of the direct method over industry multiplier approaches is inversely
related to firm size, and directly related to growth and heterogeneity. To the extent that the costs
of performing a complete pro-forma beyond the forecast horizon are not industry-specific, these
results suggest that it may be worthwhile for analysts specializing in certain industries to exert
extra efforts in order to gain a better understanding of the target firm�s post-horizon prospects,
but not so in other industries. Finally, faced with scarce resources and time constraints, the
analyst may want to keep the relative importance of firm size, growth and heterogeneity in mind
when choosing firms and/or industries to extend her pro-forma analysis beyond the forecast
horizon.
We contribute to the academic literature in three ways: First, we present a benchmark
model (the direct method) against which the efficacy of various industry multiplier approaches
may be evaluated. By comparison, the extant studies of multiples typically use current stock
price as the reference point and assess their relative performance based on the magnitude of
pricing errors, calculated as intrinsic value minus current stock price deflated by the latter. Such
pricing errors are difficult to evaluate and raise the question of how well the analyst would have
done had she NOT used an industry multiple. We fill this void in the literature by comparing
pricing errors obtained under the direct method with those obtained under the industry multiplier
approach. We document the gain in valuation accuracy from a comprehensive pro-forma
analysis, assuming that the VL analyst proxies well for other analysts. Second, we identify firm
5
characteristics and industries under which gains to direct forecasts of continuing value is
greatest, compared to the alternative of using information about the industry to come up with a
continuing value. Of course, forecast costs are expected to increase with the forecast horizon, as
does the noise in distant forecasts. Thus, the analyst must evaluate the cost and benefit tradeoff
of exhaustive analysis versus simpler heuristics using industry multiples. Third, we show the
analyst and students of financial statement analysis how to use reverse engineering techniques to
extract from comparable firms inferences about industry average growth prospects at the
horizon. Continuing values calculated based on the IHP and ETSS multiples can then be
compared with the horizon premium that the analyst has in mind for the target firm being valued.
Both industry multiplier approaches use pricing-error minimization procedures and are practical
in nature.
The remainder of this study proceeds as follows: the next section presents a literature
review and hypothesis development; Section 3 describes our research methodology; Section 4
discusses sample selection and data; Section 5 reports the empirical findings, followed by our
concluding remarks in Section 6.
2. Literature Review and Hypothesis Development
Industry multiplier-based valuation models have been quite popular among valuation experts.
These models compute an industry multiple by relating current stock price for listed firms to
selected value drivers. The intrinsic value of the target firm is then estimated by applying the
resulting industry multiple to the analyst�s forecast of the value driver for that firm.
A number of researchers have studied the valuation performance of various multiplier
approaches over the years (e.g., Bhojraj and Lee 2002; Liu, Nissim and Thomas 2002a; Liu,
6
Nissim and Thomas 2002b; Baker and Ruback 1999; Beatty, Riffe and Thompson 1999; Kim
and Ritter 1999; Alford 1992; Boatsman and Baskin 1981). Liu et al (2002a), for example,
compare the performance of a comprehensive list of value drivers relative to current stock price
for a sample of 26,613 observations covered by I/B/E/S between 1982 and 1999. They report that
the forward earnings-to-price measures, i.e., 1 0EPS P , 2 0EPS P , and both discounted and
undiscounted 5
01
tt
EPS P=∑ , yield consistently lower percentage pricing errors, compared to
historical earnings measures as well as residual income models based on ad hoc growth
assumptions beyond the forecast horizon. Of the four forward earnings measures considered by
Liu et al, the versions that display the highest degree of earnings aggregation perform the best.
Given the interest in simple earnings-price multiples among academic researchers and
practitioners (reviewed in Liu et al 2002a), we will include a similar aggregate earnings-to-price
model over four periods, labeled PE4, as one contender industry multiplier approach.
As the multiplier literature evolves, researchers have explored ever more sophisticated
ways to obtain �comparable firms�, building on Alford�s (1992) finding that matching on past
growth within an industry improves simple multiplier approaches. Bhojraj and Lee (2002,
hereafter B&L) continue with this tradition by regressing price-to-book ratios on value drivers
such as profitability, risk and growth characteristics to obtain warranted multiples. B&L then use
warranted multiples to predict future price-to-book ratios for a target firm given its value driver
characteristics, and show sharp improvements in performance over the traditional techniques of
matching firms on size and/or industry. In his discussion of B&L, Sloan (2002) points out, ��
the next step will be to wean practitioners from reliance on imperfect heuristic like valuation
multiples altogether and instead encourage them to use more rigorous valuation methodologies�.
Heeding Sloan�s advice, we seek to portray the efficacy of the direct valuation vis-à-vis selected
7
industry multiple-based valuation models. By showing that the edge of the direct method over
these multiplier approaches increases with within-industry heterogeneity, our results are quite
consistent with B&L and point to the need to carefully select comparables if the analyst chooses
to use an industry multiplier approach. While we could compare the direct method to a long list
of multiplier models, including the more refined approaches proposed by B&L, we focus instead
on three models that exploit long horizon forecasts, namely, the ETSS, IHP and PE4 approaches.
In particular, we are interested in the problem of obtaining continuing values for such forecasts.
Thus, our setting can be viewed as being nested within the much broader multiplier literature.
Recently, Courteau, Kao and Richardson (2001) show that valuation models that employ
Value Line forecasted target price in the terminal value expression outperform RIM models with
ad hoc terminal value expressions (i.e., where post-horizon abnormal earnings are a perpetuity
with no growth and 2% growth) by a wide margin. The relative performance of the direct method
vis-à-vis industry multiplier approaches, however, cannot be directly inferred from Courteau et al
(2001). The RIM models that we examine (i.e., ETSS and IHP) are potentially more powerful
than RIM models with ad hoc continuing values, since they use the current market premiums for
comparable firms to infer the market�s expectation of growth prospects in abnormal earnings for
holdout firms. The market�s expectation of growth for comparable firms is likely to dominate ad
hoc restrictions on growth estimates imposed on the holdout firms by the researchers.
Our prediction about the superiority of the direct method over multiplier approaches is
guided by the simple premise of heterogeneity across firms within an industry. Kim and Ritter
(1999) find that ratios such as price-to-earnings, market-to-book and price-to-sales have only
modest predictive ability due to wide within-industry variation in these ratios for both public and
IPO firms. While the problem is especially severe when historical accounting numbers rather
8
than forecasts are used, it remains very difficult to capture valuable growth options of young
growth firms going public, even with one-year ahead earnings forecasts. These results suggest
the naivety of attempting to use comparable firm multiples when valuing IPOs without further
adjustments, and point to a potentially important role for investment bankers, and financial
analysts more generally, to play in this setting. Kim and Ritter (1999) observe that, �(b)ecause
using the midpoint of the offer price range results in smaller prediction errors than using
comparables, investment bankers apparently are able to do superior fundamental analysis.� The
above discussion leads to our research hypothesis for the study (in alternate form):4
H1a: Benchmark pricing errors obtained under the direct method are lower than
pricing errors obtained under the three industry-multiplier approaches
considered in the study, namely, PE4, ETSS and IHP.
While H1a assumes the rationality of the VL analyst, the predicted directional effect is not
a given. If horizon premium forecasts represent pure noise, then the null version of H1a is
implied. Our discussions with personnel at Value Line indicate that each VL analyst is allowed
considerable discretion in forecasting horizon price-to-book premiums to reflect her post-horizon
growth estimates, and that horizon price forecasts are subject to the review by the analyst�s
superior. Thus, VL benchmark errors under the direct method represent the closest proxy for
valuation errors currently available to researchers on a large-scale basis. The extensive literature
on the VL stock selection anomaly (see Peterson 1995; Huberman and Kandel 1987; Copeland
and Mayers 1982) suggests that VL horizon price and premium forecasts can be taken seriously,
as price forecasts and stock selection arise from the same underlying data set.
4 While potentially interesting, it is beyond the scope of current study to make any prediction about the relative performance among the three-industry multiplier approaches.
9
A potential limitation to the empirical implementation of the direct method is that, for the
target firm, the VL analyst in fact observes current stock price before forecasting the
fundamentals. The potential circularity concern is, however, alleviated by the fact that VL�s
expected rates of return and CAPM estimates of the required rate of return are not highly
correlated, implying that the VL analyst does not obtain estimated prices at the horizon by
simply multiplying today's observed stock price by one plus the required rate of return
compounded over the next four years.5 Moreover, the extant multiplier literature, reviewed in
this section, may suffer from a similar circularity bias in that the analyst also gets to see current
stock price for the target firm before forecasting fundamentals.
3. Research Methodology
Under the direct method, the estimated intrinsic value, V DM0ijq
!, for the target firm i in industry j
at the end of quarter (subscripts i , q j and are suppressed, hereafter) are computed using the
following version of the residual income model developed by Penman (1997) and discussed in
Penman (2001, Equation 5.6, p. 147):
q
( )( )
0 4DM0 4 ,
14B ECDE P B
Vr
+ + −=
+
! (1)
where 0B is the target firm�s current book value; and are, respectively, forecasts
of aggregate cum-dividend earnings for the next four periods and forecasted horizon premiums,
both provided by the VL analyst. The first two components in the numerator capture the cum-
dividend book value and the third represents the horizon goodwill. The denominator, ( , is
ECDE 4P B− 4
)
41 r+
5 The Pearson correlation between VL�s expected rates of return and CAPM estimates of the required rate of return is 0.277, and the Spearman rank correlation is 0.284.
10
the 4-year required rate of return given by an equally weighted industry CAPM . VL
benchmark errors are computed as the difference between the target firm�s estimated intrinsic
value (i.e., Equation (1)) and its current stock price.
r
Our empirical strategy for the industry multiplier approaches is based on a holdout
procedure. Since the set of firms followed by VL changes over time, we treat every firm-quarter
observation as a separate sample observation (see Section 4 for discussion of Sample Selection
and Data). First, for each industry-quarter, we remove one firm observation at a time, and
estimate the industry multiple using the remaining firms in that industry-quarter. The withheld
firm�s intrinsic value is computed as the product of the estimated industry multiple and its
valuation attribute under each of the three industry multiplier approaches (elaborated below).
The pricing error for this firm-quarter observation is estimated by the difference between
intrinsic value obtained thereof and current market price. Since actual stock price for a given
target firm has not been previously used in the estimation process, our valuation errors
approximate those that arise when the analyst is valuing a private firm using the multiplier
approach. Second, we put the first firm back into the sample and remove a different firm. The
industry multiple and intrinsic value for the second firm are estimated, and pricing errors are
computed. The process continues until all the firms within the industry-quarter have been
withdrawn exactly once. Third, we then move on to the next industry-quarter and repeat the first
two steps. The process ends when all the industry-quarters and every industry multiplier
approach have been analyzed.
Under the first (ETSS) industry multiplier approach, we explore the performance of the
ETSS reverse engineering technique for valuation of the target firm with a 4-year ahead forecast
horizon. For any firm, there always exists some �plug�, γ , that reconciles its current market
11
premium to the analyst�s forecasts of abnormal earnings for the next four fiscal
years ( . As with ETSS, we impose the following structure on
( 0 0i.e., P B−
)., tae
)
i.e γ :
( )( )4 41
4
0 01 1t
P B γ=
− = ∑
1R G
=−
0P
( )41G g= +
( )41 1ttr d−+ −
td
( )
0
G
( )
( )( )( ) ( )4 3
04 41 1
1 1 1 11 1
tt
tt t
t t
aer
e r d rr g
−
= =
+
= + + − − + + − + ∑ ∑
B−
( )( 01ECDE R B− − (2) ) ,
)where is the current market price; ( 41R r= + is one plus the four-year expected return on
equity; is one plus the expected rate of growth in four-year abnormal earnings;
and denote forecasted period t �s earnings and dividends, respectively. The term
adds back the dividend displacement to earnings. In effect, we employ
te
3
1t=∑
1R G−
as a multiplier, estimated using forecasted aggregate abnormal earnings for estimation
firms in the industry.6 Multiplying both sides of Equation (2) by RB− and re-arranging terms
allow us to rewrite Equation (2) as follows:
( ) (0
0 0
1 PECDE G RB B
= − + − )G
(3)
To correct for the bias from measurement error, we follow ETSS (2002) and run the
following reverse regression for each industry-quarter, after withholding the target firm (see their
Equation (8), Page 663):
6 For our sample (see Section 4), the ETSS multipliers take on a value ranging between 48.77 and 1.32. The corresponding ranges for the IHP (PE4) model, discussed below, are 3.29 and �0.21 (6.10 and 1.26), respectively. All the multipliers look reasonable, and hence we choose not to impose any upper or lower cap.
12
00 1
0 0
,PECDEB B
λ λ µ= + + (4)
where and 0 1Gλ = − 1 R Gλ = − .7 The industry-specific r and can be solved for
simultaneously from the reverse regression coefficient estimates
g
( )40 1 gλ = + −1!
and
( ) (41 r − + )g 41 1λ = +!
.8 Applying these regression estimates to Equation (4), multiplying both
sides of the resulting expression by 0
1
Bλ
and re-arranging terms yield the following ETSS
estimated intrinsic value, V ETSS0
!, for the target firm:
ETSS 00 0
1 1
1 .V B Eλλ λ
−= +
CDE!!! ! (5)
At first glance, Equation (5) seems to employ two multipliers. This is, however, an
artifact of using as the valuation attribute rather than . The approach
can be easily reconciled to Equation (2).
ECDE ( ) 01ECDE R B− −
9 ETSS use their model to obtain an estimate of r , while
controlling endogenously for . We are the first researchers to explore the performance of the
ETSS model in a multiplier setting. The extension is appealing for two reasons. First, the ETSS
g
7 By comparison, ETSS arrive at their estimated and r g by pooling observations across industries each year. 8 Since the equity rate of return, , is required to compute cum-dividend earnings, estimation of Equation (4) is done iteratively for each industry. In the first regression, is arbitrarily set at 12% to compute . Then,
rr ECDE
1/ 4
1
1� 1rλ
= !
r
− is used to obtain new for the next iteration. The process continues until there is convergence
of and
ECDE
g . While and r g need to be determined jointly from a regression procedure for technical reasons, individually they are of no interest to us. 9 To see this, note that Equation (5) can be rewritten as:
( )( )ETSS 00 0 0 0 0 0
1 1
1 1 1 1 1 1 1 .G RV B ECDE B ECDE B B ECDE B ECDE R BR G R G R G R G R G
λλ λ
− − −= + = + = + + = + − − − − − − − 0
!!! !
0Moving B following the last equality sign above to the LHS yields ( )( )ETSS0 0 0
1 1ECDE R BR G
− = − −−
V B!
, which is
our Equation (2) when V ETSS0
!is replaced by . 0P
13
multiplier approach allows the analyst to circumvent the continuing value conundrum by
capitalizing forecasts of aggregate cum-dividend earnings. Unlike the direct method in Equation
(1), this approach does not require the analyst to incur time and effort associated with forecasting
. Second, the ETSS multiplier approach corrects for dividend displacement and hence
aggregates earnings in a manner more theoretically appealing (see Ohlson 1995), compared to
the forward aggregate earnings-to-price models for which earnings are simply added together.
4P B− 4
The second (IHP) multiplier approach is a variation of the ETSS approach which looks to
current stock price to reverse engineer the investor�s estimates of industry horizon premium. We
estimate the industry horizon premium-to-book multiple ( )4 4P B B− 4 , denoted as , for all
comparable firms except for the target firm i in industry
4PPR
j for quarter q from the following
minimization problem:
( ) ( )
24
4 40 0 4
1
1, 0
1 1.
kt kk k t
tK
PPR k k i k
ae B PPRP Br r
PMin=
= ≠
− + + + +
∑
∑
k i≠
(6)
The last three terms in the numerator of Equation (6) represent the intrinsic value of the
comparable firm, , where its horizon premium is given by the
product of book value four years hence and the yet-to-be determined industry horizon premium-
to-book multiple. Subtracting the present value of these three terms (discounted using industry
CAPM ) from the comparable firm�s current market price yields firm pricing error.
The resulting pricing error is then deflated by firm �s current market price to ensure that
extreme pricing errors do not exert an undue influence on the estimate.
thk 1, 2, ..., andk K=
thr k 'sk
k
4PPR
14
Equation (6) finds an optimal industry horizon premium-to-book multiple, which
minimizes the squared percentage pricing errors of all estimation firms within the industry, and
is akin to a regression approach at the industry level. The IHP estimated intrinsic value, V IHP0
!, is
computed as follows:
( ) ( )
44IHP 4
0 0 41
.1 1
tt
t
ae B PPRV Br r
∧
=
= + +
+ + ∑
! (7)
The last (PE4) multiplier approach is the aggregate four-year ahead earnings-to-price
model. As with the ETSS and IHP approaches, this heuristic model saves the analyst from
performing an exhaustive pro-forma analysis in order to estimate a continuing value for the
target firm, once forecasts to the horizon have been completed. The industry multiple for target
firm in industry i j at the end of quarter is estimated by relating current market price and
value driver for comparable firms within the same industry in the following fashion (see Page
142, Equation (2) of Liu et al 2002a):
q
4
11
0 0
1t
tEPS
P Pυα ==
∑.+ (8)
Following Liu et al (2002a), we impose the restriction, ( )0E Pυ = 0 , implying that percentage
pricing errors are on average unbiased. This specification gives less weight to extreme
percentage pricing errors, relative to estimators derived from minimizing squared percentage
pricing errors (see Page 143, Liu et al 2002a). Only one parameter needs to be estimated in
Equation (8), namely, . The estimate, 1α4
11
1 tt
E EPS Pα=
= ∑ 0
! , is the harmonic mean of
4
01
tt
P EPS=∑ across comparable firms in the industry and becomes the industry multiple for the
15
target firm. The resulting estimated intrinsic value for the PE4 model, V PE40
!, is computed as
follows:
4 4
PE40 1 4
1 10
1
1 .tt t
tt
V EPS EPSE EPS P
α= =
=
= • = •
∑∑
t∑! ! (9)
To assess the gain in valuation accuracy of the direct method over the three industry
multiplier approaches explored in the study, we consider the following performance metrics: the
mean squared pricing errors, the inter-percentile ranges in signed pricing errors, and the
adjusted 2R from regressing current stock price on intrinsic value. Mean squared pricing errors
differ from the 2R metric because the former weighs on both bias and variance, whereas the
latter measures variation about the regression line that relates current stock price with intrinsic
value, after partialling out bias. Each of these performance metrics corresponds to a different loss
function for the decision-maker, and has been used in prior studies (see for examples, Bhojraj
and Lee 2002; Liu et al 2002a; Liu et al 2002b; Courteau et al 2001; Sougiannis and Yaekura
2001; Francis, Olsson and Oswald 2000; Penman and Sougiannis 1998).
In practice, the analyst seeking to implement any of the industry multiplier approaches
examined in this study would take the ratio of current stock price to forecasted fundamentals
obtained from an investor service such as I/B/E/S or Value Line, and apply it to her own forecast
of the fundamentals for a target firm. However, if this analyst were systematically less (or more)
optimistic than the I/B/E/S or Value Line analysts, then the acquired multiplier would not be
appropriate for her forecasts of value drivers for the target firm. Adjustments to the multiplier
would therefore be necessary. If the analyst were uncertain about the nature of adjustment, this
would add another source of accuracy edge to the direct method over multiplier approaches for
the firm being valued. While interesting, we cannot explore this issue in our study, as the same
16
VL expectational data are used to compute both multipliers and the benchmark errors under the
direct method.
4. Sample Selection and Data
The initial sample includes all quarterly analyst reports, published by VL from 1990 through
2000 and contained in the VL�s Historical Estimates and Projections File. This file consists of
69,870 usable reports, of which 8,467 are eliminated because the forecast report date is too far
removed from the first forecast year to be reliable.10 Of the remaining reports, 5,504 are deleted
due to missing data. We also impose the requirement that value drivers be non-negative and
remove outliers by deleting observations for which value drivers are in the top or bottom 1% of
the respective distribution.11 These two filters result in a loss of 1,337 and 2,507 firm-quarter
observations, respectively. As discussed in Section 3, our research methodology calls for
industry-specific regressions on a quarter-by-quarter basis. To avoid imprecise estimates
resulting from small sample size, we require that there be at least 20 firms in each industry-
quarter. A total of 8,590 observations do not meet this requirement. Finally, 261 observations are
identified as outliers from the ETSS regressions and deleted, leaving us with a final sample of
43,204 firm-quarter observations. We do not require that a firm be present in all 44 quarters.
Thus, every quarter can include a different set of firms and industries.
Each VL Investment Report is prepared by a single analyst and includes forecasts of
earnings, dividends and book value per share for the first two years as well as the fifth year of the
10 We eliminated reports that were made more than 2 months either before the beginning or after the end of the first forecasted year. 11 The non-negativity constraints are applied to current book value, sum of earnings forecasted to the horizon and ECDE. Value drivers affected by the top and bottom 1% filter rules include current book value deflated by current stock price, sum of earnings forecasted to the horizon deflated by current stock price, ECDE deflated by current stock price and horizon premium deflated by book value at the horizon.
17
forecast period. The Report also indicates the share price at the time it was prepared and the price
forecast at the end of the forecast period, five years out. Unlike VL�s Investment Report, VL�s
Estimates and Projections File does not include actual accounting numbers for the year
immediately preceding the forecast period. For this reason, current book value had to be
extrapolated from forecast data for the first forecast period (see Appendix 1 for an example). We
interpolated forecasts for years 3 and 4 linearly from the second and fifth years� VL forecasted
numbers, in a manner that ensured that clean-surplus relation (CSR) holds during the interpolated
years. Similar to other researchers working with VL expectational data (Bushee 2001; Courteau
et al 2001), we observe violations of ex ante CSR, defined as outside a 5% bound of opening
book value, about 11.8% of the time. Such violations are to be expected on a per-share basis due
to clean surplus GAAP violations and forecasted share issuances (Ohlson 2000). We invoke the
assumption that GAAP-induced violations of CSR are ex ante zero in expectation and �plug� the
missing number in fresh share issuances, thus forcing CSR to hold in expectation.
±
5. Empirical Results
5.1 Descriptive Statistics
Panel A of Table 1 contains a description of the number of available firm-quarter observations,
both overall and by year. Over the 44 sample quarters beginning with 1990, VL forecasts are
available for an average of 982 (i.e., 43,204/44) firms each quarter. In any given year, between
1,236 and 1,475 firms are followed by VL in at least one quarter. The overall median market
capitalization of our sample is $1.04 billion, indicating that firms covered by VL tend to be large
relative to the population of listed firms. The overall mean and median book-to-market ratios are
0.57 and 0.51, respectively. These measures compare closely to the corresponding measures of
18
0.55 and 0.49, reported in Table 1 of Liu et al (Page 146, 2002a). For each firm-quarter
observation, we define horizon premium ratios as the present value of price minus book
premiums at the horizon four years hence, scaled by current market price (labeled HP, hereafter).
Averaging HP ratios across all firm-quarters within a year yields the annual horizon premium
ratios, reported in the second last column. By comparison, the within-industry standard deviation
of horizon premium ratios (labeled SD, hereafter) is estimated for each industry-quarter. The
annual �standard deviation�, appearing in the last column, represents the mean SD over all the
available industry-quarters for that year. During our entire (1990-2000) sample period, the 11
annual horizon premium ratios average to 0.47 and the corresponding average annual standard
deviation is 0.29. On a year-by-year basis, the annual horizon premium ratios are largest in 1998-
2000 ranging from 0.53 to 0.62, and the within-industry standard deviation is highest at 0.39 in
2000, reflecting the optimism that characterized the North American economy in the late 1990s.
Panel B of Table 1 describes the number of quarters when the minimum requirement of
20 firms per industry is met for each of the 30 Fama-French (1997) industry sectors present in
the sample, along with summary statistics on market capitalization, book-to-market ratios and
horizon premium ratios across available sample quarters on a sector-by-sector basis. The Utilities
sector meets the minimum size requirement every quarter, whereas Shipping Containers does so
only twice. In the seven high-technology sectors (flagged with an asterisk), the mean book-to-
market ratios are generally small, whereas the average market capitalization are relatively large.
More strikingly, the mean HP ratios for these sectors range from 0.54 to 0.72, indicating that
more than half of the current equity value (i.e., stock price) of high-technology firms is perceived
by VL as lying at the horizon four years hence. These results reflect the rapid growth and
substantial unrecorded post-horizon goodwill enjoyed by high-technology firms during the 1990s
19
and point out the need by the analyst to take special care in estimating continuing values at the
horizon, especially for these sectors. Take the Telecommunications sector for example. Its
market capitalization is 64.72% larger than the second ranked Banking sector (i.e., $10.27 billion
versus $6.24 billion). The Telecommunications sector also has the fourth lowest ranked mean
book-to-market ratio (0.39) and one of the largest mean HP ratios (0.55), both implying high
growth. At the other extreme, the �old� economy sectors, such as Steel Works, Aircraft and
Utilities, tend to have low market capitalization averaging from $1.54 billion to $2.50 billion,
and display relatively low growth. Mean book-to-market ratios for these sectors range from 0.66
to 0.78 and mean HP ratios range from 0.27 to 0.40.
When the degree of within-industry heterogeneity is measured by standard deviation of
horizon premium ratios averaged across all available quarters for that industry, we find that six
of the top-seven ranked sectors come from high-technology sectors, namely, Electronic
Equipment, Business Services, Computers, Medical Equipment, Telecommunications and
Pharmaceutical Products (see Panel B). The average SD�s for these sectors are large, ranging
from 0.30 to 0.35, suggesting significant variations in growth prospects facing high-technology
firms. By comparison, the average SD�s for the �old� economy sectors are ranked mostly in the
bottom half of within-industry heterogeneity distribution, implying that firms in these sectors are
relatively similar in terms of their growth potential. The high degree of within-industry
heterogeneity in horizon premiums for the high-technology sectors re-enforces our earlier
observation that the analyst must pay close attention to estimating continuing values for high-
technology firms.
[Insert Table 1 About Here]
20
5.2 Pricing-Error Analyses
For the purpose of evaluating the performance of models on a holdout sample, we first compute
pricing errors per share for the target firm and then deflate these errors using two deflators,
current book value per share and current stock price per share. Results are presented in Panels A,
B and C of Table 2, respectively. Three sets of results are reported in order to ensure that our
findings are not sensitive to the choices of deflator. No single deflator is �neutral� to all models.
For example, a stock-price deflator for holdout pricing errors is favorable to the IHP and PE4
models, as both approaches estimate multipliers using an algorithm that minimizes percentage-
pricing errors (see Equations (6) and (8)). Conversely, a book-value deflator for holdout pricing
errors favors the ETSS approach, which selects multiples using an algorithm that minimizes the
error in predicting stock price deflated by current book value (see Equation (4)). Results based
on the un-deflated (raw) pricing errors per share come closest to being neutral across the direct
method and three multiplier models, though they may suffer from noise since firms with either
very large or very small current stock prices relative to intrinsic value estimates (i.e., large
pricing errors per share) have a heavy weighting in the pricing error metrics.
When pricing errors are not deflated, the mean squared errors (MSE, hereafter), defined
as the sum of squared bias and variance, are the lowest for the direct method at 94.48 (see Panel
A). The corresponding MSE�s for the PE4, IHP and ETSS models are 163.37, 259.73 and
371.49, respectively. Over the 11-year sample period, the mean signed pricing errors for the
direct method are $1.35 per share, consistent with the general perception that VL forecasts,
especially horizon premium forecasts, tend to be quite optimistic. In contrast, all three multiplier
approaches exhibit a negative bias with mean signed pricing errors of -$0.68, -$7.25 and -$2.26
per share for the ETSS, IHP and PE4 models, respectively. Measuring accuracy by the standard
21
deviation of the signed pricing-error distribution, we find that the direct method is the most
accurate model followed by the PE4, IHP and ETSS models with standard deviations of $9.63,
$12.58, $14.39 and $19.26 per share, respectively. These accuracy model rankings are identical
to those implied by the aforementioned MSE metric, as well as rankings based on inter-
percentile ranges and median absolute per-share pricing errors. Take the 90%-10% range for
example. The difference between signed per-share pricing error ranked at the 90th percentile and
the corresponding error ranked at the 10th percentile is $19.53 for the direct method, which is
narrower than $24.68, $29.47 and $35.23 per share for the PE4, IHP and ETSS models,
respectively. These results point to the superiority of the direct method, compared to any of the
three industry-multiplier models.
The overall impression that direct valuation is superior to other models that we explore in
the study extends to the case when current book value per share is used as deflator (Panel B). In
particular, the MSE for the direct method is 1.01, significantly lower than 1.59, 2.63 and 3.42 for
the PE4, ETSS and IHP models, respectively. Ranking models along the accuracy dimension
(i.e., standard deviation of pricing-error per dollar of book-value and inter-percentile ranges)
yields similar results. Compared to the un-deflated MSE results, the ETSS approach moves up
one place from fourth to third, whereas the IHP approach falls to last place from third. These
ranking changes are not surprising since current book value is also the deflator used to estimate
the ETSS industry multiplier for the target firm (see Section 3).
When we deflate pricing errors by current stock price per share, the direct method does
not perform as well, relative to some of the industry-multiplier approaches (Panel C). According
to the MSE metric, the PE4 model is now ranked first, followed by IHP, the direct method and
ETSS. The MSE values for these models are 0.13, 0.14, 0.15 and 0.33, respectively. The
22
relatively low MSE ranking for the direct method is due in most part to its pronounced positive
bias (i.e., 14.12% of current stock price). In fact, an inspection of the (unreported) distribution of
percentage pricing errors indicates that the direct method is much more heavily skewed towards
the right tail compared to the other three models, reflecting considerable optimism in VL horizon
premium forecasts.12 The presence of extreme positive percentage pricing errors gives rise to
large standard deviation and low accuracy ranking for the direct method in this dimension, even
though the direct method prevails over the other models in the remaining accuracy dimensions
(i.e., 75%-25%, 90%-10% and 95%-5% ranges; median absolute percentage pricing errors).
Compared to the un-deflated MSE results, the IHP approach moves up one place from a third-
ranked model to the second, since the same current stock price deflator is used to estimate the
industry multiplier for IHP. Finally, the PE4 model has a very small bias with the mean signed
percentage pricing error of 0.003. Like us, Liu et al (2002a) also find little bias in their PE4
model, whose mean percentage pricing error is �0.004 (see Table 2, Page 149).
[Insert Table 2 About Here]
As a sensitivity test (not reported in a table), we remove the influence of extreme pricing
errors by winsorizing in the top 1% and bottom 1% of the respective distribution for each of the
four models under examination. Even though winsorization procedure improves accuracy for all
the models, the previously reported model rankings based on the MSE and various accuracy
metrics continue to hold when pricing errors are either un-deflated or deflated by current book
value per share. On the other hand, with current stock price per share as a deflator, winsorization
has a favorable effect on the direct method which now dominates, rather than being dominated
12 The percentage pricing errors at the 100th (99th) percentile for the direct method is 595.77% (143.42%) of current stock price and the corresponding percentages for the ETSS, IHP and PE4 are 540.77% (188.03%), 299.37% (98.21%) and 308.18% (117.41%), respectively. By comparison, the direct method exhibits the tightest distribution (not reported in a table) when pricing errors are either reported on a per share basis or deflated by current book value per share.
23
by, the other industry-multiplier approaches in the standard deviation dimension. The improved
accuracy (i.e., lower standard deviation) and reduced bias (i.e., mean signed percentage pricing
errors) move the direct method up to become the second ranked model based on the MSE metric,
just behind PE4. These results confirm our earlier observation that the extreme positive skewness
in the percentage pricing-error distribution for the direct method might have contributed to its
relatively low MSE and standard-deviation rankings prior to applying the winsorization
procedure.
Taken together, evidence presented in this section provides strong support for the
prediction of lower pricing errors under the direct method, compared to the ETSS, IHP and PE4
industry-multiplier approaches (H1a).13 Like Liu et al (2002a), we also find that the PE4 model
outperforms the residual income models in terms of valuation accuracy. The continued
domination of PE4 over RIM is likely due to the following reason. The harmonic mean
approach, which yields an unbiased (though not squared percentage pricing-error minimizing)
multiplier, gives less weight to outlier pricing errors in the estimation; whereas both the IHP and
ETSS approaches solve for industry multipliers using an approach that minimizes squared
percentage pricing-errors for the estimation sample.14
13 While not reported in a table, we also consider several variations of the IHP model. First, a simple heuristic based on average PPR across estimation firms within an industry. The target firm�s continuing value is the product of its horizon book value and industry average PPR. While easy to implement, this method is not a multiplier approach, as it is not determined by relating current market price with the value driver. Not surprisingly, the average PPR model is more biased and less accurate than the IHP multiplier approach. The mean squared percentage pricing errors for these two approaches are 0.45 versus 0.14. Second, a modified IHP model where both Equations (6) and (7) are discounted by an endogenously determined ETSS r to proxy for the market�s required rate of return. All the IHP results obtained using CAPM r (reported in Table 2) remain essentially unchanged. For example, when pricing errors are deflated by current book value (current stock price) per share, the mean squared errors for the IHP_CAPM r and IHP_ETSS r models are 3.42 versus 3.41 (0.14 versus 0.14), respectively. 14 Liu et al (2002a) report that PE4 does not perform as well when the multiplier is estimated using a standard regression approach for the estimation of Equation (8). As our aim is to explore the edge of the direct method over the best contender from the three-multiplier models considered in the study, we leave this issue unresolved.
24
5.3 Regression Analysis
In this section, we assess the valuation accuracy of the direct method over the industry multiplier
models using a regression approach that allows VL�s optimistic bias under the direct method and
predictable bias in other models to be partialled out through an estimated constant term (see
Christensen and Blackwood 1993). Suppose one adopts the perspective of a user of VL services
and wants to use VL forecast data to decide on the most accurate model for intrinsic valuation. If
VL bias is predictable, then the user of VL�s data wants a model that helps predict current stock
price. The most accurate model is indicated by the R2 from regressing current stock price on
intrinsic value, after bias is partialled out by an estimated constant term. Thus, we pay close
attention to the R2 metric and compare it with the MSE metric (Table 2), when deciding on the
most accurate valuation model. To ensure that our results hold with or without a deflator, we first
measure current stock price and intrinsic value on a per share basis, and then deflate both
variables by current book value per share. Results are reported in Panels A and B of Table 3,
respectively.15
Panel A of Table 3 portrays the relative ranking of models when data are un-deflated and
the pooled-regression R2 is used as the performance metric. The R2 of the direct method (VL
benchmark model) is 85.72%, which is higher than 75.70%, 68.06% and 55.46% for the PE4,
IHP and ETSS multiplier approaches, respectively. A Vuong test (see Dechow 1994) rejects the
null of no difference in favor of the direct method at the 1% level. These R2 rankings are
identical to the corresponding accuracy rankings based on the MSE metric (see Panel A of Table
2).
15 Unlike the pricing-error analysis, we do not consider deflating variables by current stock price per share because a constant term is required in order to partial out bias.
25
Turning next to model rankings using current book value per share as a deflator (Panel
B). The direct method continues to enjoy a significantly higher R2 than the PE4, ETSS and IHP
models (i.e., 91.55% versus 86.78%, 83.93% and 80.41%, respectively). For all three pair-wise
differences relative to the direct method, the null of no difference can be rejected at the 1% level
using a Vuong test. The findings that the direct method is ranked ahead of the PE4, ETSS and
IHP models along the R2 dimension mirror inferences drawn previously using the MSE metric
when a similar deflator is employed (see Panel B of Table 2). While the ETSS approach has a
higher R2 and performs better than IHP when current book value per share is used as a deflator,
the converse is true when data are measured on a per share basis. The reversal in R2 rankings
involving these two models is consistent with an earlier pattern based on the MSE metric (see
Panel A versus Panel B, Table 2).
[Insert Table 3 About Here]
The extent of valuation accuracy sacrificed by looking to heuristic industry multiples,
rather than forecasting directly the horizon premiums for a particular target firm, can be
quantified by comparing the ratios of R2�s associated with these two broad approaches. For
example, when the data are un-deflated, the IHP model is about 79.40% 68.06%i.e.,85.72%
as
effective as the direct method, implying a 20.60% loss in valuation accuracy when the VL
analyst uses the investor�s estimates of the average industry horizon premium on a target firm in
the industry. Using the ETSS and PE4 models results in a valuation loss of 35.30% and 11.69%
55.46% 75.70%i.e.,1 and 185.72% 85.72%
− −
, respectively, compared to the direct method. The
corresponding percentage losses in valuation accuracy can be similarly computed for the case
26
when the data are deflated by current book value per share (i.e., 12.17%, 8.32%and 5.21% for
the IHP, ETSS and PE4 models, respectively).
In short, after partialling out the effect of predictive bias, the direct method remains a
superior valuation model over the three industry-multiplier approaches considered in the study
(ETSS, IHP and PE4), whether current stock price and intrinsic value are reported on a per share
basis or if they are deflated by current book value per share. These results are consistent with the
prediction of H1a and lend support for the conclusion reached previously based on the MSE and
various accuracy metrics.
5.4 Determinants of Relative Valuation Accuracy
We now explore the determinants of relative valuation accuracy in a multivariate setting, using
the following pooled regression model:
( ) ( )2000
IM DM 0 1 2 3 4 t t1991
APE APE a + a Ln MV + a BM + a HP + a SD b Y ε.t=
− = + ∑ +
)
(10)
The dependent variable, , in Equation (10) measures the edge of the direct
method for each firm-quarter observation, where AP denotes absolute percentage pricing
errors defined as the price-deflated difference between intrinsic value estimated under the ETSS,
IHP or PE4 model and current market price, and is the similarly defined absolute
percentage pricing errors for the direct method. We use a firm-level measure of performance
edge because two of the accuracy determinants of interest to us, size and growth (i.e., Ln (MV);
BM and HP, defined below), are firm-level constructs. In this analysis, we will focus on the
differences in percentage pricing errors for reasons that two of our explanatory variables (i.e., HP
and SD, defined below) also use current stock price as the deflator, and that our main results
( IM DMAPE APE−
IME
APEDM
27
reported in Tables 2 and 3 are robust to the choices of deflator (i.e., un-deflated, deflated by
current book value or current stock price per share).
The first test variable in Equation (10), , denotes market capitalization. Since
our sample firms vary greatly in size, the natural log transformation is applied to MV to dampen
the potential effect of outliers. The next two test variables, BM and HP, denote book-to-market
and horizon-premium ratios, respectively. They are intended to measure growth for each firm-
quarter observation. The fourth test variable, SD, denotes the standard deviation of horizon
premium ratios for each industry-quarter, used to capture the degree of industry heterogeneity in
that quarter. The measurement of the variables HP and SD is explained in Section 5.1. While we
expect the performance of both the direct method and multiplier models to worsen as industry
heterogeneity increases, the rate of decline is likely to differ across these two broad approaches.
Thus, a priori, it is not obvious whether the edge of the direct method over multiplier models
would increase with industry heterogeneity.
(Ln MV
tY
)
16 Finally, to control for the general upward trend
evident throughout the 11-year sample period (see Panel A of Table 1), we include ten year-
dummy variables, . Using 1990 as our base year, we set Y equal to one for all the firm-
quarter (or in the case of SD, industry-quarter) observations that fell in the calendar year 1991,
and zero otherwise. The remaining nine year-dummies, and t = 1992, 1993, �2000, can be
similarly defined. The time effect attributable to our base year is reflected in the intercept, a
tY 1991
0.
Table 4 presents the results from three pooled regressions, based on Equation (10). The
coefficient values on the SD variable are 0.14, 0.21 and 0.13 for the ETSS, IHP and PE4 models,
respectively, all significant at the 1% level (using a one-tailed test). The positive sign implies
that industry multiplier approaches yield higher absolute percentage pricing errors and hence are
16 Recall that, under the null of H1, VL horizon premium forecasts for the direct method represent pure noise and there is no accuracy edge over industry multiplier approaches.
28
less accurate than the direct method, the more heterogeneous an industry is. These results suggest
that industry heterogeneity is an important accuracy determinant, after controlling for the
influence of firm size, growth and time trend.
For a given industry, the relative edge of the direct method can vary across firms
depending on their size and growth prospects. Focusing first on firm size, we find that for small
firms within the industry, both the ETSS and PE4 multiplier approaches are less accurate (i.e.,
with higher absolute percentage pricing errors), compared to the direct method. The coefficient
values on the Ln(MV) variable are �0.02 and �0.01, respectively, significant at the 1% level
(using a one-tailed test). In contrast, the direct method enjoys greater, rather than less, accuracy
edge over the IHP multiplier approach when firms are large. The positive coefficient for this
model (i.e., 0.003) is surprising. On balance, there is somewhat conflicting support for firm size
as a determinant of the direct method�s superiority, after controlling for the influence of industry
heterogeneity, growth and time trend.
Turning next to a firm�s growth prospects. The first measure we employ is the book-to-
market ratio (i.e., BM), which is inversely related to growth. For all three industry-multiplier
approaches, the coefficient values on the BM variable are negative and significant at the 1%
level, based on a one-tailed test (i.e., �0.22, �0.60 and �0.39 for the ETSS, IHP and PE4 models,
respectively). A negative sign indicates that, after controlling for the potential effects of
covariates, industry multiplier approaches are less accurate and yield larger absolute percentage
pricing errors than the direct method for high-growth firms with small book-to-market ratios.
The second growth measure we employ is the horizon premium ratio (i.e., HP). A larger horizon
premium ratio reflects greater post-horizon growth prospects. While we expect the sign on the
HP variable to be positive, the opposite results are found. The coefficient values for the ETSS,
29
IHP and PE4 models are, respectively, �0.29, �0.43 and �0.35, implying that the edge of the
direct method decreases, rather than increases, with post-horizon growth prospects. On the
surface, these two sets of growth results seem contradictory. However, it should be pointed out
that even though BM and HP both measure growth, they are not perfect substitutes. In fact, the
Pearson correlation between BM and HP is quite modest at �0.33. The BM variable is arguably a
less noisy proxy than HP, because it only captures the market's measure of growth. By
comparison, HP is a ratio of two growth expectations: the numerator (discounted horizon
premiums) captures VL�s expectation about a firm post-horizon growth prospects, and the
denominator (current stock price) reflects the market�s expectation about growth at time zero. A
larger HP may be associated with greater valuation error due to VL optimism, as opposed to (or
in addition to) greater growth potential. Under this alternative interpretation, as VL optimism-
driven valuation error increases, the edge of the direct method decreases, thus pointing to a
negative sign on the HP variable.
[Insert Table 4 About Here]
As a sensitivity test, we also re-estimate Equation (10) by using the standard deviation of
book-to-market ratios for each industry-quarter as a proxy for heterogeneity. Results (not
reported in a table) are analogous to those discussed above. In particular, for all three multiplier
models, the coefficient values on the �new� SD variable are positive and significant at the 1%
level, whereas the values on the BM variable are negative and significant at the 1% level. Once
again, firm size, Ln(MV), is inversely related to the edge of the direct method for the ETSS and
PE4 models, but not IHP.17 These patterns are consistent with those appearing in Table 4.
17 All the results remain qualitatively the same when the ratio of standard deviation of BM for each industry-quarter over the corresponding quarterly mean BM is used to proxy for industry heterogeneity. Finally, for both measures of heterogeneity, the ten year-dummies are mostly positive and significant, implying a general upward trend relative the base year of 1990.
30
To sum up, it would appear that, after controlling for the effects of covariates, extending
pro-forma analysis beyond the forecast horizon is most beneficial for small and fast growing
target firms from highly heterogeneous industries. Since forecasting can be a very time-
consuming and costly process, when deciding on the firms and/or industries to conduct a
comprehensive pro-forma, the analyst needs to carefully trade off costs and benefits associated
with direct valuation versus simpler heuristics using industry multiples.
6. Conclusion
The primary objective of this paper is to assess the gain in valuation accuracy when the analyst
performs an exhaustive pro-forma analysis for a target firm (the direct method), compared to the
alternative of using heuristic industry multiples to compute continuing values if she is uncertain
about the firm�s post-horizon prospects. We also examine the determinants of the edge to direct
valuation vis-à-vis industry multiplier approaches.
To implement the direct method, we assume that the VL analyst is representative of other
analysts, and combine her forecasts of earnings and book values to a four-year horizon with her
explicit estimate of the target firm�s horizon price minus book premium. A holdout procedure is
employed for the industry-multiplier approach, under which multiples applied to the target firm
are estimated using the appropriate VL forecasted valuation attributes for every firm in the
industry, except for the firm in question. We consider three industry multiplier models: first, the
ETSS multiplier model, which extends the Easton et al�s (2002) reverse engineering technique to
solve for an industry multiple that reconciles VL forecasted fundamentals to the current price
minus book premiums for industry estimation firms; second, the IHP multiplier model, which
uses a reverse engineering technique that we develop to arrive at an industry horizon premium-
31
to-book multiple which minimizes the squared price-deflated differences between current stock
price and intrinsic value for the estimation sample; and third, the PE4 multiplier approach, which
uses the forward industry average earnings-to-price ratio where earnings are summed over a
four-year forecast horizon.
Given variations in size and growth prospects across firms within an industry, we expect
to achieve greater valuation accuracy under the direct method when the continuing value is
computed by drawing on the analyst�s detailed knowledge about the target firm, as opposed to
relying on inferences made from information about comparables under any of the industry-
multiplier approaches. To assess relative valuation accuracy of the various models, three
performance metrics are employed: the mean squared errors, the inter-percentile range in signed
pricing errors and the 2R obtained from regressing current stock price on intrinsic value. Results
from the study are consistent with our prediction. The direct method generates the lowest MSE,
tightest inter-percentile ranges and highest regression 2R , compared to any of the multiplier
approaches that we explore in the study when data are either un-deflated or deflated by current
book value per share. The direct method, however, does not perform as well when current stock
price per share is used as a deflator, due to the presence of extreme positive percentage pricing
errors. The valuation gains to directly forecasting firm-specific continuing value are greatest for
small and fast growing target firms from highly heterogeneous industries.
By comparing valuation errors from industry multiplier approaches with those of our VL
benchmark model, we show the analyst and students of financial statement analysis the loss in
valuation accuracy arising from using comparable firm growth estimates, rather than forecasting
growth for the target firms to the expected end of that firm�s life. Such loss can be considerable
for the sample as a whole, if VL proxies well for the representative analyst. For example,
32
focusing on the explanatory power of intrinsic value for stock price, both scaled by current book
value, the R2 of the direct method over the entire (1990-2000) sample period is 91.55%. The
corresponding figures for the ETSS, IHP and PE4 multiplier approaches are 83.93%, 80.41% and
86.78%, respectively. While the simple PE4 model performs well relative to other multiplier
approaches (ETSS and IHP), it is nonetheless dominated by the direct method. Of course, the
analyst must weigh the costs of forecasting firm-specific post-horizon growth rates against the
benefits implied by greater valuation accuracy. Our PE4 results add to a growing body of
literature that points to the robustness of a simple forward PE model, relative to more
complicated residual income based valuation models.
Two important caveats apply to our study. First, the VL analyst observes current stock
price before forecasting the fundamentals, including estimated stock price at the forecast horizon.
However, any bias due to potential circularity would affect not just the direct method, but also
the multiplier models examined in this study and the extant multiplier literature. Moreover, for
our sample of 43,204 firm-quarter observations, VL�s expected rate of return is only moderately
correlated with CAPM estimates of the required rate of return, implying the performance of
fundamental analysis by VL analysts to support their forecasts. Second, we use the same VL
forecast data to compute both industry multiples and benchmark valuation errors. If the analyst
employing the multiplier approach were systematically less (or more) optimistic than the VL
analyst, her forecasts of fundamentals would not be consistent with the multipliers obtained from
VL. An adjustment would therefore be required before the multiplier is applied. If she is
uncertain about the required adjustment, a further accuracy edge may be accrued to the direct
method. We leave an exploration of this issue to future research.
33
References
Alford, A. 1992. The effect of the set of comparable firms on the accuracy of the price-earnings valuation method. Journal of Accounting Research (Spring, Vol. 30, No. 1): 94-108.
Baker, M. and R. Ruback. 1999. Using industry multiples. Working paper. Harvard University. Beatty, R., S. Riffe and R. Thompson. 1999. The method of comparables and tax court
valuations of private firms: An empirical investigation. Accounting Horizon (September, Vol. 13, No. 3): 177-199.
Bhojraj, S. and C. Lee. 2002. Who is my peer? A valuation-based approach to the selection of comparable firms. Journal of Accounting Research (May, Vol. 40, No. 2): 407-439.
Boatsman, J. and E. Baskin. 1981. Who is my peer? Asset valuation with incomplete markets.
The Accounting Review (January, Vol. 56, No. 1): 38-53. Bushee, B.J. 2001. Do institutional investors prefer near-term earnings over long-run value?
Contemporary Accounting Research (Summer, Vol. 18, No. 2): 207-246. Christensen, R. and L. Blackwood. 1993. Tests for precision and accuracy of multiple measuring
devices. Technometrics (November, Vol. 35, No. 4): 411-420. Copeland, T. and D. Mayers 1982. The Value Line Enigma (1965-1978): A Case Study of
Performance Evaluation Issues. Journal of Financial Economics (10): 289-322. Courteau, L., J. Kao, and G. Richardson. 2001. Equity valuation employing the ideal versus ad
hoc terminal value expressions. Contemporary Accounting Research (Winter, Vol. 18, No. 4): 625-661.
Easton, P., G. Taylor, P. Shroff, and T. Sougiannis. 2002. Using forecasts of earnings to simultaneously estimate growth and the rate of return on equity investment. Journal of Accounting Research (June, Vol. 40, No. 3): 657-676.
Fama, E. and K. French. 1997. Industry cost of equity. Journal of Financial Economics
(February, Vol. 43, No. 2): 153-194. Francis, J., P. Olsson, and D. Oswald. 2000. Comparing the accuracy and explainability of
dividend, free cash flow and abnormal earnings equity value estimates. Journal of Accounting Research (Spring, Vol. 38, No. 1): 45-70.
Huberman and Kandel 1987. Value Line Rank and Size. Journal of Business (60): 577-589. Kim, M. and J. Ritter. 1999. Valuing IPOs. Journal of Financial Economics (September, Vol.
53, No. 3): 409-437.
34
Liu, J., D. Nissim, and J. Thomas. 2002a. Equity valuation using multiples. Journal of Accounting Research (March, Vol. 40, No. 1): 135-172.
Liu, J., D. Nissim, and J. Thomas. 2002b. International equity valuation using multiples.
Working paper. Columbia University. Ohlson, J. 2000. Residual income valuation: The problems. Working paper. New York
University. Ohlson, J. 1995. Earnings, book values and dividends in equity Valuation. Contemporary
Accounting Research (Spring, Vol. 11, No. 2): 661-687. Penman, S. 2001. Financial statement analysis and security valuation. McGraw-Hill Irwin. Penman, S. 1997. A synthesis of equity valuation techniques and the terminal value calculation
for the dividend discount model. Review of Accounting Studies (Vol. 2, No. 4): 303-323. Penman, S. and T. Sougiannis. 1998. A Comparison of dividend, cash flow, and earnings
approaches to equity valuation. Contemporary Accounting Research (Fall, Vol. 15, No. 3): 343-383.
Peterson, D. 1995. The informative Role of the Value Line Investment Survey: Evidence from
Stock Highlights. Journal of Financial and Quantitative Analysis (30): 607-618. Sloan, R. 2002. Discussion of �Who is my peer? A valuation-based approach to the selection of
comparable firms.� Journal of Accounting Research (May, Vol. 40, No. 2): 441-444. Sougiannis, T. and Yaekura. 2001. The accuracy and bias of equity values inferred from analysts'
earnings forecasts. Journal of Accounting, Auditing, and Finance (Fall, Vol. 16, No. 4): 331-362.
35
Table 1 Descriptive Statistics Over the Entire Sample (1990-2000)
Panel A: By Year
Market Value (in millions)
Book-to-Market Ratio
Horizon Premium Ratiosa
Sample Year
# of Firms Present in at
Least One Quarter
# of Firm-Quarters
Mean Median Mean Median Mean Standard Deviationb
1990 1,236 2,787 1,537 487 0.760 0.701 0.466 0.304 1991 1,306 4,011 1,772 576 0.684 0.631 0.421 0.276 1992 1,356 4,404 1,852 651 0.640 0.592 0.451 0.287 1993 1,408 4,250 2,164 849 0.555 0.519 0.454 0.273 1994 1,425 4,164 2,200 881 0.584 0.546 0.459 0.256 1995 1,447 4,176 2,557 999 0.546 0.516 0.423 0.235 1996 1,401 4,156 3,044 1,144 0.517 0.474 0.435 0.253 1997 1,475 4,276 4,031 1,542 0.443 0.399 0.444 0.238 1998 1,432 3,699 4,628 1,683 0.474 0.423 0.529 0.323 1999 1,418 3,953 4,534 1,536 0.518 0.462 0.552 0.299 2000 1,256 3,328 4,723 1,686 0.553 0.459 0.619 0.389
1990-2000 2,602 43,204 3,081 1,043 0.565 0.514 0.474 0.290
36
Table 1
Panel B: By Industry
Market Value (in millions)
Book-to-Market Ratios
Horizon Premium Ratiosa
Industryc Number of Quartersd Mean Median Mean Median Mean Standard
Deviatione
Food Products 33 3,051 1,142 0.454 0.399 0.575 0.235Printing and Publishing 35 3,667 2,160 0.390 0.343 0.592 0.194Consumer Goods 40 3,319 975 0.511 0.446 0.505 0.240Apparel 29 1,302 555 0.618 0.530 0.525 0.282Healthcare 8 2,689 1,553 0.542 0.378 0.564 0.315Medical Equipment* 18 2,089 794 0.381 0.326 0.631 0.303Pharmaceutical Products* 41 2,592 741 0.262 0.231 0.715 0.300Chemicals 41 3,353 1,307 0.473 0.428 0.500 0.223Construction Materials 43 1,182 400 0.625 0.540 0.489 0.260Steel Works 41 1,536 580 0.781 0.664 0.401 0.254Machinery 43 2,026 598 0.566 0.474 0.513 0.246Electrical Equipment 21 4,086 1,001 0.475 0.371 0.508 0.204Automobiles and Trucks 43 3,517 821 0.617 0.555 0.453 0.213Aircraft 14 2,503 665 0.783 0.689 0.348 0.257Petroleum and Natural Gas 39 5,256 2,006 0.519 0.487 0.570 0.280Utilities 44 2,260 1,113 0.658 0.642 0.274 0.238Telecommunications* 43 10,272 4,240 0.391 0.355 0.548 0.303Business Services* 44 2,258 847 0.434 0.346 0.652 0.348Computers* 43 2,641 733 0.522 0.441 0.631 0.334Electronic Equipment* 43 2,896 824 0.568 0.474 0.543 0.351Measuring and Control Equipment* 30 1,347 379 0.555 0.471 0.573 0.248Business Supplies 43 2,409 1,201 0.613 0.584 0.422 0.227Shipping Containers 2 1,793 406 0.787 0.693 0.532 0.231Transportation 34 2,687 1,001 0.676 0.591 0.411 0.215Wholesale 43 1,440 502 0.609 0.521 0.507 0.287Retail 43 2,364 816 0.575 0.487 0.520 0.294Restaurants and Hotels 35 1,068 494 0.557 0.466 0.512 0.258Banking 43 6,236 2,309 0.627 0.590 0.330 0.189Insurance 41 3,729 2,109 0.696 0.646 0.323 0.234Trading 27 4,118 2,424 0.529 0.478 0.371 0.245
37
N = 43,204 firm-quarter observations.
a. Horizon premium ratios are computed as ( )4 4
0
PV P BP
−, where is the present value of VL
forecasted price minus book premiums, four years hence; is the most recent stock price for the target firm, published in the VL forecast report.
( 4 4PV P B− )
0P
b. For each industry-quarter, we first estimate the within-industry standard deviation of horizon premium ratio. The annual �standard deviations�, reported in Panel A, represent the average of standard deviations across all available industry-quarters in that year.
c. Defined in Appendix A of Fama and French (pp. 179-181, 1997). d. Represent the number of quarters in which an industry meets the minimum 20 firms requirement. e. For each industry-quarter, we first estimate the within-industry standard deviation of horizon premium ratio.
The sector-by-sector �standard deviations�, reported in Panel B, represent the average of standard deviations across all the available quarters for that industry.
f. Asterisk indicates high-tech industries.
38
Table 2 Pricing Errors Distribution for Various Valuation Models (1990-2000)
Panel A: Pricing Errors Per Share
Signed Pricing Errors Per Sharea
Non-Parametric Dispersionb Mean Median Standard Deviation 75%-25% 90%-10% 95%-5%
Mean Squared Errorsc
Median Absolute
Pricing Errors Per Sharea
Direct Method 1.352 1.523 9.626 8.894 19.530 28.505 94.483
4.621 ETSS -0.682 -0.703 19.262 14.402 35.235 52.863 371.493
7.218*
IHP -7.247 -4.279 14.395 13.537 29.469 42.104 259.731
6.344*
PE4 -2.260 -0.937 12.580 10.223 24.678 37.060 163.366
4.961*
Panel B: Pricing Errors Per Share Deflated by Current Book Value Per Share
Signed Pricing Errors Per Dollar Book Valuea
Non-Parametric Dispersionb Mean Median Standard Deviation 75%-25% 90%-10% 95%-5%
Mean Squared Errorsc
Median Absolute
Pricing Errors Per Dollar Book
Valuea Direct Method 0.161 0.119 0.991 0.689 1.610 2.562 1.008 0.346 ETSS 0.069 -0.053 1.621 1.142 2.801 4.378 2.632 0.576* IHP -0.819 -0.316 1.658 1.145 2.818 4.443 3.419 0.451* PE4 -0.275 -0.069 1.232 0.795 2.082 3.389 1.594 0.381*
Panel C: Pricing Errors Per Share Deflated by Current Stock Price Per Share
Signed Percentage Pricing Errorsa
Non-Parametric Dispersionb Mean Median Standard Deviation 75%-25% 90%-10% 95%-5%
Mean Squared Errorsc
Median Absolute
Percentage Pricing Errorsa
Direct Method 0.141 0.062 0.364 0.373 0.781 1.095 0.153 0.168 ETSS 0.002 -0.028 0.578 0.554 1.339 1.952 0.335 0.278* IHP -0.134 -0.168 0.355 0.426 0.855 1.138 0.144 0.261* PE4 0.003 -0.039 0.361 0.388 0.839 1.159 0.130 0.199* N = 43,204 firm-quarter observations.
39
a. Pricing errors are computed using a holdout procedure discussed in Section 3. For the target firm in industry
for quarter (subscripts i , and are suppressed), Panels A, B and C present, respectively, the distribution based on the signed/absolute pricing errors per share, signed/absolute pricing errors per dollar book value and signed/absolute percentage pricing errors. These errors are computed as follows:
ij q j q
Signed pricing errors per share = V ; absolute pricing errors per share = 0
�t P− 0t 0 0
�t tV P− ;
Signed pricing errors per dollar book value = 0 0
0
�t
t
V PB− t ; absolute pricing errors per dollar book value = 0 0
0
�t t
t
V PB−
;
Signed percentage pricing errors = 0 0
0
�t
t
V PP− t ; absolute percentage pricing errors = 0 0
0
�t t
t
V PP−
,
where 0P : The most recent stock price for the target firm, published in the VL forecast report.
: The intrinsic value estimates for the target firm are calculated according to Equations (1), (5), (7) and (9) for the Direct Method, ETSS, IHP and PE4, respectively. For a summary of these equations and related notations, please refer to Appendix 2.
0�V
: The current book value for the target firm. 0B
b. To compute the three inter-percentile ranges in Panel A, we first rank signed pricing errors per share in an ascending order for each model. The 75%-25% range represents the difference between the signed pricing error per share ranked at the 75th percentile and that ranked at the 25th percentile; the 90%-10% range represents the difference between the signed pricing error per share ranked at the 90th and the 10th percentile; the 95%-5% range represents the difference between the signed pricing error per share ranked at the 95th and the 5th percentile.
An analogous procedure is used to determine the three inter-percentile ranges for the signed pricing errors per
dollar book value and the signed percentage pricing errors in Panels B and C, respectively. c. In Panel A, mean squared errors are calculated as the sum of (mean signed pricing errors per share)2 and
variance. An analogous procedure is used to compute mean squared error for the signed pricing errors per dollar of book
value and the signed percentage pricing errors in Panels B and C, respectively. * Significant difference from the direct method, at the 1% level, using a Wilcoxon signed rank test.
40
Table 3 Results from Pooled Regression of Current Price on Intrinsic Value (1990-2000)
Pooled Regression Results Modelsa
Panel A. Un-deflated Panel B. Deflated by B0
Direct Method Intercept 0α -1.788* -1.090* Slope 1α 1.013* 0.962* Adjusted 2R 85.72% 91.55%
ETSS Intercept 0α 11.127* 5.579* Slope 1α 0.676* 0.649* Adjusted 2R 55.46%b 83.93%b
IHP Intercept 0α 6.690* 4.466* Slope 1α 1.022* 1.299* Adjusted 2R 68.06%b 80.41%b PE4 Intercept 0α 3.413* 2.015* Slope 1α 0.962* 1.034* Adjusted 2R 75.70%b 86.78%b
N = 43,204 firm-quarter observations.
a. Regression Model (un-deflated): ; 0 0 1 0
�P Vα α= + + 1e
Regression Model (deflated by current book value): 0 00 1
0 0 0
�1Pe
B B Bα α= + + 2
V , where
: The most recent stock price for the target firm in industry for quarter q (subscripts i , and are suppressed), published in the VL forecast report.
0P i j j q
: The intrinsic value estimates for the target firm are calculated according to Equations (1), (5), (7) and (9) for the Direct Method, ETSS, IHP and PE4, respectively. For a summary of these equations and related notations, please refer to Appendix 2.
0�V
0B : The current book value for the target firm. The slope coefficient on the intrinsic value estimates is predicted to be 1.
b. Each of the multiplier model R2 is significantly different from the direct method R2 at the 1% level, using a Vuong test.
* Significant difference from 0 for and from 1 for , at the 1% level. 0α 1α
41
Table 4 Determinants of Relative Valuation Accuracy
Regression Model:a ( ) ( )2000
IM DM 0 1 2 3 4 t t1991
APE APE a + a Ln MV + a BM + a HP + a SD b Y εt=
− = + ∑ +
Superiority of the Direct Method Over Industry Multiplier
Approaches Measured by ( )IM DMAPE APE−Coefficient Estimates (t-Values)
Pooled Regression Results
Expected Signs
ETSS IHP PE4 Intercept (Base year, 1990)
N/A
0.509* (31.83)
0.649* (57.85)
0.475* (46.05)
Ln(MV) - -0.018* (-13.63)
0.003* (3.13)
-0.005 (-5.35)
BM - -0.219* (-33.50)
-0.602* (-130.02)
-0.386* (-91.13)
HP + -0.291* (-74.25)
-0.425* (-155.10)
-0.345* (-137.08)
SD + 0.142* (10.20)
0.208* (21.24)
0.128* (14.26)
Y1991 N/A 0.043* (4.64)
0.025* (3.91)
0.038* (6.29)
Y1992 N/A 0.043* (4.69)
-0.007 (-1.05)
0.016* (2.65)
Y1993 N/A 0.024** (2.52)
-0.028* (-4.33)
-0.004 (-0.62)
Y1994 N/A 0.041* (4.38)
0.008 (1.21)
0.039* (6.53)
Y1995 N/A 0.096* (10.19)
-0.001 (-0.11)
0.038* (6.31)
Y1996 N/A 0.089* (9.43)
-0.002 (-0.23)
0.032* (5.31)
Y1997 N/A 0.048* (5.01)
-0.040* (-5.94)
0.005 (0.76)
Y1998 N/A 0.041* (4.30)
-0.062* (-9.34)
-0.014** (-2.26)
Y1999 N/A 0.148* (15.86)
0.003 (0.42)
0.045* (7.54)
Y2000 N/A 0.200* (20.79)
-0.005 (-0.80)
0.028* (4.48)
R2 13.31% 46.05% 36.38%
42
N = 43,204 firm-quarter observations.
a. Regression Model: ( ) , where ( )2000
IM DM 0 1 2 3 4 t t1991
APE APE a + a Ln MV + a BM + a HP + a SD b Y ε.t=
− = + ∑ +
)
: Represents absolute percentage pricing errors, defined as the difference between intrinsic value estimated using the ETSS, IHP or PE4 industry multiplier approaches and current market price, scaled by current market price.
IMAPE
: Represents absolute percentage pricing errors, defined as the difference between intrinsic value estimated using the direct method and current market price, scaled by current market price.
DMAPE
: Denote log-transformed market capitalization for each firm-quarter observation. (Ln MVBM : Denote the book-to-market ratio for each firm-quarter observation. HP : Denote the horizon premium, scaled by current market price, for each firm-quarter
observation. SD : Denote standard deviation of horizon premium ratios for each industry-quarter.
tY : Represents ten year dummies, t = 1991, 1992, � 2000. For observations that fell in the calendar year 1991, takes on a value of one, and zero otherwise. The remaining nine year-dummies can be analogously defined.
1991Y
* Significant difference from 0, at the 1% level (one-tailed test). ** Significant difference from 0, at the 5% level (one-tailed test). .
43
Appendix 1 Relation between Fiscal Year-Ends and VL Report Dates
VL forecast reports are published once every 13 weeks for each firm that is followed by VL analysts. We define the forecast report date as t = 0, which becomes the beginning of the first year of the forecast period. Our estimation methodology requires that each year of forecast period be of the same length. Thus, forecast years do not normally correspond to the firm�s fiscal years.
Denote the the number of days left in the first forecasted year at the forecast date, scaled by 365, as f . Further assume that dividends are paid at the end of the fiscal year (e.g., forcasted dividends for fiscal year 1, , are capitalized for1d 3 f+
0
years). The aggregate four-year cum-dividend earnings, , and current book value,ECDE B , can be expressed as follows:
( ) ( )( )( )( ) ( )( ) ( )( )
41 2 3 4 5 1
3 2 12 3
1 1 1
1 1 1 1 1 1
f
f f
ECDE fe e e e f e r d
r d r d r
−
− −
= + + + + − + + −
+ + − + + − + + − 4f d−
)1 1
(A1)
( )(0 1qB B f e= + − −d (A2) where and are VL forecasted earnings and dividends for fiscal years t = 1, 2, 3 and 4, and
te
q
tdB is the book value at the beginning of fiscal year 1, and is the one-year equity rate of
return (i.e., ).
r
( )1/ 41 1r R= + −
For example, if the forecast for fiscal year 1999 (January 1-December 31) was made on October 1, 1999, then the first forecast year is defined as the period between October 1999 and September 2000 (the first shaded bar in the figure below). In this case, the first year VL forecasted earnings will include f = ¼ of the forecast for 1999 (i.e., October 1999 to December 31 1999) plus (1 � f ) = ¾ of the corresponding figure for 2000 (i.e., January 2000 to September 2000). Forecasted earnings for the remaining three forecast years can be analogously defined. The current book value is computed as book value as at the end of fiscal 1998 plus (1 � f ) = ¾ of the difference between the VL 1999 forecasts of earnings and dividends. As a result, andECDE 0B for this example are given by:
( )
( ) ( ) ( )
154
11 7 34 4
1 2 3 4 5 1
2 3
1 3 1 14 4
1 1 1 1 1 1
ECDE e e e e e r d
r d r d r d
= + + + + + + −
+ + − + + − + + −
4
4
(A3)
(0 13 .4q )1B B e d= + − (A4)
(A3) and (A4) become the first and second expressions in Equation (1) under the direct method. The third expression is given by forecasted horizon premiums, , at December 31, 2003. 4P B− 4
44
31-122003
31-12 1998 t=4t=3t=2t=1t=0
While the vast majority of VL forecasts are published during the first fiscal year, this is not the case for some firm-quarter observations. When VL forecasts appear outside the fiscal year in question, they are included as part of our sample provided these forecasts are within 2 months of the fiscal year at either end (see footnote 10). For these observations, to calculate andECDE 0B , we need to suitably modify (A1) and (A2).
45
Appendix 2 Summary of Intrinsic Value Estimates
Direct Method
( )( )
0 4DM0 41
4B ECDE P BV
r
+ + −=
+
!
ETSS
ETSS 00 0
1 1
1V Bλλ λ
−= +
ECDE!!! ! , where 0λ
! and 0λ
! are estimated from the reverse regression:
00 1
0 0
PECDEB B
λ λ µ= + + ; 0 1Gλ = −!
and 1 R Gλ = −!
.
IHP
( ) ( )
44IHP 4
0 0 41 1 1
tt
t
ae B PPRV Br r
∧
=
= + + + +
∑!
, where is estimated from the minimization problem: 4PPR∧
( ) ( )
24
4 40 0 4
1
1, 0
1 1.
kt kk k t
tK
PPR k k i k
ae B PPRP Br r
PMin=
= ≠
− + +
+ +
∑
∑
PE4
4 4
PE40 1 4
1 10
1
1t t
t tt
t
V EPS EPSE EPS P
α= =
=
= • = •
∑ ∑∑
! ! .
Notations:
0B : The current book value for the target firm. ECDE : VL�s forecasts of aggregate cum-dividend earnings for the next four periods.
4 4P B− : VL=s forecasted horizon premiums, four years hence.
( )41 r+ : The 4-year required rate of return given by an equally weighted industry CAPM . rG : One plus the ETSS expected rate of growth in four-year abnormal earnings R : One plus the ETSS four-year expected return on equity. ae : Abnormal earnings, on a per share basis. EPS : Earnings per share.
46