use of forecasts of earnings to estimate and compare cost of capital across regimes

Use of Forecasts of Earnings toEstimate and Compare Cost of Capital

Across Regimes

PETER EASTON*

Abstract: I critically examine several of the methods used in the recent literature to estimate andcompare the cost of capital across different accounting/regulatory regimes. I focus on the centralimportance of expectations of growth beyond the short period for which forecasts of future pay-offs (dividends and/or earnings) are available. I illustrate, using the stocks that comprised the DowJones Industrial Average (DJIA) at December 31, 2004, as an example, the differences betweenthe growth rates implied by the data, and growth rates that are often assumed in the literature.My analyses show that assumptions about growth beyond the (short) forecast horizon mayseriously affect the estimates of the expected rate of return and may lead to spurious inferences.

Keywords: cost of capital, accounting regimes, GAAP differences

1. INTRODUCTION

In this paper, I critically examine several of the methods used in the recentburgeoning literature to estimate and compare the cost of capital across differentaccounting/regulatory regimes.1 I focus on the central importance of expectationsof growth beyond the short period for which forecasts of future pay-offs (dividendsand/or earnings) are available. I illustrate, using the stocks that comprised the DowJones Industrial Average (DJIA) at December 31, 2004, as an example, the differ-ences between the growth rates implied by the data, and growth rates that are oftenassumed in the literature. Also, using these stocks, I demonstrate the fact thatdescriptively invalid growth rate assumptions may lead to incorrect conclusionsabout differences in cost of capital across accounting/regulatory regimes.

*The author is Notre Dame Alumni Professor at Notre Dame, IN. He thanks Keji Chen, Lorie Marsh,John O’Hanlon, Greg Sommers, Gary Taylor and Peter Pope for their comments on an earlier draft. Theassistance of Notre Dame Research Analyst, Hang Li, is greatly appreciated.

Address for correspondence: Peter Easton, Notre Dame Alumni Professor, 305A Mendoza, Notre DameIN 46556, USA.e-mail: [email protected]

1 A representative and well-executed example of a paper in this literature is Daske (2005) who comparesproxies for the cost of capital for firms that used HGB (German) GAAP, for firms that switched toInternational Accounting Standards (International Financial Reporting Standards), and for firms thatswitched to US standards. I will refer to Daske’s paper more than other similar papers because the initialimpetus for my analysis was to provide a discussion of the issues surrounding the methodologies he uses.

Journal of Business Finance & Accounting, 33(3) & (4), 374–394, April/May 2006, 0306-686Xdoi: 10.1111/j.1468-5957.2006.00627.x

# 2006 The AuthorJournal compilation # 2006 Blackwell Publishing Ltd, 9600 Garsington Road, Oxford OX4 2DQ, UK

374 and 350 Main Street, Malden, MA 02148, USA.

The literature that reverse-engineers valuation models to obtain estimates of theexpected rate of return on equity investment is very new. These reverse-engineeredvaluation models include the dividend capitalization model (see, Botosan, 1997), theresidual income valuation model (see, O’Hanlon and Steele, 2000; Gebhardt, Lee andSwaminathan, 2001; Claus and Thomas, 2001; Easton, Taylor, Shroff and Sougiannis,2002; and Baginski and Wahlen, 2003), and the abnormal growth in earnings model(see, Gode and Mohanram, 2003; and Easton, 2004). Literature that has used theseestimates to test hypotheses regarding factors that may affect the expected rate of returnhas developed almost simultaneously (see, for example, Daske, 2006; Dhaliwal, Krull, Liand Moser, 2005; Francis, Khurana and Periera, 2005; Francis, LaFond, Olsson andSchipper, 2004; Hail and Leuz, 2005; Hribar and Jenkins, 2004; and Lee, Myers andSwaminathan, 1999). This has happened despite the facts that (1) some of thesemethods were not designed to provide firm-specific estimates (see, in particular, Clausand Thomas, 2001; Easton, Taylor, Shroff and Sougiannis, 2002; and Easton, 2004),and (2) there is very little evidence regarding the empirical validity of these methods.

The conclusion from the very recent studies examining the validity of firm-specific estimates of expected rate of return that are derived from these reverseengineering exercises is that these estimates are poor, indeed. I will briefly outlinethree of these recent studies (Botosan and Plumlee, 2005; Easton and Monahan,2005; and Guay, Kothari and Shu, 2005).

Perhaps the most important issue in estimating the expected rate of return is theestimation of growth beyond the forecast horizon. Three approaches are common:(1) assuming that residual income (in Claus and Thomas, 2001) or abnormal growthin earnings (in Gode and Mohanram, 2003) grows at the same rate for all firms(this rate is an estimate of the expected real growth in GDP), (2) fading the terminalreturn-on-equity to an industry median return-on-equity (see Gebhardt, Leeand Swaminathan, 2001), and (3) estimating the residual income growth rate(in O’Hanlon and Steele, 2000; and in Easton, Taylor, Shroff and Sougiannis,2002) or the rate of change in abnormal growth in earnings (in Easton, 2004) thatis implied by the data as well as the expected rate of return that is implied by thedata.2 The advantage of the first two of these approaches is that they ostensiblyprovide firm-specific estimates of the implied expected rate of return while thelatter approaches only provide estimates of the implied expected rate of return forportfolios of stocks.3 The disadvantage of the first two approaches is that the

2 Several studies have used estimates of the expected rate of return based on a restricted form of theabnormal growth in earnings model in which the rate of change in abnormal growth in earnings isassumed to be zero. This method is outlined in Easton (2004). He shows that the implied estimates of theexpected rate of return based on this method are downward biased.3 Although the method in Claus and Thomas (2001) has been used by others to obtain firm-specificestimates of the implied expected rate of return, the fact that the method uses the same growth rate for allstocks after a short (three-year) forecast horizon suggests that the implied expected rate of return isunlikely to be reliable at the firm-specific level. Claus and Thomas (2001) discuss the reason that this is so:expected growth is affected by both the expectation of future economic rents and the conservative natureof accounting – the effects of conservative accounting on the short-horizon forecasts of earnings and bookvalues will differ from firm to firm, thus affecting the base from which earnings are assumed to grow inperpetuity. A similar observation applies to the method in Gode and Mohanram (2003) who also use thesame growth rate for all firms. Daske (2006) observes that the Gode and Mohanram (2003) procedureuses ‘economically plausible’ assumptions and ‘can be applied to a single firm’. I disagree with thisconclusion. Although the Gode and Mohanram (2003) assumptions may be plausible at the economylevel, there is no reason to conclude that their assumption is descriptively valid at the firm level.

COST OF CAPITAL ACROSS REGIMES 375

# 2006 The AuthorJournal compilation # Blackwell Publishing Ltd. 2006

assumed growth rate beyond the short forecast horizon may (probably will) differfrom the growth rate implied by the data. I will elaborate on the differencesbetween the approaches and compare the estimates of the implied expected rateof return when the growth rate is assumed with the estimates when the growth rateis (simultaneously) estimated from the data.4

In light of the fact that assumptions about the terminal growth rate are unlikely tobe descriptively valid, the inferences based on the estimates of the expected rate ofreturn that are based on these assumptions may be spurious. The appeal ofO’Hanlon and Steele (2000), Easton, Taylor, Shroff and Sougiannis (2002) andEaston (2004) is that they simultaneously estimate the expected rate of return andthe expected rate of growth that are implied by the data. The other methods assumea growth rate and calculate the expected rate of return that is implied by the dataand the assumed growth rate. Differences between the true growth rate and theassumed growth rate will lead to errors in the estimate of the expected rate ofreturn.

I use the stocks that comprised the DJIA at December 31, 2004, to compare theestimates of the expected rate of return from the various extant estimation methodsthat have been applied to I/B/E/S forecasts. One of these methods (Easton, Taylor,Shroff and Sougiannis, 2002) simultaneously estimates the expected rate of returnand the expected growth in residual income that are implied by market prices, thebook value of common equity, and forecasts of accounting earnings. I use theseestimates as a benchmark against which to compare other estimates which rely onassumptions about expected growth rates beyond the forecast horizon. The focus ofthis comparison is on highlighting the errors that will be introduced if invalidassumptions are made about growth beyond the short horizon for which analysts’forecasts of earnings are available. I also comment on use of the Easton (2004)method to simultaneously estimate the expected rate of return and growth incontexts other than the context used in that study.

Most studies that invert either the residual income valuation model or the abnor-mal growth in earnings model rely on forecasts of earnings that are made by sell-side analysts who are in the business of giving investment advice (that is, makingbuy/hold/sell recommendations). It seems reasonable to assume that analysts mak-ing strong sell (buy) recommendations are implicitly forecasting a negative (positive)abnormal return – that is, they are forecasting a rate of return that will be less(more) than the cost of capital.5 In light of analysts’ tendency to be optimistic, theseestimates of the expected rate of return are generally likely to be higher than thecost of capital.6 In order to provide a sense of the bias introduced when using

4 Both Easton, Taylor, Shroff and Sougiannis (2002) and Easton (2004) use ordinary least squares regres-sion as the basis for estimation. It follows that the estimates of the implied expected rate of return and theimplied expected rate of growth reflect portfolio weights that are dictated by the minimization of the sum ofsquared errors. Other weights may, of course, lead to different estimates of the growth rate and the rate ofreturn for the portfolio. Nevertheless, ordinary least squares regression is a reasonable starting point forestimating the expected rate of return and the expected growth rate implied by the data.5 Cost of capital is an equilibrium concept, which relies on the no arbitrage assumption. In the absence ofarbitrage opportunities, the market’s expected rate of return is equal to the cost of capital. The estimateof the expected rate of return implied by prices and analysts’ forecasts of earnings may not be equal to thecost of capital for two reasons (1) the forecasts may not be a reasonable proxy for the market’s expecta-tions, and (2) prices may be inefficient (that is, arbitrage opportunities may exist).6 Williams (2004) makes this point in his discussion of Botosan, Plumlee and Xie (2004).

376 EASTON


analysts’ forecasts to estimate the expected rate of return, I compare estimatesimplied by prices, book values, and forecasts of earnings (based on the method inEaston, Taylor, Shroff and Sougiannis, 2002) with the expected rate of returnimplied by prices, book values, and realized earnings (using an adaptation of themethod in O’Hanlon and Steele, 2000).

I provide suggestions for future research in the concluding section of the paper.In my view, the emphasis of future work should be on understanding the propertiesof the estimates of expected rate of return and improving on them. Much workmust be done before we can confidently claim that our methods may be used toestimate and understand differences in cost of capital across accounting regimes.

2. ERROR AND BIAS IN MEASUREMENT OF THE EXPECTED RATE OF RETURN ONEQUITY CAPITAL

(i) Errors in Firm-specific Estimates of the Expected Rate of Return

In this section, I briefly outline three recent studies that examine the validity of firmspecific estimates of the expected rate of return.

Botosan and Plumlee (2005) rank estimates of expected rates of return by com-paring the cross-sectional variation in the estimates that is explained by variousassumed risk factors (for example, CAPM beta, equity market value, leverage, etc.).They obtain r-squares as high as 65%, perhaps supporting the conclusion that theestimates of the expected rate of return may be reliable. There are, however, severalreasons why the validity of the estimates should still be questioned; (1) the implicitassumption that the risk factors evaluated are correct and exhaustive is unlikely tobe valid as a practical matter, and (2) the regression r-square may reflect no morethan correlations between the measurement error in the assumed risk factors andthe measurement error in the estimate of the expected rate of return.

The focus of the analyses in Guay, Kothari and Shu (2005) is on the correlationbetween realized return and various expected return proxies. They show, for all ofthe estimates that they evaluate, this correlation is not significantly different fromzero and it is often negative. Easton and Monahan (2005) point out that thesecorrelations may be biased measures of the association between realized returnsand expected returns because of the existence of correlated omitted variables(namely, cash flow news – that is, news about the expected future payoffs – andreturn news – that is, news about the future ‘discount rate’). They develop anempirical approach that allows them to evaluate the reliability of an expected returnproxy from its association with realized returns even if realized returns are biasedand noisy measures of expected returns.

The results in Easton and Monahan (2005) suggest that the seven accountingbased proxies that they consider are not reliable measures of expected returns.None of the proxies has a significant positive association with realized returns evenafter controlling for the bias and noise in realized returns attributable to contem-poraneous information surprises. Moreover, the simplest proxy, which is based onthe least reasonable assumptions ex ante, contains no more measurement error thanthe remaining proxies. These results are robust as they remain descriptive evenafter Easton and Monahan (2005) attempt to purge the proxies of measurement



error via the use of instrumental variables and grouping. Additional analyses,however, demonstrate that some proxies are somewhat reliable when the con-sensus long-term growth forecasts are low and/or when analysts’ forecast accuracyis high.

(ii) Bias in Estimates of the Expected Rate of Return

None of the studies discussed in the previous sub-section addresses the issue ofpotential bias in estimates of the expected rate of return due to bias in analysts’forecasts of earnings. Nevertheless, the possibility that bias in analysts’ forecasts ofearnings may affect the results in studies that compare estimates of the impliedexpected rate of return should be considered. For example, it is possible thatanalysts’ forecasts for firms that have changed from domestic to internationalaccounting standards (as in Daske, 2006, for example) may tend to have a differentdegree of optimism than forecasts for firms that have not changed. These more(less) optimistic forecasts will bias the estimate of the expected rate of return upward(downward), potentially leading to the (possibly erroneous) conclusion that the costof capital is higher (lower) for these firms.

All studies that invert either the residual income valuation model or the abnormalgrowth in earnings model rely on forecasts of earnings that are made by sell-sideanalysts who are in the business of providing investment advice (that is, making buy/hold/sell recommendations). It seems reasonable to assume that analysts makingstrong sell (buy) recommendations are implicitly forecasting a negative (positive)abnormal return; they are forecasting a rate of return that will be less (more) thanthe cost of capital. In light of analysts’ tendency to be optimistic, estimates of theexpected rate of return implied by analysts’ forecasts of earnings are likely togenerally be higher than the cost of capital.7 This effect of analysts’ optimism isexacerbated by the fact that all studies that use analysts’ forecasts to calculate animplied expected rate of return use forecasts that are made well in advance (usuallyat least a year) of the earnings announcement. These forecasts tend to be muchmore optimistic than those made closer to the earnings announcement (seeRichardson, Teoh and Wysocki, 2001).

3. DIFFERENCES IN GAAP ACROSS ACCOUNTING REGIMES MAY INDUCEDIFFERENCES IN TERMINAL GROWTH

Differences in generally accepted accounting principles and practices (GAAP) acrossaccounting regimes will almost inevitably lead to differences in reported book valueand forecasts of earnings.8 These book values and forecasts of earnings are the basefrom which residual earnings or abnormal growth in earnings grows beyond theforecast horizon. It follows that GAAP differences will induce differences in growthbeyond the forecast horizon and these differences must be taken into account in

7 Easton and Sommers (2005) provide evidence consistent with this conjecture.8 Throughout the manuscript, I use the acronym GAAP to denote generally accepted accountingprinciples and the way that these principles are variously applied as a practical matter in variousaccounting regimes.

378 EASTON


order to avoid spurious inferences regarding the effect of GAAP differences on thecost of capital. Easton (2004) provides an illustration of this point.

At the end of fiscal year 2001 (June 30), Microsoft was trading at a price per shareof $75 and analysts were forecasting earnings of $1.90 and $2.15 for fiscal years2002 and 2003. At that time Microsoft was not expected to pay dividends in theforeseeable future. If we assume, for the sake of the illustration, that Microsoft’sexpected rate of return was 10%, its abnormal growth in earnings from 2002 to2003 would have been $2.15 � 1.1($1.90) ¼ $0.06.9 Inverting the abnormalgrowth in earnings valuation model to obtain the change in the abnormal growthin earnings (beyond 2003) that equates a price of $75 and the 2002/2003 abnormalgrowth in earnings of $0.06 yields a change in the abnormal growth in earningsof 8.9%.

Notice that the abnormal growth in earnings of $0.06 and the growth from thisbase at 8.9% are a consequence of GAAP. To see this, note that with an expectedrate of return of 10%, Microsoft’s expected economic earnings for 2002 and 2003will be $7.50 and $8.25 and there will be no abnormal growth in earnings ($8.25� 1.1($7.50) ¼ $0.00) in 2002/2003 and thereafter.

Differences in accounting regime will lead to differences in growth beyond theforecast horizon. Suppose that under a different accounting regime, the forecast ofMicrosoft’s earnings for 2003 excludes an expense of $0.50, so that an alternativeforecast is $2.65 rather than $2.15. This higher forecast implies a higher expectedabnormal growth in earnings from 2002 to 2003 and a much lower (in fact, zero)growth rate beyond 2003.

The main point is that assuming the same growth rate beyond the forecasthorizon may (in fact, probably will) lead to spurious inferences as there are reasonsto expect that growth will differ across accounting regimes just due to differences inGAAP. Further, even if the assumed growth rates differ across regimes, the assump-tions regarding these differences in growth rates may be invalid. The appeal ofO’Hanlon and Steele (2000), Easton, Taylor, Shroff and Sougiannis (2002) andEaston (2004) is that they simultaneously estimate the expected rate of return andthe expected rate of growth that are implied by the data. No other method doesthis. The other methods assume a growth rate and calculate the expected rate ofreturn that is implied by the data and the assumed growth rate.

4. A CRITICAL COMPARISON OF THE EXTANT METHODS USINGTHE DJIA AS AN ILLUSTRATION

This section proceeds as follows. I begin by estimating the expected rate of returnand the growth in residual income beyond the forecast horizon that are implied bythe prices, book values and forecasts of earnings for the stocks comprising the DJIAat December 31, 2004. These estimates are derived using the methodology fromEaston, Taylor, Shroff and Sougiannis (2002). I then use these estimates as abenchmark to critically examine the estimates of the expected rate of return basedon the methods in Gebhardt, Lee and Swaminathan (2001), Easton (2004), Godeand Mohanram (2003) and O’Hanlon and Steele (2000).

9 The abnormal growth in earnings valuation model is described in some detail in Section 4(iv).



(i) Sample Description

All analyses in this section are performed on the firms that comprised the DJIAon December 31, 2004. Price at the close of trade on December 31, 2004, equitybook value and number of shares outstanding at that date, dividends for the yearending December 31, 2004, and equity book value as at December 31, 2003, areobtained from the Compustat annual file.10 I/B/E/S ‘actual’ earnings for 2004, I/B/E/S (median) consensus forecasts of earnings for 2005 and 2006 and of thelong-term earnings growth rate are obtained from the unadjusted summary file(the date of these forecasts is December 16, 2004).11 These data are included asTable 1.

(ii) Easton, Taylor, Shroff and Sougiannis (2002)

The method in Easton, Taylor, Shroff and Sougiannis (2002) is based on theresidual income valuation model which may be written as follows:

pjt ¼ bpsjt þEt½ðROEjtþ1 � rjÞ�bpsjt�

ðrj � gjÞð1Þ

where pjt is price per share for firm j at time t, bpsjt is the book value of commonequity per share of firm j at time t, rj is the expected rate of return for firm j, gj is theexpected rate of growth in residual income beyond period t þ 1 required to equatepjt � bpsjt and the present value of an infinite implied residual income stream,ROEjtþ1 is the return-on-equity for firm j for time period t to t þ 1, and Et is theexpectation operator.12 The period t to t þ 1 is 4 years so that ROEjtþ1 is aggregateexpected cum-dividend earnings per share for the four years after date t divided bybook value per share at time t, that is, aggearnjtþ1/bpsjt.

Easton, Taylor, Shroff and Sougiannis (2002) transform this model to form thefollowing regression relation:

aggearnjtþ1

bpsjt¼ �0 þ �1

pjt

bpsjtþ �jt ð2Þ

10 Five firms in the DJIA at December 31, 2004, did not have a 31 December fiscal year end. Calculationsof the implied expected rate of return for a portfolio of firms at a point in time requires formation ofexpectations at the same point in time for all stocks in the portfolio but this introduces considerablecomplications associated with dealing with partial time periods. Since these firms are used for illustrativepurposes only, I ignore this in my calculations – that is, I average estimates across all 30 stocks eventhough some are at different points in time and/or I run regressions across stocks with different fiscal-year-end-dates. This, of course, introduces inaccuracies in the estimations but comparisons across thedifferent methods are still meaningful. The advantage is that my sample size is 20% larger when theseobservations are included. Daske (2006) provides methods that may be adapted to facilitate the inclusionof observations with different fiscal year end. In the interest of simplicity in exposition, I do not use thesemethods in this illustration.11 For observations with non-December fiscal year end, I use I/B/E/S forecasts made on the thirdThursday of the fiscal-year-end-month.12 The definition of rj and of gj does not imply that either the expected rate of return or the expectedrate of growth are constant over all future years. Rather, rj and gj may be seen as geometric averages of amore probable term-structure of rj and pattern of growth in residual income.

380 EASTON


Tab

le1

Var

iab

les

Use

din

Est

imat

ing

the

Imp

lied

Ex

pec

ted

Rat

eo

fR

etu

rnfo

rth

eS

tock

sC

om

pri

sin

gth

eD

JIA

on

Dec

emb

er3

1,

20

04

Com

pan

yN

ame

Indu

stry

pric

e 04

bps 0

4bp

s 03

dps 0

4ep

s 05

eps 0

6ltg

Alc

oa

Inc.

Ste

elw

ork

set

c.3

1.4

21

5.2

21

3.8

10

.00

2.4

22

.73

12

.00

Am

eric

anIn

tern

atio

nal

Gro

up

Insu

ran

ce6

5.6

73

0.9

52

7.3

60

.00

5.2

15

.90

14

.46

Am

eric

anE

xp

ress

Ban

kin

g5

6.3

71

2.7

61

2.2

10

.00

3.1

03

.48

12

.72

Bo

ein

gC

o.

Air

craf

t5

1.7

71

3.4

49

.69

0.0

02

.57

3.0

31

1.5

4C

itig

rou

pIn

c.B

ank

ing

48

.18

20

.84

18

.67

0.0

14

.35

4.7

01

1.4

5C

ater

pilla

rIn

c.M

ach

iner

y9

7.5

12

1.8

81

7.8

10

.00

7.1

08

.30

13

.00

Du

Po

nt

(EI)

De

Nem

ou

rsC

hem

ical

s4

9.0

51

0.3

18

.84

0.0

12

.74

3.1

41

0.6

7D

isn

ey(W

alt)

Co

.T

elec

om

mu

nic

atio

ns

22

.55

12

.69

11

.58

0.0

01

.18

1.3

51

5.0

6G

ener

alE

lect

ric

Co

.M

isce

llan

eou

s3

6.5

01

0.4

37

.49

0.0

01

.80

2.0

21

0.8

7G

ener

alM

oto

rsC

orp

.A

uto

mo

biles

and

tru

cks

40

.06

49

.09

44

.74

0.0

04

.92

5.6

46

.00

Ho

me

Dep

ot

Inc.

Ret

ail

35

.47

9.8

58

.70

0.0

02

.04

2.3

31

2.7

2H

on

eyw

ell

Inte

rnat

ion

alIn

c.A

ircr

aft

35

.41

13

.08

12

.47

0.0

01

.99

2.3

61

2.4

9H

ewle

tt-P

ack

ard

Co

.C

om

pu

ters

18

.66

12

.44

12

.50

0.0

01

.48

1.6

41

0.8

9In

tlB

usi

nes

sM

ach

ines

Co

rp.

Bu

sin

ess

serv

ices

98

.58

17

.87

16

.74

0.0

05

.54

6.0

11

0.7

0In

tel

Co

rp.

Ele

ctro

nic

equ

ipm

ent

23

.39

6.1

05

.99

0.0

01

.18

1.3

01

6.0

6Jo

hn

son

&Jo

hn

son

Ph

arm

aceu

tica

lp

rod

uct

s6

3.4

21

0.7

29

.05

0.0

03

.34

3.6

51

2.2

2JP

Mo

rgan

Ch

ase

&C

o.

Ban

kin

g3

9.0

12

9.5

61

2.6

70

.01

3.2

73

.60

10

.62

Co

ca-C

ola

Co

.A

lco

ho

lic

bev

erag

es4

1.6

46

.59

5.8

20

.00

2.0

32

.22

8.9

3M

cDo

nal

d’s

Co

rp.

Res

tau

ran

t,h

ote

l,m

ote

l3

2.0

61

1.3

09

.53

0.0

02

.00

2.1

98

.49

3M

Co

.B

usi

nes

ssu

pp

lies

82

.07

13

.33

10

.13

0.0

04

.17

4.6

01

1.7

5A

ltri

aG

rou

pIn

c.T

ob

acco

pro

du

cts

61

.10

14

.96

12

.22

0.0

05

.15

5.5

68

.67

Mer

ck&

Co

.P

har

mac

euti

cal

pro

du

cts

32

.14

7.8

07

.02

0.0

02

.46

2.4

25

.10

Mic

roso

ftC

orp

.B

usi

nes

sse

rvic

es2

8.5

66

.93

5.6

50

.00

1.3

41

.46

11

.37

Pfi

zer

Inc.

Ph

arm

aceu

tica

lp

rod

uct

s2

6.8

99

.04

8.6

50

.00

2.3

12

.46

11

.76

Pro

cter

&G

amb

leC

o.

Co

nsu

mer

go

od

s5

4.4

41

3.2

51

2.3

80

.10

2.5

62

.83

10

.81

SB

CC

om

mu

nic

atio

ns

Inc.

Tel

eco

mm

un

icat

ion

s2

5.7

71

2.2

21

1.5

40

.00

1.3

71

.59

7.1

4U

nit

edT

ech

no

log

ies

Co

rp.

Air

craf

t1

03

.35

27

.41

22

.91

0.0

06

.17

6.7

91

1.0

4V

eriz

on

Co

mm

un

icat

ion

sIn

c.T

elec

om

mu

nic

atio

ns

40

.51

13

.56

12

.09

0.0

02

.66

2.7

35

.89

Wal

-Mar

tS

tore

sR

etai

l5

3.8

51

0.0

89

.09

0.0

02

.32

2.6

71

3.7

3E

xx

on

Mo

bil

Co

rp.

En

erg

y5

1.2

61

5.7

71

3.9

40

.00

3.4

03

.17

6.8

3

Not

es:

pric

e 04

isp

rice

per

shar

eo

fth

est

ock

atth

een

do

ffi

scal

year

20

04

,bp

s 04

isth

eb

oo

kva

lue

per

shar

eat

the

end

of

fisc

alye

ar2

00

4,bp

s 03

isth

eb

oo

kva

lue

per

shar

eat

the

end

of

fisc

alye

ar2

00

3,

dps 0

4is

div

iden

ds

per

shar

ep

aid

on

the

sto

ckd

uri

ng

fisc

alye

ar2

00

4,

eps 0

5an

dep

s 06

are

the

I/B

/E/S

fore

cast

so

fea

rnin

gs

per

shar

efo

rfi

scal

year

s2

00

5an

d2

00

6,

and

ltg

isth

eI/

B/E

/Sfo

reca

sto

flo

ng

-ter

mg

row

th.



where �0 ¼ [(1 þ g)4 � 1], �1 ¼ [(1 þ r)4 � (1 þ g)4], g is the expected annual rateof growth in residual income and r is the expected annual rate of return. Thisregression may be estimated for any group/portfolio of stocks to obtain estimates ofthe expected rate of return, r, and the expected growth rate, g, for the portfolio.The estimates of �0 and �1 are 0.30 (t-statistic of 3.47) and 0.20 (t-statistic of 8.72)with associated implied estimates of the annual growth rate of 6.8% and expectedannual rate of return of 10.6%.13 That is, market prices, accounting book value, andforecasts of earnings at December 31, 2004, imply an expected rate of return on theDJIA of 10.6%.14 In the subsequent sections, I will compare this estimate withestimates of the expected rate of return obtained when the growth rate beyondthe forecast horizon is assumed rather than estimated from the data.15

(iii) Gebhardt, Lee and Swaminathan (2001)

The residual income model, as it is implemented in Gebhardt, Lee andSwaminathan (2001) may be expressed as:

pjt ¼ bpsjt þX11

�¼1

Et½ðROEjtþ� � rjÞ�bpsjtþ��1�ð1þ rjÞ�

þEt½ðROEjtþ12 � rjÞ�bpsjtþ11�

rj�ð1þ rjÞ11ð3Þ

where t indexes years. Expected earnings for the first three years are obtained fromthe same forecasts as in Easton, Taylor, Shroff and Sougiannis (2002), with fore-casted book value based on the assumptions that forecasted earnings are clean-surplus and the dividend payout ratio is constant. Gebhardt, Lee and Swaminathan(2001) assume that beyond year three, expected return-on-equity fades to thehistorical industry median and then residual income is constant beyond yeart þ 12.16 The historical industry median return-on-equity is the median over timeand across firms for all firms in the same Fama and French (1997) industryclassification that have available data in any of the years 1995 to 2004.17

The key variables and the Gebhardt, Lee and Swaminathan (2001) estimates ofthe expected rate of return for the DJIA firms are included as Table 2. Theseestimates range from 6.3% for General Electric Co. to 20.5% for Altria Group Inc.with an average of 9.7%. The key assumption in the Gebhardt, Lee and

13 The adjusted r-square from this regression is 0.72.14 The Easton, Taylor, Shroff and Sougiannis (2002) method may also be used with just one year offorecasted earnings (rather than four years as in their paper). This yields an implied expected rate ofreturn of 10.7% and an implied expected rate of growth in residual income of 6.5%.15 Daske (2006) uses two methods that rely on assumptions about growth beyond the forecast horizon(namely, Gebhardt, Lee and Swaminathan (2001) and Gode and Mohanram, 2003) and two methods thatsimultaneously estimate the expected rate of return and the expected growth rate that are implied by thedata (namely, Easton, Taylor, Shroff and Sougiannis 2002; and Easton, 2004). Unfortunately, since theseestimates are based on different samples of observations, comparison of the estimates (as in this paper) isnot meaningful.16 I use the DJIA stocks to demonstrate that, although the idea of fading to the median return-on-equityof a group of comparable firms is intuitively appealing, and despite the fact that this idea is used byanalysts in practice, finding a group of comparable firms is very difficult particularly in a research contextwhere the samples are large.17 As in Gebhardt, Lee and Swaminathan (2001), all observations with negative net income are excludedfrom the calculation of the industry median return-on-equity.

382 EASTON


Tab

le2

Key

Var

iab

les

and

the

Est

imat

eso

fth

eIm

plied

Ex

pec

ted

Rat

eo

fR

etu

rnU

sin

gth

eM

eth

od

inG

ebh

ard

t,L

eean

dS

wam

inat

han

(20

01

)

Com

pan

yN

ame

Indu

stry

r GL

S%

p/b

�0

7�¼

05

earn

j�=bp

s 04

NIR

OE

RO

E0

7

Alc

oa

Inc.

Ste

elw

ork

set

c.9

.92

.06

0.5

47

46

0.1

30

.15

Am

eric

anIn

tern

atio

nal

Gro

up

Insu

ran

ce1

0.2

2.1

20

.58

20

56

0.1

30

.15

Am

eric

anE

xp

ress

Ban

kin

g9

.54

.42

0.8

29

80

0.1

70

.19

Bo

ein

gC

o.

Air

craf

t8

.63

.85

0.6

72

02

0.1

50

.17

Cit

igro

up

Inc.

Ban

kin

g1

2.1

2.3

10

.69

98

00

.17

0.1

7C

ater

pilla

rIn

c.M

ach

iner

y9

.64

.46

1.1

31

60

10

.14

0.2

4D

uP

on

t(E

I)D

eN

emo

urs

Ch

emic

als

8.6

4.7

60

.91

89

50

.15

0.2

1D

isn

ey(W

alt)

Co

.T

elec

om

mu

nic

atio

ns

9.8

1.7

80

.32

15

42

0.1

50

.10

Gen

eral

Ele

ctri

cC

o.

Mis

cellan

eou

s6

.33

.50

0.5

87

74

0.1

00

.15

Gen

eral

Mo

tors

Co

rp.

Au

tom

ob

iles

and

tru

cks

15

.00

.82

0.3

48

20

0.1

60

.10

Ho

me

Dep

ot

Inc.

Ret

ail

8.2

3.6

00

.71

25

81

0.1

30

.18

Ho

ney

wel

lIn

tern

atio

nal

Inc.

Air

craf

t9

.52

.71

0.5

42

02

0.1

50

.15

Hew

lett

-Pac

kar

dC

o.

Co

mp

ute

rs1

1.3

1.5

00

.40

15

97

0.1

50

.11

Intl

Bu

sin

ess

Mac

hin

esC

orp

.B

usi

nes

sse

rvic

es8

.45

.52

1.0

24

93

00

.15

0.2

2In

tel

Co

rp.

Ele

ctro

nic

equ

ipm

ent

8.2

3.8

30

.65

24

16

0.1

40

.17

Joh

nso

n&

Joh

nso

nP

har

mac

euti

cal

pro

du

cts

9.5

5.9

21

.03

11

45

0.1

80

.22

JPM

org

anC

has

e&

Co

.B

ank

ing

12

.81

.32

0.3

79

80

0.1

70

.11

Co

ca-C

ola

Co

.A

lco

ho

lic

bev

erag

es7

.36

.32

1.0

12

23

0.1

40

.22

McD

on

ald

’sC

orp

.R

esta

ura

nt,

ho

tel,

mo

tel

7.8

2.8

40

.58

10

32

0.1

20

.15

3M

Co

.B

usi

nes

ssu

pp

lies

7.5

6.1

61

.04

68

10

.13

0.2

2A

ltri

aG

rou

pIn

c.T

ob

acco

pro

du

cts

20

.54

.08

1.1

28

70

.38

0.2

3M

erck

&C

o.

Ph

arm

aceu

tica

lp

rod

uct

s1

0.8

4.1

20

.95

11

45

0.1

80

.20

Mic

roso

ftC

orp

.B

usi

nes

sse

rvic

es7

.94

.12

0.6

44

93

00

.15

0.1

6P

fize

rIn

c.P

har

mac

euti

cal

pro

du

cts

12

.12

.97

0.8

31

14

50

.18

0.1

9P

roct

er&

Gam

ble

Co

.C

on

sum

erg

oo

ds

7.7

4.1

10

.64

85

00

.14

0.1

7S

BC

Co

mm

un

icat

ion

sIn

c.T

elec

om

mu

nic

atio

ns

9.3

2.1

10

.38

15

42

0.1

50

.11

Un

ited

Tec

hn

olo

gie

sC

orp

.A

ircr

aft

9.1

3.7

70

.75

20

20

.15

0.1

8V

eriz

on

Co

mm

un

icat

ion

sIn

c.T

elec

om

mu

nic

atio

ns

9.1

2.9

90

.61

15

42

0.1

50

.15

Wal

-Mar

tS

tore

sR

etai

l6

.95

.34

0.8

02

58

10

.13

0.1

9E

xx

on

Mo

bil

Co

rp.

En

erg

y8

.63

.25

0.6

31

90

30

.14

0.1

5

Not

es:

r GL

Sis

esti

mat

eo

fth

eim

plied

exp

ecte

dra

teo

fre

turn

ob

tain

edu

sin

gth

em

eth

od

inG

ebh

ard

t,L

eean

dS

wam

inat

han

(20

01

),p/

bis

the

rati

oo

fp

rice

per

shar

eo

fth

est

ock

atth

een

do

ffi

scal

year

20

04

tob

oo

kva

lue

per

shar

eat

the

end

of

fisc

alye

ar2

00

4.

�0

7�¼

05

earn

j�=b

ps0

4,

isth

esu

mo

fth

efo

reca

sts

of

earn

ing

sp

ersh

are

for

fisc

alye

ars

20

05

to2

00

7,

Nis

the

nu

mb

ero

fst

ock

-yea

ro

bse

rvat

ion

su

sed

toca

lcu

late

the

ind

ust

rym

edia

nre

turn

-on

-eq

uit

y,IR

OE

isth

ein

du

stry

med

ian

retu

rno

neq

uit

y,an

dR

OE

07

isth

eI/

B/E

/Sfo

reca

sted

retu

rn-o

n-e

qu

ity

for

fisc

alye

ar2

00

7.



Swaminathan (2001) method is that the return-on-equity fades beyond the forecasthorizon to the industry median return-on-equity. These industry medians are alsoincluded in Table 2. Of course, determination of the ‘true’ expected return-on-equity is impossible and judgments regarding the validity of comparable firms willvary. Thus, I will make only a few comments about these data.

The number of observations used to calculate the industry median return-on-equity ranges from 87 for Altria Group Inc. to 4,930 for IBM and Microsoft. Acloser look at these stocks and the stocks in the same Fama and French (1997)industry group is revealing.

Altria Group Inc. is in the industry dubbed ‘smoke’ by Fama and French (1997).It is the holding company of Kraft Foods, Philip Morris International, Philip MorrisUSA, and Philip Morris Capital Corporation. Altria Group is also the largest share-holder in the world’s second-largest brewer, SABMiller, with an approximate 33.9%economic interest. Seventeen firms are the basis of the 87 firm-year observationsused to calculate the industry median return-on-equity. The comparison groupincludes four American Depositary Receipts.

I will not present a detailed debate regarding the comparability of the Altria Groupand the firms used to calculate the ‘smoke’ industry median return-on-equity but a fewobservations are in order. One might argue that an expected return-on-equity in 2016of 0.38 is somewhat ambitious and that this suggests that the estimate of the expectedrate of return (20.5%) is too high. One might also argue that, in view of the similar size,similar legal environment, and similar structure that RJ Reynolds might be the mostappropriate comparison (RJ Reynolds follows US GAAP and hence has a return-on-equity that is based on similar accounting principles and RJ Reynolds is not only in thetobacco business but it is also in the food and beverage business). Yet RJ Reynoldsentered the comparison group only four times – in 1999, 2000, 2001 and 2004 withreturns-on-equity of 0.21, 0.26, 0.05 and 0.23 – these returns-on-equity are more inline with the forecasted 2007 return-on-equity for Altria of 0.23 based on I/B/E/S data.18

On the other hand, it is hard to accept that the 1,338 firms that comprise the4,930 firm-year observations used to calculate the industry median return-on-equityfor IBM and Microsoft are comparable with these very large well-establishedfirms.19 One could also debate whether Hewlett-Packard Company should beexcluded as a comparable firm.

It is evident from equation (3) that cross-sectional variation in the Gebhardt, Lee andSwaminathan (2001) estimate of the expected rate of return is driven by three factors –the current difference between price and book value, the forecasts of earnings over theI/B/E/S forecast horizon, and the industry median return-on-equity. The contributionof each of these variables to the cross-sectional variation in the expected rate of returnmay be demonstrated empirically for the DJIA stocks via the following regression:

rj ¼ �0 þ �1½pjt=bjt� þ �2

X3

�¼1

epsj�=bpsjt

" #þ �3Iroejt þ ejt ð4Þ

18 RJ Reynolds had negative return-on-equity in the other sample years and, hence, following Gebhardt,Lee and Swaminathan (2001), these years were not included in the calculation of the ‘smoke’ industrymedian return-on-equity.19 The number of firms in this comparison group increased 219 during 2004. These additional firms areunlikely to be comparable with IBM and Microsoft.

384 EASTON


where rj is the implied expected rate of return on shares of firm j at time t, �3�¼1 epsj�

is the sum of forecasts of earnings for firm j over the three-years after time t, andIroejt is the median industry return-on-equity. The estimates of the coefficients onpjt/bjt, �3

�¼1 earnj�=bpsjt, and Iroejt, are �0.01 (t-statistic of �6.91), 0.05 (t-statistic of3.44) and 0.45 (t-statistic of 11.89).20 That is, the forecast of terminal return-on-equity (the key determinant of growth beyond the earnings forecast horizon) hasthe highest incremental explanatory power for the Gebhardt, Lee and Swaminathan(2001) estimate of expected returns.

These regression statistics demonstrate the distinct possibility that differences inestimates of the expected rate of return across accounting regimes may reflect nomore than the effect of the accounting regimes on (1) the difference between pricesand book values, and (2) the industry median return-on-equity. For example,methods of accounting for asset revaluations, which may vary considerably acrossregimes, will affect both of these variables. Further, the observation that differencesin the industry median return-on-equity have such an effect on differences in theestimates of the expected rate of return, draws attention to the questions: What ifthe way the industry return-on-equity is calculated differs across accountingregimes? Should the industry median return-on-equity be calculated using GAAPof the old regime or of the new regime? What should researchers do if some firms inthe industry are under one accounting regime while others are under a differentregime?21

Related questions are: Why fade to the industry median return-on-equity? Whatis the appropriate industry comparison group? The argument for fading to theindustry median return-on-equity is that residual earnings capture economic rents.Gebhardt, Lee and Swaminathan (2001) argue that:

the mean reversion in return-on-equity attempts to capture the long-term erosion ofabnormal return-on-equity over time and the notion that, in the long-run, individualfirms tend to become more like their peers.

But abnormal earnings capture both (1) economic rents (positive net present valueopportunities – that is, economic value added), and (2) differences betweenthe accountant’s measure of the expected rate of return on equity capital (return-on-equity) and the market’s expected rate of return (that is, accounting valueadded).22

In view of the conservative nature of accounting in particular, and the differencebetween GAAP earnings and economic earnings in general, it is probable that mostof residual earnings will not capture economic rents but, rather, will be due to theaccounting methods that under-pin the book value and the forecasts of earnings. Itfollows that abnormal growth in earnings is also due to choice of accounting methodand will reflect both real growth and a correction for GAAP differences betweenshort-run forecasts of earnings and ‘economic earnings’.

20 The adjusted r-square from this regression is 0.93.21 Daske (2006) also draws attention to some of these issues. He observes: ‘certainly industry ROEs areaffected by the (changing) accounting rules of the firms analyzed in the industry. It is, a priori, difficult tojudge how they are affected and how a potential bias could be induced.’22 See Easton (2001) for a detailed discussion of this difference.



In order to illustrate the effects of the assumption in Gebhardt, Lee andSwaminathan (2001) about the terminal growth in return-on-equity (fading to theindustry median return-on-equity), I split the sample into two sub-samples – onehaving higher industry median return-on-equity, the other having lower industrymedian return-on-equity. This sort is implicitly based on two things: (1) the ‘true’expected long-run sequence of returns-on-equity (that is, the unobservable marketexpectation of the long-run sequence of returns-on-equity), and (2) the error in theproxy for the expected sequence of long-run returns-on-equity (that is, the differ-ence between the industry median return-on-equity and the implied sequence ofreturns-on-equity after the forecast horizon and the ‘true’ expected long-runsequence of returns-on-equity).

It follows that the group with the lower (higher) industry median return-on-equity will (1) have a lower (higher) expected rate of growth in residual income tothe extent that the industry median return-on-equity captures the growth rate thatis implied by the data (implicitly, the ‘true’ expected return-on-equity), and (2) tendto have a downward (upward) biased estimate of the expected long-run return-on-equity because we are also sorting on error. Notice that, analogously, if differencesin accounting regimes cause differences in the error in the estimate of terminalreturn-on-equity (as would be the case, for example, if in one regime asset revalua-tions were encouraged or mandatory while in another regime they were discour-aged or prohibited) these differences will induce spurious differences in theestimate of the cost of capital.

I calculate the expected rate of return implied by the data (via the method inEaston, Taylor, Shroff and Sougiannis, 2002) for each of the groups of stocks.Consistent with the foregoing predictions, the expected rate of growth in residualincome for the sub-sample with the lower median industry return-on-equity is 5.8%;the expected rate of growth in residual income for the sub-sample with the highermedian industry return-on-equity is 7.4%. Also, as predicted, the implied expectedrate of return for the sub-sample with lower median industry return-on-equity is9.7%; higher than the average of the firm-specific estimates obtained via theGebhardt, Lee and Swaminathan (2001) method, which is 8.4%. However, theimplied expected rate of return for the sub-sample with higher median industryreturn-on-equity is 11.3%, which is also higher than the average of the firm-specificestimates obtained via the Gebhardt, Lee and Swaminathan (2001) method of 11%.The observation that the average estimates of the expected rate of return obtainedvia the Gebhardt, Lee and Swaminathan (2001) method are, for both sub-samples,higher than the estimates implied by the data, suggests that the growth rate impliedby the Gebhardt, Lee and Swaminathan (2001) assumptions is too low.

(iv) Easton (2004)

The method in Easton (2004) is based on the abnormal growth in earnings modelwhich may be written as follows:

pjt ¼epsjtþ1

rjþ

agrjtþ1

rj�ðrj ��agrjÞð5Þ

386 EASTON


where agrjtþ1 is the expected abnormal growth in earnings for firm j for year t þ 1to t þ 2 (that is, epsjtþ2 þ rjdpsjtþ1 � (1 þ rj)epsjtþ1), dpsjtþ1 is expected dividends pershare for firm j for year t þ 1, and �agrj is the rate of change in abnormal growth inearnings beyond the two year forecast horizon required to equate the differencebetween price and capitalized earnings pjt � epsjtþ1

rjand the present value of an infinite

stream of abnormal growth in earnings.23

Easton (2004) transforms this model to form the following regression:

cepsjtþ2

pjt¼ �0 þ �1

epsjtþ1

pjtþ ujt ð6Þ

where cepsjtþ2 is cum-dividend earnings per share for firm j for year t (that is,epsjtþ2 þ rjdpsjtþ1), �0 ¼ r(r � �agr), �1 ¼ (1 þ �agr), r is the estimate of theexpected rate of return for the sample of stocks in the regression, and �agr is theestimate of the expected rate of change in abnormal growth in earnings for thesample.

This regression is designed for a particular context and works well in that contextbecause the samples are selected such that the regression r-square is very close toone. When this is so, the fact that both the dependent variable and the independentvariable are measured with error does not pose problems. If the r-square differsfrom one, this regression (and the corresponding reverse regression) can only beused to establish the bounds on the estimate of the expected rate of return.24

For the DJIA firms as at December 31, 2004, the estimates of the coefficients(t-statistics) for �0 and �1 in regression (6) are 0.0008 (0.32) and 1.0905 (28.02) and,hence the estimate of the expected rate of return is 9.9%. The coefficients from thereverse regression:

epsjtþ1

pjt¼ �R

0þ �R

1

cepsjtþ2

pjtþ uR

jtð7Þ

are 0.0014 (0.63) and 0.8854 (28.02). Since �R0¼ rðr��agrÞ=ð1þ�agrÞ and

�R1¼ 1=ð1þ�agrÞ, the implied expected rate of return is 13.9%. That is, the

Easton (2004) regressions establish that the estimate of the expected rate of returnimplied by the prices and forecasts of earnings for these DJIA stocks lies between9.9% and 13.9%.

23 Easton (2004) derives a special case of the abnormal growth in earnings model which is used in severalrecent studies to estimate an implied expected rate of return (see, for example, Francis, Khurana andPeriera, 2005; and Hail and Leuz, 2005). This special case is based on the assumption that �agr is equal tozero. Under this assumption, r ¼

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffieps2 � eps2/pjt

p. Easton (2004) shows that estimates of the implied

expected rate of return based on this method are generally biased downward – in other words, the �agrimplied by the data is greater than zero.24 Easton (2004) uses regression (6) to determine the implied expected rate of return for stocks groupedon PEG-ratios. When stocks are grouped in this way, the r-square for this regression is very high because:ceps2/P0 ¼ 1/PEG-ratio þ rdps1/P0 þ eps1/P0 and, since portfolios are formed on the basis of PEG ratios,the variance of 1/PEG-ratio (within the portfolio) will be very small relative to the variance of eps1/P0. Also,the variance of rdps1/P0 will be small relative to the variance of eps1/P0. It follows that ceps2/P0 and eps1/P0

will be highly correlated. Daske (2005) also forms portfolios based on the PEG ratio but the r-squares inhis regressions are much lower than one (0.904 and 0.839) because his sample size is smaller and hencethe PEG ratios differ considerably within his sub-samples.



(v) Use of the ETSS and/or Easton (2004) Regression Methods

When faced with the choice of the Easton, Taylor, Shroff and Sougiannis (2002) orthe Easton (2004) regression method, the chosen option will almost always beEaston, Taylor, Shroff and Sougiannis (2002) because, as Easton (2004) pointsout, the estimates of the expected rate of return (and expected growth) will bebiased due to measurement error unless the set of observations is such the regres-sion r-square is very high. This is due to the fact that both the dependent variable(forecasted cum-dividend two-period-ahead earnings) and the independent vari-able (forecasted one-period-ahead earnings) in Easton (2004) are measured witherror. Hence, reverse regression cannot be used to overcome the measurementerror problem. Reverse regression can only be used to determine the bounds of theestimates of the expected rate of return. These bounds are large if the r-square issmall.25 Easton, Taylor, Shroff and Sougiannis (2002) does not suffer from thisproblem because the dependent variable (forecasted return-on-equity) is measuredwith error while the independent variable (price-to-book) is not.26

(vi) Gode and Mohanram (2003)

Like Easton (2004), Gode and Mohanram (2003) also invert the abnormal growth inearnings valuation model to obtain estimates of the implied expected rate of return.Unlike Easton (2004), they assume a rate of change in abnormal growth in earnings(the risk free rate minus 3%) beyond the forecast horizon rather than estimating thisgrowth rate from the data. The key variables, price per share, forecasted 2005earnings per share, and abnormal growth in earnings per share from 2005 to2006 for the calculation of the Gode and Mohanram (2003) estimates of theexpected rate of return are included in Table 3 together with firm-specific estimatesof the expected rate of return based on their method.27 Also included in this tableare the Gebhardt, Lee and Swaminathan (2001) estimates. The Pearson (Spearman)correlation between these estimates is only 0.32 (0.49). The difference betweenthese estimates is large for some companies. These differences highlight the import-ant role of assumptions about growth in these models.

The largest difference between the estimates of the expected rate of return is forAltria Group where the Gebhardt, Lee and Swaminathan (2001) estimate is 20.5%and the Gode and Mohanram (2003) estimate is 8.2%. In the case of Altria Group,the method in Gebhardt, Lee and Swaminathan (2001) assumes that the expectedreturn-on-equity will increase from the (relatively high) forecasted return-on-equityof 0.23 in 2008 to the (very high) industry median of 0.38 nine years later and this

25 Even with r-squares as high as 0.903 as in Daske (2006), the range of estimates of the implied expectedrate of return based on the ‘forward’ and the ‘reverse’ form of the Easton (2004) regression is large. Itfollows that conclusions from Daske’s (2006) study should rely on the estimates from the Easton, Taylor,Shroff and Sougiannis (2004) method rather than the estimates based on Easton (2004).26 Easton, Taylor, Shroff and Sougiannis (2002) note that they set up their regression with return-on-equity as the dependent variable in order to avoid measurement error issues.27 Meaningful estimates of the expected rate of return cannot be obtained for Merck and Co. or forExxon Mobil Corp. because, for these stocks, the I/B/E/S forecasts of 2006 earnings are less than theforecasts of 2005 earnings. All of the subsequent discussion of the Gode and Mohanram (2003) method isbased on the remaining 28 observations.

388 EASTON


return-on-equity is the base for the perpetuity thereafter. The effect is a relativelyhigh expected rate of return (20.5%). On the other hand, the method in Gode andMohanram (2003) grows abnormal growth in earnings from a very low (in fact,negative) base of �0.01; in other words, expected earnings beyond the forecasthorizon serve to decrease the estimate of the expected rate of return (hence it islow, 8.2%).

In order to illustrate the effects of the assumption in Gode and Mohanram (2003)regarding the change in abnormal growth in earnings beyond 2006, I split thesample into two sub-samples – one where the expected abnormal growth in earn-ings is relatively high (abnormal growth in earnings deflated by price is above the

Table 3

Key Variables and Estimates of the Implied Expected Rate of Return Using theMethod in Gode and Mohanram

Company Name price04 eps05 agr05/06 rGM% rGLS%

Alcoa Inc. 31.42 2.42 0.07 10.1 9.9American International Group 65.67 5.21 0.15 10.4 10.2American Express 56.37 3.10 0.12 8.4 9.5Boeing Co. 51.77 2.57 0.21 9.7 8.6Citigroup Inc. 48.18 4.35 �0.02 8.5 12.1Caterpillar Inc. 97.51 7.10 0.40 11.3 9.6Du Pont (E I) De Nemours 49.05 2.74 0.15 9.3 8.6Disney (Walt) Co. 22.55 1.18 0.06 8.9 9.8General Electric Co. 36.50 1.80 0.08 8.0 6.3General Motors Corp. 40.06 4.92 0.06 13.5 15.0Home Depot Inc. 35.47 2.04 0.10 9.3 8.2Honeywell International Inc. 35.41 1.99 0.16 10.5 9.5Hewlett-Packard Co. 18.66 1.48 0.02 9.4 11.3Intl Business Machines Corp. 98.58 5.54 0.08 7.0 8.4Intel Corp. 23.39 1.18 0.03 7.4 8.2Johnson & Johnson 63.42 3.34 0.07 7.2 9.5JP Morgan Chase & Co. 39.01 3.27 0.03 9.3 12.8Coca-Cola Co. 41.64 2.03 0.05 6.9 7.3McDonald’s Corp. 32.06 2.00 0.03 7.8 7.83M Co. 82.07 4.17 0.12 7.4 7.5Altria Group Inc. 61.10 5.15 �0.01 8.2 20.5Merck & Co. 32.14 2.46 �0.29 n/a 10.8Microsoft Corp. 28.56 1.34 0.03 6.7 7.9Pfizer Inc. 26.89 2.31 �0.02 7.4 12.1Procter & Gamble Co. 54.44 2.56 0.08 7.3 7.7SBC Communications Inc. 25.77 1.37 0.09 9.5 9.3United Technologies Corp. 103.35 6.17 0.13 7.9 9.1Verizon Communications Inc. 40.51 2.66 �0.03 3.7 9.1Wal-Mart Stores 53.85 2.32 0.16 8.4 6.9Exxon Mobil Corp. 51.26 3.40 �0.57 n/a 8.6

Notes:price04 is price per share of the stock at the end of fiscal year 2004, eps05 is the I/B/E/S forecast of earningsper share for fiscal year 2005, agr05/06 is the abnormal growth in earnings implied by I/B/E/S forecasts ofearnings per share for fiscal years 2005 and 2006, rGM is estimate of the implied expected rate of returnobtained using the method in Gode and Mohanram (2003), and rGLS is estimate of the implied expectedrate of return obtained using the method in Gebhardt, Lee and Swaminathan (2001).



median), the other with relatively low expected abnormal growth in earnings(abnormal growth in earnings deflated by price is below the median).28 The formergroup has a relatively high base from which earnings grow while the latter has arelatively low base. It follows that, ceteris paribus, one would expect a higher (lower)rate of change in abnormal growth in earnings beyond 2006 for the group with alower (higher) base. Indeed, this is the case. The expected rate of change inabnormal growth in earnings for the sub-sample with the lower base is 8.0% whilethe expected rate of change in abnormal growth in earnings for the sub-sample withthe higher base is 5.0%.29 It is also pertinent to note that the rates of change inabnormal growth in earnings implied by the data for both of the sub-samples arehigher than the rate prescribed by the Gode and Mohanram (2003) growth rateassumption (1.24%) so that the mean estimate of the expected rate of return for theDJIA stocks calculated via the Gode and Mohanram (2003) method (8.0%) is lowerthan the rate of return implied by the data (10.6%).30

I calculate the expected rate of return implied by the data (via the method inEaston, Taylor, Shroff and Sougiannis, 2002) for each of these groups of stocks. Theimplied expected rate of return for the sub-sample with lower abnormal growth inearnings is 11.5% and the implied expected rate of return for the sub-sample withhigher abnormal growth in earnings is 9.3%. Both of these expected rates of returnare higher than the average of the firm-specific estimates obtained via the Gode andMohanram (2003) method (7.9% for the sub-sample with lower abnormal growth inearnings and 9.2% for the group with higher abnormal growth in earnings), pre-sumably due to the fact that Gode and Mohanram (2003) assume a very low growthrate. Nevertheless, the very low average estimate of the expected rate of return forthe low abnormal growth in earnings group (7.9%) compared with the rate impliedby the data (11.5%) underscores the point that assuming the same rate of growth forall stocks may lead to spurious inferences. Notice that, analogously, if differences inaccounting regime cause differences in abnormal growth in earnings (as illustratedin the Microsoft example in Section 3 these differences will induce spurious differ-ences in the estimate of the cost of capital.

(vii) O’Hanlon and Steele (2000)

The methods that use market prices, book values, and analysts’ forecasts to obtainestimates of the expected rate of return implicitly include analysts’ expectations of

28 Since Gode and Mohanram (2003) assume the same rate of growth for all stocks, it seems reasonableto expect that the estimate of the expected rate of return for the stocks with a low abnormal growth inearnings will be too low while the estimate of the expected rate of return for the stocks with a highabnormal growth in earnings will be too high. A similar point may be made with respect to studies thatuse Claus and Thomas (2001) to obtain firm-specific estimates of the implied expected rate of return – itseems reasonable to expect that the estimate of the expected rate of return for the stocks with a lowresidual income will be too small while the estimate of the expected rate of return for the stocks with ahigh residual income will be too high.29 These rates of growth are calculated via the method in Easton, Taylor, Shroff and Sougiannis (2002).This method explicitly yields a rate of growth in residual income. Since we are implicitly assuming thatthis growth rate is the steady-state growth rate beyond the forecast horizon, this rate of growth in residualincome will be implicitly equal to the rate of change in abnormal growth in earnings.30 Gode and Mohanram (2001) assume growth at the risk free rate minus 3%. The risk free rate as atDecember 31, 2004 was 4.24% (this is the 10-Year Treasury Constant Maturity Rate provided by theFederal Reserve Bank of St. Louis).

390 EASTON


both normal returns (the cost of capital) and abnormal returns in these estimates.31

On the other hand, the O’Hanlon and Steele (2000) method compares marketprices with accounting fundamentals (earnings and book values) avoiding the effectsof analysts optimism/pessimism relative to the market. In this section, I compare theestimate of the expected rate of return implied by prices, book values, and forecastsof earnings (based on the method in Easton, Taylor, Shroff and Sougiannis, 2002)with the expected rate of return implied by prices, book values, and realized earn-ings (based on the method in O’Hanlon and Steele, 2000).

The method in O’Hanlon and Steele (2000) is based on the following form of theresidual income valuation model:

pjt ¼ bpsjt þ½ðROEjt � rjÞ�bpsjt�1�ð1þ gj ¢Þ

rj � gj ¢� � : ð8Þ

The major difference between this form of the model and the form used byEaston, Taylor, Shroff and Sougiannis (2002) is that gj¢ is the perpetual growthrate from a base of current residual income that implies a residual income stream suchthat the present value of that stream is equal to the difference between price andbook value (whereas in Easton, Taylor, Shroff and Sougiannis (2002), gj is theperpetual growth rate from a base of next-period residual income that implies a residualincome stream such that the present value of that stream is equal to the differencebetween price and book value).

O’Hanlon and Steele (2000) transform this model to form the following regres-sion relation:32

epsjt

bpsjt�1¼ �0 þ �1

pjt � bpsjt

bpsjt�1þ �jt ð9Þ

where �0 ¼ r, �1 ¼ (r � g¢)/(1 þ g¢). This regression may be estimated for anygroup/portfolio of stocks to obtain estimates of the expected rate of return, r, andthe expected growth rate, g¢, for the portfolio.

As O’Hanlon and Steele (2000) observe, there are a number of choices of the‘actual’ earnings per share variable that may be used in this regression.33 Ideally we

31 It seems reasonable to assume that an analyst issuing a ‘buy’ recommendation is making thisrecommendation based on the expectation that there will be a positive abnormal return (that is, a returngreater than the cost of capital). Easton and Sommers (2005) provide evidence consistent with thisconjecture.32 I attribute this model to O’Hanlon and Steele (2000) because they capture its essential elements. Thesimilarity to their model may not, however, be immediately apparent. Since the derivation in O’Hanlonand Steele (2000) is based on Ohlson (1989), the observation that the regression intercept is an estimateof the implied expected rate of return is not evident and O’Hanlon and Steele (2000) do not use it in thisway. Rather, they estimate the implied expected rate of return at the firm-specific level by applying theirmodel to time-series data and then measuring the risk premium as the slope of the Securities Market Lineestimated from a regression of these firm-specific rates of return on corresponding beta estimates.33 The book value variable must be calculated such as to correspond with the earnings per share variablein order to maintain an ‘apples-to-apples’ comparison. For example, if the earnings per share variableexcludes ‘one-time’ items, these items should also be excluded from the end-of-year book value per sharevariable.



might seek an earnings number that most closely represents core (or sustainable)earnings. An obvious candidate is ‘actual’ earnings provided by analysts since theytend to forecast earnings before one-time items and hence they remove these itemsfrom the number they call ‘actual’ earnings.34 The estimates of �0 and �1 are 0.123(t-statistic of 6.41) and 0.037 (t-statistic of 6.48) with associated implied estimates ofthe annual growth rate of 8.3% and expected annual rate of return of 12.3%.35 Thatis, market prices and accounting book value at December 31, 2004, and earnings forthe year ended December 31, 2004, imply an expected rate of return on the DJIA of12.3%. This estimate is 1.7% greater than the Easton, Taylor, Shroff and Sougiannis(2002) estimate based on market prices, book value, and forecasts of earnings; thissuggests that analysts were pessimistic compared with markets’ expectations for theDJIA as at December 31, 2004.36

5. SUMMARY AND SUGGESTIONS FOR FUTURE RESEARCH

It is evident from the analyses of estimates of the expected rate of return for theDecember 31, 2004 DJIA firms that the assumptions about growth beyond the(short) forecast horizon may seriously affect the estimates of the expected rate ofreturn and may lead to spurious inferences. Thus, where possible, methods thatsimultaneously estimate growth and the expected rate of return should be used.

Although not immediately obvious from Easton, Taylor, Shroff and Sougiannis(2002), their method may be adapted to compare differences in the estimate of theexpected rate of return across regimes. The essence of the analyses would be basedon the following regression:

epsjtþ1

bpsjt¼ �0 þ �1

pjt

bpsjtþ �2Dþ �3D

pjt

bpsjtþ �jt ð10Þ

where D is a dummy variable to capture regime differences. Since �2 capturesgrowth differences across regimes, and �3 captures differences in the impliedexpected rate of return minus differences in growth, the test of significance of�2 þ �3 examines the significance of the differences in the expected rate of returnacross regimes.

34 Bhattacharya, Black, Christensen and Larson (2003) show that, for a sample of 1,149 observations,the mean pro-forma earnings in corporate press releases is 3.8 cents higher than I/B/E/S earnings,supporting the notions that (1) analysts are, indeed, forecasting (and recording) core earnings, and (2)these ‘actual’ earnings are not biased (upward) to provide the impression that the firm is performingbetter.35 The adjusted r-square from this regression is 0.59.36 The observation that the O’Hanlon and Steele (2000) estimate, which is based on current accountingdata is higher than the estimate based on forecasts (the Easton, Taylor, Shroff and Sougiannis, 2002,estimate) is at odds with the more pervasive evidence that analysts’ forecasts tend to be optimistic (see, forexample, O’Brien, 1993; Lin, 1994; and Richardson, Teoh and Wysocki, 2001). Two points should benoted, however. First, the evidence in the extant literature compares forecasts with subsequent actualrealizations whereas I am comparing expectations based on forecasts with estimates based on currentrealizations. Second, although the O’Hanlon and Steele (2000) estimate is higher than the Easton, Taylor,Shroff and Sougiannis (2002) estimate for this set of data, Easton and Sommers (2005) show that theEaston, Taylor, Shroff and Sougiannis (2002) estimate is, on average, almost three percent higher thanthe estimate based on O’Hanlon and Steele (2000) for a large sample of I/B/E/S stocks over the period1993 to 2003.

392 EASTON


An adaptation of the O’Hanlon and Steele (2000) method which could be used tocompare estimates of the implied expected rate of return across regimes would beas follows:

epsjt

bpsjt�1¼ �0 þ �1

pjt � bpsjt

bpsjt�1þ �2Dþ �3D

pjt � bpsjt

bpsjt�1þ �jt ð11Þ

where, as in the suggested adaptation of Easton, Taylor, Shroff and Sougiannis(2002), D is a dummy variable to capture regime differences.

The disadvantage of these adaptations is that it is not obvious how one controlsfor other factors that may lead to differences in the implied rate of return (though amatched-sample design may be a reasonable approach or, alternatively the firmmay be used as its own control – as in Daske, 2006). Another shortcoming of theEaston, Taylor, Shroff and Sougiannis (2002) method (and all methods that rely onanalysts’ forecasts) is that the estimates of the implied expected rate of return maynot be an indication of the cost of capital.37 The method in O’Hanlon and Steele(2000) does not suffer from this bias.

In my view, the emphasis of future work should be on understanding the proper-ties of the estimates of expected rate of return and on improving on them. Muchwork must be done before we can confidently claim that our methods may be usedto estimate and understand differences in cost of capital across accountingregimes.38

REFERENCES

Baginski, S. and J. Wahlen (2003), ‘Residual Income, Risk, Intrinsic Values, and SharePrices’, The Accounting Review, Vol. 78, pp. 327–51.

Bhattacharya, N., E. Black, T. Christensen and C. Larson (2003), ‘Assessing the RelativeInformativeness and Permanence of Pro Forma Earnings and GAAP OperatingEarnings’, Journal of Accounting and Economics, Vol. 36, pp. 285–319.

Botosan, C. (1997), ‘Disclosure Level and the Cost of Equity Capital’, The Accounting Review,Vol. 72, pp. 323–49.

——— and M. Plumlee (2005), ‘Assessing Alternative Proxies for the Expected RiskPremium’, The Accounting Review, Vol. 80 (January), pp. 21–53.

———, ——— and Y. Xie (2004), ‘The Role of Information Precision in Determining theCost of Equity Capital’, Review of Accounting Studies, Vol. 9 (Jun–Sep), pp. 233–59.

Claus, J. and J. Thomas (2001), ‘Equity Risk Premium as Low as Three Percent? Evidencefrom Analysts’ Earnings Forecasts for Domestic and International Stocks’, Journal ofFinance, Vol. 56, pp. 1629–66.

Daske, H. (2006), ‘Economic Benefits of Adopting IFRS or US-GAAP – Have the ExpectedCosts of Equity Capital Really Decreased?’ Journal of Business, Finance, & Accounting,Vol. 33, Nos. 3/4.

Dhaliwal, D., L. Krull, O. Li and W. Moser (2005), ‘Dividend Taxes and Implied Cost ofCapital’, Journal of Accounting Research, Vol. 43, pp. 675–708.

Easton, P. (2001), ‘Discussion of: When Capital Follows Profitability: Non-linear ResidualIncome Dynamics’, Review of Accounting Studies, Vol. 6, pp. 267–74.

37 This point is at the heart of the analyses in Easton and Sommers (2005).38 All methods that rely on market prices must admit the caveat that the resulting estimates of the cost ofcapital will be biased estimates if the prices are inefficient.



Easton, P. (2004), ‘PE Ratios, PEG Ratios, and Estimating the Implied Expected Rate ofReturn on Equity Capital’, The Accounting Review, Vol. 79, pp. 73–96.

——— and S. Monahan (2005), ‘An Evaluation of Accounting-based Measures of ExpectedReturns’, The Accounting Review, Vol. 80, pp. 501–38.

——— and G. Sommers (2005), ‘Bias in Expected Rates of Return Implied by Analysts’Forecasts’, Working Paper (University of Notre Dame).

———, G. Taylor, P. Shroff and T. Sougiannis (2002), ‘Using Forecasts of Earnings toSimultaneously Estimate Growth and the Rate of Return on Equity Investment’,Journal of Accounting Research, Vol. 40, pp. 657–76.

Fama, E. and K. French (1997), ‘Industry Costs of Equity’, Journal of Financial Economics,Vol. 43, pp. 153–93.

Francis, J., I. Khurana and R. Periera (2005), ‘Disclosure Incentives and Effects on Cost ofCapital Around the World’, The Accounting Review (forthcoming).

———, R. LaFond, P. Olsson and K. Schipper (2004), ‘Costs of Capital andEarnings Attributes’, The Accounting Review, Vol. 79, pp. 967–1011.

Gebhardt, W., C. Lee and B. Swaminathan (2001), ‘Towards an Ex-ante Cost of Capital’,Journal of Accounting Research, Vol. 39, pp. 135–76.

Gode, D. and P. Mohanram (2003), ‘Inferring the Cost of Capital Using the Ohlson-JuettnerModel’, Review of Accounting Studies, Vol. 8, pp. 399–431.

Guay, W., S. Kothari and S. Shu (2005), ‘Properties of Implied Cost of Capital Using Analysts’Forecasts’, Working Paper (University of Pennsylvania, Wharton School).

Hail, L. and C. Leuz (2005), ‘International Differences in the Cost of Equity Capital: Do LegalInstitutions and Securities Regulation Matter?’, Working Paper (University ofPennsylvania, Wharton School).

Hribar, P. and N. Jenkins (2004), ‘The Effect of Accounting Restatements on EarningsRevisions and the Estimated Cost of Capital’, Review of Accounting Studies, Vol. 9,pp. 337–56.

Lee, C., J. Myers and B. Swaminathan (1999), ‘What is the Intrinsic Value of the Dow?’,Journal of Finance, Vol. 54, pp. 1693–741.

Lin, H. (1994), ‘Security Analysts’ Investment Recommendations’, Ph.D. Dissertation(Stanford University).

O’Brien, P. (1993), ‘Earnings Forecasts and the Macroeconomy’, Working Paper (Universityof Michigan).

O’Hanlon, J. and A. Steele (2000), ‘Estimating the Equity Risk Premium Using AccountingFundamentals’, Journal of Business Finance & Accounting, Vol. 27, pp. 1051–84.

Ohlson, J. (1989), ‘Accounting Earnings, Book Value and Dividends: The Theory of theClean Surplus Equation (Part I), Reproduced in R. Brief and K. Peasnell (eds.), CleanSurplus: A Link Between Accounting and Finance (Garland), pp. 167–227.

Richardson, S., S. Teoh and P. Wysocki (2001), ‘Tracking Analysts’ Forecasts Over theAnnual Earnings Horizon: Are Analysts’ Forecasts Optimistic or Pessimistic? WorkingPaper (University of Michigan).

Williams, M. (2004), ‘Discussion of: The Role of Information Precision in Determining theCost of Equity Capital’, Review of Accounting Studies, Vol. 9 (Jun-Sep), pp. 261–64.

394 EASTON


use of forecasts of earnings to estimate and compare cost of capital across regimes

Documents