Q Jin Zhang 2011a

THEACCOUNTINGREVIEW

Vol.86,No.2

2011

pp.605–635AmericanAccountingAssociationDOI:10.2308/accr.00000028

InvestmentGrowthandtheRelationbetween

EquityValue,Earnings,andEquityBook

Value

ShengquanHao

ShanghaiJiaotongUniversity

QingluJin

ShanghaiUniversityofFinanceandEconomics

GuochangZhang

HongKongUniversityofScienceandTechnology

Abstract:UsingZhang 2000 asthetheoreticalbasis,wepredictandempiricallytest

theeffectofinvestmentgrowthontherelationbetweenequityvalueandaccounting

variables.We ndthat 1 growthincreasestheslopeinthevalue-earningsrelationfor

high-pro tability rms consistentwithgrowthhavingpositiveNPV ,buthasaninsig-

ni cantornegativeeffectontheslopeforlower-pro tability rms consistentwith

growthhavingnon-positiveNPV ; 2 givenearnings,growthincreasesthe positive

slopeoftherelationbetweenequityvalueandequitybookvalueforlow-pro tability

rms,butreducesthisslopeandcausesequityvaluetodecreasewithbookvaluefor

high-pro tability rms;and 3 givenpro tability ROE ,equityvalueuniformlyin-

creaseswithbookvalue,andgrowthincreasestheslopeofthisrelation.Wealso

examinethevaluationimpactofpastinvestmentactivitiesthatarisesfromaccounting

conservatism.We ndthattheearningscoef cientisgreaterintheyearsfollowing

fasterinvestmentincreases whichcauseearningstobemoreconservativelystated .

Keywords:investmentgrowth;equityvaluation;earnings;equitybookvalue;

pro tability;conservatism.

DataAvailability:Thedatausedinthisstudyareavailablefrompublicsources.

WethankPeterChenforhisinvolvementandinputduringearlystagesofthisproject.Wealsothankthreeanonymous

referees,GaryBiddle,BobBowen,KevinChen,ZhihongChen,JerryFeltham,InchiHu,KunJiang,CharlesLee,Clive

Lennox,StevePenman,TerryShevlin,PaulZarowin editor ,TianyuZhang,andworkshopparticipantsatHarvardBusi-

nessSchool,HongKongUniversityofScienceandTechnology,KoreaUniversity,NationalTaiwanUniversity,Singapore

ManagementUniversity,UniversityofBritishColumbia,UniversityofToronto,andUniversityofWashingtonfortheir

comments.ProfessorJinacknowledgesthe nancialsupportoftheMOEthroughtheInstituteofFinanceandAccounting

atSUFEandoftheNationalNaturalScienceFoundationofChina projectnumbers71032005and71072036 .Allerrors

areourown.

Editor’snote:AcceptedbyPaulZarowin.

Submitted:December2008

Accepted:July2010

PublishedOnline:March2011

605

606Hao,Jin,andZhang

I.INTRODUCTION

rowthopportunitiesconstituteanimportantpartof rmvalue MillerandModigliani

1961;DixitandPindyck1994 .Wheninvestorsdetermine rmvaluebasedonreported

accountingdata,itisessentialthattheyconsiderhowmuchthe rmisexpectedtogrow.

ButasHolthausenandWatts 2001 observe,empiricalresearchonaccounting-basedvaluation

haslargelyneglectedthegrowthfactor.Inthisstudy,wereexaminetheaccounting-valuelinkby

http://wendang.chazidian.comingthereal-options-basedmodelof

Zhang 2000 asthetheoreticalbasis,wepredictandempiricallytesthowtherelationbetween

equityvalueandaccountingdatabehavesinadistinctlynonlinearfashionand,inparticular,how

investmentgrowthmediatesthisnonlinearrelation.

Inthisstudy,growthreferstoincreases ordecreases intheamountofcapitalinvestedin

businessoperations.1Economicreasoningsuggeststhatwhetherinvestmentgrowthenhances

valuegenerationdependsonpro tability,2de nedasearningsinaperioddividedbytheequity

bookvalueatthebeginningoftheperiod ROE .Pro tabilityrepresentsa rm’sabilitytogen-

eratevaluefrominvestedcapital,thusindicatingthedesirabilityofincreasingorreducingthe

scaleofoperations.Mirroringitsinvestment-guidingrole,pro tabilitythushelpsinvestorstoinfer

the rm’scourseofoperationsgoingforward.Becauseofitsfundamentalroleindetermining

investmentdecisionsunderlyingvaluegeneration,pro tability asopposedtoearnings servesas

anappropriatevaluationmetric.3Obviously,investmentgrowthundertakenbyapro table rm

enhancesinvestorvalue,whereasthatbyanunpro table rmcreatesnovalueorevendestroys

value.Ouranalysisdemonstrateshowthisbasicnotionaboutgrowth,pro tability,andvalue

creationmanifestsinmappingaccountingdatatovalue.

Wedevelopfourhypothesesconcerningvariousaspectsofthegrowtheffectonthevaluation

function.We rsttestthesehypothesesseparatelywithpartialmodelspeci cations whichcol-

lapsesoneofthedimensionsofthevaluationspace ,andthenjointlywith“full”modelspeci -

cations.Inanextendedanalysis,wefurtherfollowZhang 2000 ,whopredictsalinkbetweenthe

trendofpastinvestmentchangesandearningsbiases,tointroducetheeffectofconservative

accounting.There,weadoptamorecomprehensiveempiricalmodelwithinwhichwetestthe

effectsofbothconservatismandinvestmentgrowth.

Existingresearchshowsthat,givenequitybookvalue,equityvalueincreaseswithearnings,

andgrowthincreasestheslopeofthevalue-earningsrelation CollinsandKothari1989;Kothari

2001 .Wepredictthat,whereasgrowthstrengthensthevalue-earningsrelationintermsofa

steeperslopeforhigh-pro tability rms whoseinvestmentgrowthwillgenerallyhavepositive

NPV ,theeffectisexpectedtobesmallerandcanevendisappearforlow-pro tability rms

whosegrowthwillgenerallyhavelowornon-positiveNPV .4Ourempiricalresultsareconsis-

tent.We rstshowthatinregressionsofstockpriceonearningscontrollingforbookvalue,the

slopeispositiveandbecomesincreasinglysteeper,con rmingconvexityaspredictedbyrealG

1

2

3

4Thegrowthconstructinthisstudyisinput investment based.Thisisconceptuallydistinctfrom,thoughrelatedto, output-based earningsgrowth.Whetherinvestmentgrowthtranslatesintoearningsgrowthdependsona rm’sprof-itability.OhlsonandJuettner-Nauroth 2005 provideamodelthatrelatesequityvaluetoexpectedearningsandearningsgrowth.FamaandMiller 1972 provideanillustrationofthisbasicnotion.Bar-Yosefetal. 1987 empiricallyinvestigatetherelationbetweeninvestmentandearnings.Notethatearningscannotbecompareddirectlyacross rmswithdifferentscalesofoperations.Theimportanceofpro tabilityforvaluationmeansthatincomestatementdatashouldbeinterpretedinconjunctionwiththebalancesheet,consistentwiththeopinionoftheFinancialAccountingStandardsBoard seeSFACNo.5,paragraph24a .Therationaleisthata rm’sstrength/weaknessinbusinessfundamentalsshouldpersist tosomeextent fromoneperiod

tothenext,sothat rmswithhigherpro tabilitycurrentlyareexpectedtohavehigherpro tabilityinthefollowing

periods.EmpiricalevidencefromDechowetal. 1999 andBiddleetal. 2001 isconsistentwiththepremiseofour

argument.

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InvestmentGrowthandtheRelationbetweenEquityValue,Earnings,andEquityBookValue607

options BurgstahlerandDichev1997;Zhang2000 .Moreimportantly,whilegrowthincreases

theslopeofthevalue-earningsrelationinhigh-pro tabilityregions,ithaseitheraninsigni cantor

anegativeeffectontheslopeinlow-pro tabilityregions.

Accordingtopriorstudies BurgstahlerandDichev1997;Collinsetal.1999 ,equityvalueis

positivelyrelatedtoequitybookvaluegivenearnings,butlittleisknownabouthowgrowth

intervenesinthisrelation.Weexplainthat,whileapositiverelationshouldgenerallyholdabsent

growth,investmentgrowthwillreducetheslopeofthisrelationinhigh-pro tabilityregions

wheregrowthoptionsareimportant ;infact,thenegativeeffectofgrowthcanbesodominant

thatitcausesequityvaluetodecreasewithequitybookvalue.Thisnegativerelationinhigh-

pro tabilityregionscausedbygrowthoptionsiscontrarytoapredictedpositiverelationinlow-

pro tabilityregionscausedbyadaptationoptions BurgstahlerandDichev1997 .Together,the

twoforcesproduceanequityvaluefunctionthatchangesnonmonotonicallywithbookvalueover

awidepro tabilityrange.

Ourresultssupportthesepredictions.Controllingforearnings,we ndanegativecoef cient

onequitybookvalueintheregionsoflowbookvalue correspondingtohighpro tability ;

however,theslopeturnspositiveintheregionsofhighbookvalue lowpro tability .After

explicitlyrecognizingthegrowtheffectinregressions,we ndthatgrowthreducestheslope

coef cient i.e.,makesitmorenegative onbookvalueinhigh-pro tabilityregions,butincreases

theslope i.e.,makesitmorepositive inlow-pro tabilityregions.

However,theabove-describedbehaviordoesnotportrayafullviewoftherelationbetween

equityvalueandequitybookvalueincrosssections.Ifweholdpro tability insteadofearnings

constant,thentherelationchangessharply.Inthiscase,equityvalueincreasesuniformlywith

bookvalue,andgrowthincreasestheslopeofthisrelation.Theintuitionisthatamong rms

equallyef cientingeneratingvaluefrominvestedcapital,thosewithmorecapitalinvestedwill

havehighervalues;thisistrueespeciallyfor rmsexpectedtoundertakehighgrowth.

Whereastheaboveeffectsofinvestmentgrowthareinducedbyeconomicforcesforvalue

creation,Zhang 2000 explainsthatinvestmentactivitiescanalsoin uencethevalue-accounting

relationforaccountingreasons.Underconservativeaccountingpractices,thespeedofincreased

investmentinrecentyearswilldeterminethedegreeofconservatisminearnings.Consistentwith

thisprediction,we ndthattheearningscoef cientisgreaterinthehigh-versuslow-earnings

conservatismgroup fasterinvestmentincreasesintherecentpast .Atthesametime,we ndthat

thepredictedgrowtheffectholdsinbothhigh-andlow-earnings-conservatismgroups,con rming

thattheeconomic-driveneffectofinvestmentgrowthisdistinctfromtheconservatism-driven

effectofpastinvestments.

Ourstudyextendstheempiricalvaluationliteraturebyshowinghowthenonlinearrelation

betweenequityvalue,earnings,andequitybookvalueisdependentoninvestmentgrowth.Pre-

viousresearchhasreliedheavilyonlinearvaluationrelations,5motivatedbyeitherheuristic

argumentsorthemodelsofOhlson 1995 andFelthamandOhlson 1995 ,assuminglinear

informationdynamics.However,empiricalevidencegenerallydoesnotsupporttheselinearmod-

els Dechowetal.1999;CallenandSegal2005 .Somecriticizethesemodelsasnondescriptive

becausetheydonotcapturepositiveeconomicrentsorgrowthoptions LoandLys2000;Biddle

etal.2001;HolthausenandWatts2001 .BurgstahlerandDichev 1997 explicitlyexaminenon-

linearityinvaluation,buttheyfocusontheroleofadaptationoptions relevanttounpro table

rms ,notthatofgrowthoptions relevantmainlytopro table rms .

5ExamplesincludeLandsman 1986 ,Barth 1991 ,andShevlin 1991 ,whousebalancesheetdata,Barthetal. 1992 ,

whouseincomestatementdata,andCollinsetal. 1999 ,LevandZarowin 1999 ,andCoreetal. 2003 ,whousea

linearcombinationofearningsandequitybookvalue.SeeHolthausenandWatts 2001 forasurvey.

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608Hao,Jin,andZhang

OurstudyanswersthecallbyHolthausenandWatts 2001 formorevaluationresearchthat

incorporatesrentsandgrowthoptions.Althoughseveralstudieshavedemonstratedtheimportant

roleofgrowthoptions,theirfocusesdifferfromours.Zhang 2000 buildsgrowthoptionsintoa

theoreticalmodel,butdoesnotconductacorrespondingempiricalexamination.Biddleetal.

2001 explorethenonlineardynamicbehaviorofresidualincomeunderthenotionof“capitalfollowingpro tability” thekeyassumptiongivingrisetorealoptions ,butdonotexaminethe

behaviorofequityvalue.Finally,ChenandZhang 2007 testareturnmodelderivedfromthe

valuemodelofZhang 2000 .Butdeterminingequityreturnoveratimeperiodisadistinctly

differentproblemfromdeterminingequityvalueatagivenpointintime.Returnsderivefrom

changesinvalue butonecannotdeterminea rm’svaluefromobservedreturns ,sothevaluation

questionexaminedinourstudyismorebasicthanthatinChenandZhang 2007 .Importantly,

unlikeChenandZhang 2007 ,whousethegrowthvariableasaseparateexplanatoryfactor—

alongwiththeiraccountingvariables—inthereturnmodel,ourstudyexploreshowthevaluation

impact theslopecoef cients ofaccountingvariablesisdependentongrowth,thusemphasizing

theinteractiveeffectsofgrowthandaccountingvariablesinvaluation.

Inadditiontoexaminingtheroleofprospectiveinvestment growthoptions ,thisstudy

contributestotheliteraturebyshowinghowpastinvestmentactivitiesaffectthevalue-accounting

relationasaresultofconservativeaccountingpractices.Finally,beyondtestingthehypothesesof

thisstudy,theempiricalmodelsweestimatealsocon rmresultsestablishedfrompreviousstudies

concerning,forexample,convexity BurgstahlerandDichev1997 ,andtherelativeimportanceof

earningsversusequitybookvalueforpositiveandnegativeearnings rms similartoourhigh-

andlow-pro tability rms;Collinsetal.1999 .Ourstudythushelpstounifyvariousempirical

ndingswithinacommonframework.

InSectionII,wedevelopthehypotheses.SectionIIIdescribesthesample.SectionIVuses

partialmodelspeci cationstotestthehypotheses,whileSectionVusesfullmodelspeci cations.

SectionVIteststheimplicationsofconservativeaccounting.Finally,wedescribeourrobustness

checksinSectionVIIandconcludeinSectionVIII.Themathematicalderivationsofthehypoth-

esesareintheAppendix.

II.THEORETICALFOUNDATIONANDHYPOTHESES

Inthissection,we rstuseasimpli edversionofZhang’s 2000 model,whichassumes

unbiasedaccountingdepreciation,todevelopfourhypothesesonthevaluationeffectofinvest-

mentgrowth;thesehypothesesallarisefromeconomicincentivesforvaluegeneration.Wethen

considerthegeneralversionofZhang’smodeltodevelopour fthhypothesis,whicharisesfrom

accountingconservatism asrepresentedbyaconservativedepreciationpolicyinZhang 2000 .

ASimpli edVersionofZhang’s(2000)Model

LetVbethe current equityvalueofanall-equity- nanced rm,Bthecorrespondingequity

bookvalue,Xthecurrent-periodearnings,gtheextenttowhichthescaleofoperationsmaygrow

inthefuture,andktheearningscapitalizationfactor.6De neq X/Basthe rm’s current-

period pro tability.Then,followingZhang 2000 andassumingunbiasedaccountingdeprecia-

tion,equityvaluecanbeexpressedas:

V=B P q +kq+gC q =BP q +kX+gBC q 1

whereP . isthe put optiontoabandonoperations,andC . isthe call optiontogrow,both

6Sincewearefocusingontheroleofcontemporaneousaccountingdata,wesuppressthetimesubscriptsonvariablesfor

simplicity.

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InvestmentGrowthandtheRelationbetweenEquityValue,Earnings,andEquityBookValue609

normalizedbythescalemeasure,B.Thedecisionstoexercisetherealoptionsaredependenton

pro tability,makingtheoptionsfunctionsofq.PanelsAandBofFigure1providegeometric

viewsofmodel 1 inthespacede nedbyaxesq,B,andV,fortwodifferentvaluesofg.The

valuationfunctionisrepresentedasacurvedsurfacethatmaps q,B combinationsintoVs.7

GrowthandtheRelationbetweenEquityValueandEarnings,GivenBookValue

Wenowemploymodel 1 toexplorehowequityvaluechangeswithearningsatagiven

equitybookvalue.ThebasicV-XrelationisdepictedinFigure1,PanelA.AtagivenB,moving

alongtheq-axis,wetraceoutVasanincreasingandconvexfunctionofX seePredictions1and

2ofZhang 2000,283 ,asrepresentedbycurveab.Intheextremelylow possiblynegative q

region,theslopeintheV-Xrelationisclosetozero.Thereasonisthatwhenoperationsareso

unpro tablethattheyarelikelytobediscontinued,equityvaluedependsprimarilyonbookvalue

proxyingfortheexitoradaptationvalue ,withearningsbeingoflittleuseinpredictingvaluegeneration.AsXincreases andhenceqincreases,givenB ,theprobabilitiesalsoincreasethatthe

rmwillstayinbusinessanditsoperationswillgrow.Thisraisesexpectationsaboutfuture

earnings,thusincreasingtheslopeintheV-Xrelation.

Inmodel 1 ,growthparametergmagni esthevalueofthegrowthoption.Inhigh-qregions

wheretheoptionisinthemoney,theslopeoftheV-Xrelationwillincreasewithgrowth,as

illustratedinPanelsAandBofFigure1fortwodifferentvaluesofg.Movingtothelower-q

FIGURE1

GeometricalViewsofValuationModel(1)

PanelA:Lowg

This gurepresentsgeometricalviewsofequityvalue(V)asafunctionofpro tability(q)andbookvalue(B)

basedonmodel(1)forlowgrowth(PanelA)andhighgrowth(PanelB).AtagivenB,Visanincreasingfunction

ofq,asindicatedbycurveabinPanelA,andtheslopeincreaseswithq.Atagivenq,Visanincreasingfunction

ofB,asindicatedbylinecdinPanelA.

7AxesBandqareorthogonalbecausetheirinformationcontentsarecomplementaryinnature.Notethatearningsare

dependentonscale,andthuswouldbecorrelatedwithbookvalue.

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