The Role of Disaggregation of Earnings in Stock Valuation and Earnings Forecasting. Pengguo Wang 1

Transcription

1 Th Rol of Disaggrgaion of Earnings in Sock Valuaion and Earnings Forcasing Pngguo Wang Xfi Cnr for Financ and Invsmn Exr Univrsiy Businss School Exr EX4 4ST UK I am graful for hlpful commns rcivd from David Ashon, Danilla Ackr, Colin Clubb, Elisabh Ddman, Suar Mclay, John O Hanlon, Kn Pasnll, Mark Tipp and Marin Walkr on h arlir vrsion of h papr. This papr has also bnfid from h commns of paricipans a h EAA0 and Warwick Univrsiy. Paricular hanks ar du o h dior, Paulin Wman, wo anonymous rfrs for hir consruciv and hlpful suggsions.

2 Th Rol of Disaggrgaion of Earnings in Sock Valuaion and Earnings Forcasing Absrac This papr compars and conrass wo accouning informaion sysms, h aggrga arnings sysm and h disaggrgad cash flow/accrual sysm, xamining hir rlaiv prformanc in sock valuaion and in forcasing of arnings. I finds, in gnral, ha h forcass of arnings and prdicd mark valus from h cash flow and accrual sysm hav smallr forcasing rrors han hos from h aggrga arnings sysm. Th adjusd R-squards from h disaggrgad sysm ar in h main highr han hos from h aggrgad sysm whn considring h xplanaory powr of h modl-prdicd valus. Th rsuls also show ha h cash flow and accrual sysm forcass domina h aggrga arnings sysm forcass in a larg majoriy of indusris. Kywords: cash flow, accruals, componns of arnings, forcass of arnings, sock valuaion JEL: C53 G M4

3 . Inroducion Rcivd wisdom suggss ha modls incorporaing informaion abou arnings componns should gnra br forcass of fuur arnings and lad o a grar accuracy in sock valuaion. Surprisingly, h valuaion and forcasing implicaions of dcomposing aggrga arnings ino accrual and cash flow componns ar largly unxplord. On rason is ha accruals ar subjc o accouning ruls and can b manipulad by managmn. Mor imporanly, xising horical liraur provids only limid guidanc on how o map arnings and is componns ino quiy valus. This papr invsigas whhr, and o wha xn, dcomposing aggrga arnings ino opraing cash flows and oal accruals improvs h forcasing of arnings and h valuaion of quiy. Th gnral blif is ha in an accrual accouning sysm, currn arnings ar a br indicaor of fuur arnings han cash flows. Howvr, i is no clar whhr, givn h noisy naur of accruals, h combind informaion conn mbddd in cash flows and accruals is infrior or suprior o ha in aggrga arnings. Accruals rly on accouning ruls, which hav discrionary lmns, and many accruals involv simas, which will unavoidably conain rrors. Morovr, accruals may b manipulad by managmn. I is no surprising ha financial analyss frqunly focus on forcasing fuur arnings rahr han is wo componns: cash flows and accruals. Nvrhlss, h valu-rlvanc of an arnings componn rlis on is abiliy o prdic fuur (abnormal) arnings and cash flows (Dchow, 994; Sloan, 996; Ohlson, 999; Barh, Cram and Nlson, 00). Exising sudis show ha if h informaion dynamics of cash flows and accruals do no saisfy crain condiions, hn hy will arac diffrn valuaion wighs (Flham and Ohlson, 995; Sark, 997; Barh, Bavr, Hand and Landsman, 999; 3

4 Walkr and Wang, 003; Pop, 005). Sinc hr is no on-o-on mapping bwn forcasing rlvanc and valuaion rlvanc of an arnings componn (Pop and Wang, 005), i is worhwhil xamining mpirically h implicaions of h informaion conn in h aggrgad and disaggrgad accouning sysms for boh arnings forcasing and sock valuaion. In xamining h incrmnal rol of accruals in valuaion and forcasing, prior liraur documns ha accruals ar man-rvring and ar lss prsisn han cash flows. Sloan (996) argus ha sock prics ac as if invsors do no undrsand h lowr prsisnc of h accrual componn of arnings, which lads o incorrc forcass of fuur arnings and mispricing of socks. Clubb (996) shows ha incrmnal informaion conn for unxpcd accrual/cash flow byond aggrga arnings dpnds on h invsmn opporuniy s. Dchow, Kohari and Was (998) xplor h forcasing propris of cash flows and accruals. Consisn wih Dchow (994), hy find ha arnings ar br prdicors of fuur opraing cash flows han ar currn opraing cash flows. Pfiffr and Elgrs (999) find accruals hav lss valu rlvanc han cash flows as masurd by h significanc of h cofficins in rgrssions of sock rurns. Barh al. (999) apply Ohlson (999) o invsiga h incrmnal rol of cash flows and accruals in forcasing fuur abnormal arnings, givn aggrga abnormal arnings, whr abnormal arnings ar dfind as h diffrnc bwn arnings and capial chargs. Sloan (999) suggss ha cash flows and accruals may hav diffrn incrmnal rols in forcasing arnings du o diffrn ramn of cash flows and accruals in h xising GAAP. Mor rcnly, Barh, Bavr, Hand and Landsman (005) s ou o drmin whhr indusryspcific valuaion paramrs ar an aid o prdicing conmporanous quiy valus. Thy documn ha accruals and cash flows hav diffrn abiliis in forcasing abnormal arnings 4

5 and find ha h rols of abnormal arnings and accruals in sock valuaion vary significanly across indusris. This papr diffrs from prior liraur by dircly modlling and conrasing wo accouning informaion sysms on dscribing an opraing cash flow and oal accrual sysm and anohr dscribing an aggrga arnings sysm. I xamins h rlaiv prformanc of ach accouning sysm in sock valuaion and in forcasing of arnings in rms of forcasing rrors and h xplanaory powr of h modl prdicd valus o h ralisaions of arnings and obsrvd mark valus of quiy. I is wll sablishd ha accouning ra of rurns ar man rvring a rflcion of unsusainabl conomic condiions in profiabiliy in a compiiv mark (s, for xampl, Bavr, 970; Frman, Ohlson and Pnman, 98; Sloan, 996; Nissim and Pnman, 00). Th accouning informaion dynamics in his papr ar accordingly basd on h assumpion ha rurn on quiy (ROE) follows a man-rvring procss. Th dfiniion of ROE dpnds on h accouning sysm bing modlld. Spcifically, on accouning informaion sysm spcifis opraing cash flows, oal accruals and book valu of quiy; h ohr is basd on h voluion of boom lin numbrs, namly aggrga arnings and book valu of quiy. In h firs accouning sysm I dfin wo masurs of ROE, on for ach of h arnings componns: cash flows dividd by book valu and accruals dividd by book valu, whras in h scond sysm ROE is dfind as aggrga arnings scald by book valu. Th assumpion of man rvrsion for all ROE masurs is inrnally consisn in h sns ha h prsisnc and ROE masurs saisfy wo spcific rsricions, i.., h prsisnc of arnings and is componns ar qual, Alln, Larson and Sloan (00) argu ha accouning accruals anicipa fuur conomic bnfis and mus ulimaly rvrs. Ohrs also xamin h man-rvring propry of h accrual componn, for xampl, Basu (997), Fairfild, Whisnan and Yohn (003), Richardson, Sloan, Soliman and Tuna (005), Chan, Chan, Jgadsh and Lakonishok (006), and Ohlson (00). 5

6 and h long-run man aggrga ROE is qual o h sum of h long-run mans of h cash- ROE and h accrual-roe. This consisncy in h horical modls is imporan bcaus i ss a common bas for comparing h aggrgad and h disaggrgad accouning informaion sysms. Th assumd accouning informaion dynamics nabl m o obain analyic form forcass of arnings and mark valus of quiy. I can hrfor xamin whhr, and h xn o which, prdicd arnings and quiy valus from ach sysm xplain rpord arnings and obsrvabl quiy valus. In his xrcis, h paramrs for ach of h accouning informaion dynamics ar simad using ou-of-sampl simaions on an indusry basis. Bcaus firms in h sam indusry comp for mark shar, analysis of h compiiv srucur of inpu and oupu marks is bs conducd a h indusry lvl (Lundholm and Sloan, 007). I find ha h lowr prsisnc of accruals in h disaggrgad accouning sysm dos no imply ha h dcomposd accouning sysm is infrior. On h conrary, h vidnc shows ha hr is a clar advanag o dcomposing aggrga arnings ino cash flow and accrual componns for sock valuaion and arnings forcasing rsuling in improvd forcass of obsrvabl mark valus and rpord arnings. In gnral, h forcass of arnings and prdicd mark valus from h cash flow and accrual sysm hav smallr rlaiv rrors han hos from h aggrga arnings sysm. Whn xamining h xplanaory powr of prdicions of arnings and mark valus in ach of h wo sysms, h adjusd R-squards in h disaggrgad accouning sysm ar mosly highr han hos from h aggrgad sysm. Th analysis also shows ha h cash flow and accrual sysm forcass domina h aggrga arnings sysm forcass in h sns ha forcass of arnings and prdicd mark valus from h lar hav no incrmnal informaion abou h ralisaions of arnings and obsrvd 6

7 mark valus afr conrolling for forcass of arnings and prdicd mark valus from h formr in a larg majoriy of indusris. Whil in gnral hr is an advanag in dcomposing arnings for h purpos of valuaion and forcasing, whhr, and h xn o which, h disaggrgad sysm ouprforms h aggrgad sysm is indusry-spcific. This papr conribus o h liraur in svral ways. Firs, i joinly modls h gnraing procsss for h opraing cash flow lmn of ROE and h accrual lmn of ROE on h grounds of conomic and accouning ralism. Propris of h man-rvring of individual accouning raios ar wll sablishd, bu h impac of h corrlaions bwn hs raios ar no xplord in prior liraur. Scond, i sablishs a formal horical link bwn h valu of quiy and componns of arnings. This compuaionally-simpl modl can b usful for invsmn pracic. Third, i provids vidnc showing ha spliing arnings ino is opraing cash flow and accrual componns is likly o yild mor prcis forcass of fuur payoffs and hrfor br simas of h valu of quiy. Finally, i shows ha forcass from h aggrgad arnings sysm is largly rdundan for forcasing and valuaion if on conrols for forcass from h disaggrgad cash flow and accrual sysm bu no vic vrsa. Th rs of h papr is organisd as follows. In Scion, I dscrib h accouning informaion dynamics of aggrga arnings, cash flows and accruals, and hn I driv h horical valu for arnings forcass and mark valu of quiy. Scion 3 xplains h simaion procdurs and rsarch dsign; Scion 4 dscribs h daa and rpors sampl saisics; Scion 5 prsns h mpirical rsuls and robusnss ss. Finally, Scion 6 concluds h papr.. Modl Dvlopmn 7

8 In h spiri of Bavr (970) and ohrs, I assum ha boh h opraing cash flow-roe and h oal accrual-roe follow man-rvring procsss as blow: CFO + CFO ACC µ = α ( µ ) + α ( µ ) + ε c, +, b b b () ACC + ACC µ = α ( µ ) + ε a, +, b b () whr CFO and ACC ar rspcivly h wo arnings componns: cash from opraions and oal accruals, b is book valu of h firm a im. 3 α and α > 0 ar prsisnc of h cash- ROE and h accrual-roe. 4 µ and µ ar h xpcd long-run man of h cash-roe and long-run man of h accrual-roe rspcivly. Th α rm capurs how h convrgnc of h accrual-roe affcs h convrgnc of h cash-roe. ε c, + and ε a, + ar wo zro man disurbanc rms. 5 Th cash flow dynamic, (), can b rwrin as E[ CFO + ] = αcfo + α ACC + (( α ) µ α µ ) b. (3) Hnc, h prsisnc in () ar h prsisnc of h componns of arnings in h cash flow dynamics afr conrolling for h book valu of quiy. Th α rm capurs h imporanc of accruals as forcass of fuur cash flows. I rcogniss h rol of accruals in smoohing ou cash flows and rducs h nois in prformanc masurmn. This is consisn wih Barh al. (00), who invsiga h rol of accrual componns in cash flow forcass and sock 3 CFO ACC Sricly spaking, ROE on h righ-hand sid of quaions () and () should b b and b. Using b as a dflaor is for h parsimony of modl dvlopmn. This parsimony has is cos. ROE has a ndncy bu i can nvr approach is man unlss book valu has no growh. Th rsuling informaion dynamics of cash flows and accruals ar consisn wih prior liraur, s Barh al. (00) and Barh al. (999, 005). 4 No ha low valus of paramrs, α and α, indica high spds of convrgnc of h cash-roe and h accrual-roe. 5 If cash flows and accruals ar ngaivly corrlad as documnd (.g. Barh al., 999), hn h sum of h rrors, ε, + = ε c, + + ε a, + will b lss volail han h individual rrors: ε c, + and ε a, +. Prhaps his is h undrlying rason for som analyss o bliv ha forcas of aggrga arnings should b h focus. 8

9 valuaion. Flham and Ohlson (996) assum a similar cash flow dynamic, whr accruals du o dprciaion ar hir focus. Unlik Barh al. (00), h oal accrual hr is modlld joinly by h informaion dynamic (), which can b rwrin as E[ ACC + ] = αacc + ( α ) µ b. (4) This is similar o h accrual sysm in Barh al. (999, 005). 6 I dno h xpcd arnings a im + basd on availabl informaion a im, E[ + ], whr h suprscrip rfrs o valu drivd from h cash flow and accrual dynamics. By consrucion, h arnings of h firm a im, CFO + ACC, and E [ ] E [ CFO ] + E [ ACC ]. Equaions (3) and (4) imply: E[ + ] = αcfo + ( α + α) ACC + (( α ) µ + ( α α ) µ ) b = α ( α α α ) ACC + (( α )( µ + µ ) + ( α α α ) µ ) b. (5) This is similar o Sloan (996), which firs documns accrual anomaly and hypohsiss ha invsors naivly fixa on aggrga arnings and do no apprcia h rlaiv magniuds of h cofficins α and ( α + α) in h firs lin of quaion (5), rsuling in incorrc forcass of arnings and h mispricing of socks. Whn cash flows and accruals ar qually prsisn in arnings dynamic (5), i.. α = α + α, aggrga arnings is a sufficin arnings consruc for forcasing. Th following dgnra arnings dynamic follows: E [ ] ( ) ( ( )), + µ + µ = α µ + µ b b 6 No ha Barh al. (00) and Barh al. (999, 005) do no modl h corrlaion bwn h prsisnc of arnings componns and prsisnc of book valu. 9

10 whr ( µ + µ ) is h implid xpcd long-run man of aggrga ROE in h disaggrgad sysm. This dgnra cas ofn moivas h following scond accouning sysm as a pracic ool. Spcifically i assums ha aggrga ROE follows a man rvring procss (Frman al., 98): 7 b + µ = α ( µ ) + ε, +, (6) b whr α > 0 is h prsisnc of h aggrga ROE, and µ is h xpcd long-run man of h aggrga ROE. ε, + is a disurbanc rm wih zro man. Equaion (6) implis ha h xpcd aggrga arnings can b wrin as: E[ + ] = α + ( α ) µ b, (7) whr E [ + ] dnos h xpcd arnings a im + basd on availabl informaion a im, wih h suprscrip rfrring o forcass drivd from h aggrga arnings sysm. Similar o quaion (5), quaion (7) illusras h imporanc of profiabiliy and book quiy in h gnraion of fuur arnings. I is imporan o no ha µ is h xpcd long-run man of aggrga ROE corrsponding o h aggrga arnings sysm (6), whil ( µ + µ ) is h implid xpcd long-run man of aggrga ROE corrsponding o h disaggrgad cash flow/accrual sysm () and (). E[ + ] in quaion (7) and E[ + ] in quaion (5) ar gnrad by diffrn dynamics, which dscrib diffrn accouning ims. For insanc, if α ( α + α), and an analys blivs ha quaions 7 Sloan (996) assums ha arnings dflad by asss follow an auorgrssiv procss, which ffcivly assums ha h accouning ra of rurn on asss follows a man-rvring procss. No ha quaions () and () imply quaion (6) if α = α = α + α, µ = µ + µ and ε, + = εc, + + ε a, +. 0

11 () and () ar a corrcly spcifid accouning sysm, hn quaion (6) will b mis-spcifid, and vic vrsa. As a consqunc, mpirical implmnaion may rsul in µ bing a biasd sima of ( µ + µ ). For h convninc and clariy of xposiion in h following analysis, I rfr o h sum of h long-run mans of cash-roe and accrual-roe from h disaggrgad cash flow and accrual sysm as h implid xpcd long-run man ROE µ o diffrnia i from µ. Givn h informaion dynamics of h arnings componns in () and (), w nd o sablish h voluion of h book valu of quiy for h purpos of sock valuaion. This is imporan sinc a bnchmark wih which o assss h usfulnss of dcomposing aggrga arnings is prdicion of h mark valu of quiy. 8 Mainaining parsimony, I follow prior liraur by assuming ha book valus hav an xpcd consan growh ra δ (Flham and Ohlson, 995; Barh al., 999, 005; Myrs, 999) as quaion (8) blow: b = δb + ε, (8) + b, + whr δ < R, which is plus h cos of capial. ε b, + is a disurbanc rm wih zro man. Assuming ha h clan surplus accouning rlaion holds, i.., dividnds ar qual o arnings lss chang in book valus of quiy, h mark valu of quiy in a no-arbirag conomy can b wrin in rms of h arnings componns { CFO, ACC } and book valus as follows: MV = ( + β ) b + β CFO + β ACC, (9) 0 whr 8 Fw prior sudis sablish a formal horical link bwn h valu of quiy and h incrmnal rol of accruals. Two xcpions ar Barh al (999, 005).

12 α ( α α α)( R ) β 0 = R( µ + µ ) + Rµ R +, R δ R α ( R α)( R α) α β =, R α α R α α ( ) R α α β = + = α. R α ( R α )( R α ) R α ( R α )( R α ) (0) Proof of quaion (9) can b found in Appndix A. Equaion (9) indicas ha accrual accouning rcogniss accruals or noncash valus as par of h valu addd. As argud by Sloan (996), i is clar ha h rlaiv prsisnc of cash flows and accruals in h arnings dynamic (5), α ( α + α), is on of h imporan facors in quiy pricing. Th long-run man of accrual-roe also plays a dcisiv rol via h book valu of quiy. Whn cash flows and accruals ar qually prsisn, i.. α = α + α, aggrga arnings is a sufficin arnings consruc no only for forcasing, bu also for valuaion, sinc α h valuaion wighs on h wo arnings componns ar h sam ( β = β = ). R α Whn α = α + α = α, and µ + µ = µ, quaions (9) and (0) imply ha h corrsponding mark valu of quiy in a no-arbirag conomy can b xprssd in rms of h aggrga arnings and book valu as follows: α α MV = [ + ( Rµ R + )] b +, ( R δ ) R α R α () whr MV is h mark valu of quiy a im basd on aggrga arnings sysm. In summary, h aggrga arnings informaion dynamic (6) can b viwd as a rsricd vrsion of h cash flow and h accrual informaion dynamics () and (), whn h prsisnc paramrs in h informaion dynamics saisfy: α = α + α = α, and h long-run man

13 aggrga ROE, µ, is qual o h implid xpcd long-run man ROE, µ, from h disaggrgad sysm. 9 Alhough such rsricions do no imply ha on accouning informaion sysm is ncssarily infrior/suprior o h ohr, quaions (5) and (7) (h forcasing quaions) oghr wih quaions (9) and () (h valuaion quaions) provid us wih a basis o compar and conras h wo accouning informaion sysms. On poin nds o b mphasisd hr: my focus is on which accouning sysm br dscribs ralisd arnings and obsrvd quiy valus, no on h absolu accuracy of h forcass and valuaions. Th simpl parsimonious informaion dynamics inviably gnra biasd prdicions bcaus non-accouning informaion and growh componns in forcasing and sock valuaion ar ignord in h analysis. Nvrhlss, if capial mark paricipans assum ha ohr informaion and invsmn dcisions ar indpndn of ihr accouning informaion sysm, hn hy can convninly and fairly compar and conras h prformanc of h wo accouning informaion sysms for valuaion and forcasing. 3. Esimaion Procdur and Empirical Dsign To compar and conras h wo accouning informaion sysms, w nd o sima prsisnc paramrs, αs, and h long-run mans, µs, in quaions (), () and (6), as wll as h growh paramr, δ, in quaion (8). In viw of h possibl corrlaions among h rror rms in quaions (), () and (8) for h dynamics of h cash-roe, h accrual-roe and h book valu of quiy, I run h smingly unrlad rgrssions: 9 This papr xamins informaion dynamic (6) as an indpndn procss, alhough i can b viwd as a rducd form of informaion dynamics () and (). 3

14 CFO CFO ACC = c + α + α + ε b b b + c, + ACC b + ACC = c + α + ε a, + b b = c + ( δ ) b + ε, + 3 b, +,, () whr b = b b and c i (i =,,3) ar inrcps. 0 Whil h prsisnc paramrs, α, α, + + and α, can b dircly simad, h long-run man cash-roe and accrual-roe can b drivd αc from h corrsponding inrcps and prsisnc as µ = ( c + ) α α c and µ =. α Similarly, I sima h aggrga arnings dynamics by running h smingly unrlad rgrssions: b + = c + α + ε 4, + b b = c + ( δ ) b + ε, + 5 b, +, (3) whr c i (i = 4, 5) ar inrcps. Th long-run man aggrga ROE can hn b wrin as: µ c α 4 =. Sinc prior liraur documns ha valuaion paramrs ar indusry-spcific, I sima indusry-spcific informaion paramrs from boh h aggrgad and disaggrgad accouning sysms. Following Barh al. (005), I us a jack-knifing procdur o sima firm-indusry spcific paramrs. Spcifically, I run cross-scional rgrssions using h prvious fiv yars of daa for ach firm-yar in an indusry wihou using ha firm s daa o gnra paramrs in ihr of h wo accouning sysms. By doing so, h paramrs ar firm-indusry-yar spcific simas, which incorpora yarly updad informaion. For xampl, for firm i in 0 In ordr o dal wih saionariy, I run rgrssions on chang in book valus. Th rsuls for hs rgrssions ar consisn wih h rsuls by using prvious 0 yars of daa. 4

15 indusry j in yar 99, h firm s spcific informaion paramrs, αs and µs, ar simad basd on daa for all ohr firms in h indusry. Th prdicion of firm i s arnings in yar + in indusry j is h prdicd valu from h arnings modls, E[ i, + ] in (5) and E[ i, + ] in (7), using paramrs simad from sysms () and (3), and using all firms in indusry j xcp firm i s from yar -4 o yar. Th rsuling prdicions ar sricly ou-of-sampl sinc firm i s daa in yar ar no usd o sima h cofficins. Similarly, h simaion of firm i s quiy mark valu in yar in indusry j is h simad valu from h valuaion modls, MV i, in (9) and MV i, in (), again using paramrs simad from sysms () and (3), and using all firms in indusry j xcp firm i s from yar -4 o yar. Th prdicions in mark valus ar consqunly dmd ou-of-sampl. To g a sns and assss h diffrncs in prdicion rrors across accouning informaion sysms, I calcula a commonly applid prdicion rror mric h absolu prcnag rror in forcasing and in valuaion. I calcula absolu rrors bcaus i is xpcd ha h prdicd sock valus ar undrsimad by ignoring non-accouning informaion and any growh componns in h sysms. Th rrors in quiy mark capialisaion drivd from boh h cash flow and accrual dynamics, and h aggrga arnings dynamic ar compud as blow. For indusry j, dno MDMV = Man of absolu prcnag Diffrnc in Mark Valu, ( MV MV ) / MV j ij ij ij for all firm i and im from cash flow and accrual dynamics, Th firm-indusry-yar paramrs ar availabl from 99 and onwards sinc opraing cash flows ar availabl from 987 in Compusa by using 5-yar daa in h cross-scional rgrssions. This approach conrass wih Barh al. (005), who sima paramrs for ach firm ha ar consan ovr im. In ohr words, hir paramrs ar firm-indusry spcific bu no firm-indusry-yar spcific. As nod in Barh al. (005), h jack-knifing approach ffcivly assums ha paramr simas ar gnrad from a randomly collcd sampl and ha obsrvaions in h sampl ar indpndn. Thrfor, h saisics obaind for hypohsis sing do no rly on unknown paramric disribuions. 5

16 (4) and MDMV = Man of absolu prcnag Diffrnc in Mark Valu, ( MV MV ) / MV j ij ij ij for all firm i and im from aggrga arnings dynamics, (5) whr MV ij is mark capialisaion for firm i a im in indusry j. Th sam prdicion rror mric is applid o h forcasd arnings on an indusry basis. For indusry j, dno MDE = Man of absolu prcnag Diffrnc in Earnings, ( ) / j ij ij ij for all firm i and im from cash flow and accrual dynamics, (6) and MDE = Man of absolu prcnag Diffrnc in Earnings, ( ) / j ij ij ij for all firm i and im from aggrga arnings dynamics, (7) whr ij is rpord arnings for firm i a im in indusry j. Wih h xpcd arnings drivd from h cash flow and accrual informaion dynamics, [ E i, + ] in (5), and h xpcd arnings drivd from h aggrga arnings dynamics, E i, + [ ] in (7), adjusd R-squards, and Vuong Z-saisics (Mincr and Zarrowiz, 969; Vuong, 989; Dchow, 994) can b usd o xamin whhr E[ i, + ] or E[ i, + ] br xplains h rpord arnings, i, +. Similarly, wih h simad sock valu drivd from h cash flow and accrual informaion dynamics, MV i, in (9), and h simad sock valu drivd from h aggrga arnings dynamics, MV i, in (), adjusd R-squards, and Vuong Z-saisics can b usd o xamin whhr MV i, or MV i, br xplains quiy mark capialisaion, MV i,. If h Z- saisic is posiiv and saisically significan, h s indicas ha h cash flow and accrual 6

17 informaion dynamics ar br han h aggrga arnings dynamics, in h sns ha h rsiduals gnrad by h following rgrssions: = k + γ E [ ] + ε and MV = k + γ MV + ε, (8) i, + i, + i, + i, 3 3 i, i, ar smallr han hos from h corrsponding rgrssions in (9): = k + γ E [ ] + ε and MV = k + γ MV + ε, (9) i, + i, + 3 i, + i, 4 4 i, 4 i, whr k i (i=-4) ar inrcps, and γ i (i=-4) ar slops. On h ohr hand, if h Z-saisic is ngaiv and saisically significan, hn h aggrga arnings dynamics ar suprior. Finally, I run an ncompassing rgrssion: = k + γ E [ ] + γ E [ ] + ε, (0) i, i, + 5 i, + 5 i, + whr k 5 is h inrcp, and γ 5i (i=-) ar slops. If γ 5 is clos o and saisically diffrn from zro, and γ 5 is no significanly diffrn from zro, hn h cash flow and accrual sysm forcass can b said o domina h aggrga arnings sysm forcass. On h ohr hand, if γ 5 is no saisically significanly diffrn from zro, and γ 5 is clos o and saisically diffrn from zro, hn h aggrga arnings sysm forcass can b said o domina h cash flow and accrual sysm forcass. For ohr (saisically significan) valus of h rgrssion slop paramrs, nihr sysm forcass domina h ohr, so ha boh forcass conain usful informaion abou h ralisaion of arnings. Similarly, I run h following ncompassing rgrssion o s whhr MV i, and/or MV i, conain usful informaion abou h obsrvd quiy valus: MV = k + MV + MV + () i, 6 γ 6 i, γ 6 i, ε 6 i,, whr k 6 is h inrcp, and γ 6i (i=-) ar slops. 7

18 4. Sampl Dscripion I collc rlvan accouning daa from Compusa s nir daas for yars Yar 987 is h firs yar whn opraing cash flows ar availabl in Compusa. Aggrga arnings ar masurd as n incom bfor xraordinary ims (Compusa im: IB). 3 Following Barh al. (999, 005), oal accruals ar masurd by h diffrnc bwn aggrga arnings and opraing cash flows (OANCF). 4 Mark capialisaion is qual o pric pr shar muliplid by numbrs of shars of ousanding (CSHO). Pric pr shar is masurd hr monhs afr h nd of h fiscal yar from h Cnr for Rsarch in Scuriy Prics (CRSP) o nsur ha accouning informaion is known bfor valu is compud. Firms wih ngaiv book valus (CEQ) ar dld. To avoid h influnc of small firms, I rsric h sampl o firms wih mark capialisaion in xcss of $0 million. 5 To miiga h ffcs of oulirs, firms in h xrm prcnils of arnings, book valus, numbrs of shar ousanding, opraing cash flows, accruals and ROEs ar also xcludd (Ball, Kohari and Robin, 000; Barh al., 999, 005). All variabls ar xprssd in millions of dollars and masurd as of fiscal yar nd, xcp quiy mark valu. <Insr Tabl abou hr> Panl A of Tabl conains dails of h sampl. Summary dscripiv saisics can b found in Panl B. I shows ha lss han 5% of firms hav posiiv accruals and ha h man accrual is ngaiv. Th main rason for his is ha dprciaion xpns is includd in accruals bu capial xpndiurs ar includd in invsing cash flows (Sloan, 996; Barh al., 00). Th avrag 3 This may viola h clan surplus accouning assumpion. Howvr i liminas ponially confounding ffcs of on-im ims and is consisn wih prior liraur (Dchow al., 999; Barh al., 005). 4 Hribar and Collins (00) suggs using h samn of cash flows o calcula accruals, du o problms wih non-ariculaion vns in using h balanc sh approach. 5 Th rsuls ar similar whn ha cu-off is $.00 pr shar. 8

19 aggrga ROE is 5.6%, and h avrag cash-roe and avrag accrual-roe ar 7.% and -.6% rspcivly ovr h sampl priod. Panl C of Tabl shows h corrlaion marix of h inpu variabls. Th Parson corrlaion is h lowr half and h Sparman corrlaion is h op half. Thy show ha accruals ar highly ngaivly corrlad wih mark capialisaion, book valu of quiy, arnings and opraing cash flows. I bas my indusry classificaions on hos in Barh al. (998) and Barh al. (999, 005). Panl D of Tabl dscribs h indusry composiion of h sampl. I rvals ha indusris wih h largs concnraions of firm-yar obsrvaions ar Compurs, 3.0%, Rail, 9.94%, Financial Insiuions, 8.86%, and Srvics, 8.6%. Consisn wih prior liraur, I us a cos of capial of prcn in quiy valuaion modls (9) and (), and s ngaiv prdicd quiy mark valus o zro Empirical Rsuls 5.. Paramrs in h wo accouning informaion sysms Tabl rpors h prsisnc paramrs, α, α, α and α, in h informaion dynamics () and (3), basd on smingly unrlad rgrssions on h poold sampl. Th growh paramr of book valu, δ, and h long-run mans of rurns, µ, µ and µ, ar also rpord. <Insr Tabl abou hr> 6 Th numbr of ngaiv prdicd quiy mark valus is approximaly 0 prcn. Thr is no doub ha ohr informaion and growh opions will conribu a posiiv quiy valu componn. Unlik Barh al (005), h prdicd quiy mark valu in his papr is dircly drivd from arnings and is componn informaion dynamics, rahr han simulanously simad from boh informaion dynamics and xpcd valuaion modl. Ashon and Wang (0) suggs a plausibl rang for h cos of quiy capial for US mark ovr h priod o b bwn 0% o %. Rsuls ar mainly unalrd whn using 9% or 5% as a discoun ra. 9

20 Tabl shows ha h prsisnc of cash flows is much largr han ha of accruals, α = 0.84 > α = In ohr words, h accrual-roe rvrs o is man much mor quickly han dos cash-roe. This of cours rflcs h naur of accrual accouning. A Wald s on h paramrs of h fid modl shows ha h null hypohsis of qualiy, H 0 : α = α, is srongly rjcd. Tabl also shows ha α = 0.84 > α = 0.0, i.., high cash flow prformanc ha is aribuabl o h cash flow componn is mor likly o prsis han ha which is aribuabl o h accruals. This implis ha cash flows conain mor informaion han accruals abou h nx priod s cash flows (Barh al., 00). As shown in quaion (5), h cofficin of accrual in arnings forcasing in h disaggrgad accouning sysm is ( α α + ). Tabl shows ha α + α = < α = Hr again h null hypohsis of qualiy, H 0 : α = α + α, is srongly rjcd. This is consisn wih Sloan (996), which finds ha a good arnings prformanc ha is aribuabl o h cash flow componn is mor likly o prsis han ha which is aribuabl o h accrual componn of arnings. No ha h cofficin of accruals, α + α, in h arnings dynamic hr is implid by joinly rgrssing cash flow dynamic and accrual dynamic, whras in conras Sloan s finding is basd on dircly rgrssing on priod ahad arnings on currn cash flows and accruals. Th long-run mans of h cash-roe and h accrual-roe drivd from h inrcp rms and h cofficins of α, α, α ar rspcivly µ = 0.7 and µ = Th ngaiv long-run man accrual-roe rflcs h smoohing ffc of accruals on h long-run man aggrga ROE. Th growh ra of book valu in boh h accouning sysms is roughly qual o 5.8% p.a. 0

21 ovr h sampl priod. 7 Th prsisnc of arnings and h long-run man ROE ar shown in Panl B wih α = and µ = On an indusry-by-indusry basis, I us h jack-knifing approach o sima firm-yar paramrs for h informaion dynamics () and (3) for ach indusry. 8 In ordr o mak h comparison maningful on an indusry-by-indusry basis, I dl h Pharmacuicals indusry sinc is long-run man aggrga ROE is ngaiv ( µ < 0), which suggss ohr informaion could b significan in drmining is fuur arnings and currn quiy valu. 9 Th avrag valus of h informaion paramrs for ach indusry ar rpord in Tabl 3. Ths paramrs ar rspcivly h prsisnc of cash flows (α ) and accruals (α ) in h cash flow dynamics, h prsisnc of accruals (α ), and h prsisnc of aggrga arnings (α), h long-run mans of h cash-roe ( µ ), h accrual-roe ( µ ), and h aggrga ROE ( µ ), and h longrun growh ras of book valu of quiy (δ and δ ). < Insr Tabl 3 abou hr> Panl A of Tabl 3 shows characrisics similar o hos in Tabl. Accruals rvr o hir man mor quickly han do cash flows for all sampl indusris (wih prsisnc ras of α = and α = 0.74 rspcivly). In h cash flow dynamic (3), cash flows ar mor prsisn han accruals, wih h man prsisnc ras of α = 0.74 and α = 0.0 rspcivly, indicaing ha cash flows conain mor informaion han accruals abou fuur cash flows. Hnc a good arnings prformanc ha is aribuabl o h cash flow componn is mor likly o prsis han ha which is aribuabl o h accruals componn of arnings for all sampl 7 A sligh diffrnc bwn h wo inrcps for b is du o running smingly unrlad rgrssions. 8 Whi (980) corrcions ar usd o h sandard rrors in h simaions. 9 Barh al. (999) also find ha convrgnc faild o occur during sysm simaion for Pharmacuicals firms.

22 indusris ( α + α < α ). A paird -s of α agains α + α basd on h 8 indusris has a -valu of.68, indicaing ha α + α is saisically significanly diffrn from α. Panl B of Tabl 3 shows ha h man valu of α = for h sampl indusris, and α > α + α, for all indusris. A paird -s of α agains α, basd on h 8 indusris has a - valu of -.88, suggsing ha α is no saisically significanly diffrn from α a h 5% lvl. Th man of long-run growh in book quiy is 6.6% in ach of h accouning sysms ovr h sampl priod. Tabl 3 also shows ha h long-run accrual-roe is ngaiv for all sampl indusris ( µ < 0 ). Howvr, h implid xpcd long-run man ROE µ ( = µ + µ ) from h disaggrgad sysm is largr han h long-run aggrga ROE ( µ ), for all bu on indusry ha of Financial Insiuions. 0 Th long-run man cash-roe for h sampl indusris is 5.5 prcn, and h long-run man accrual-roe is abou (ngaiv).9 prcn. Th implid xpcd long-run man ROE µ from h disaggrgad sysm is 0.6 and h long-run man aggrga ROE ( µ ) is 0.0. Th s of µ µ = basd on h 8 indusris has a -valu of -3.68, suggsing ha µ is significanly smallr han µ. Thrfor, h disaggrgad accouning sysm diffrs from h aggrgad sysm in boh h prsisnc and long-run man of ROEs: h prsisnc of accruals is lowr han ha of cash flows as documnd in h xising liraur, and h xpcd long-run man aggrga ROE is lss han h implid xpcd long-run man ROE from h disaggrgad sysm. Th indusry-spcific ffc on h informaion paramrs is clarly obsrvd in boh accouning sysms. In Tabl 3, h hr indusris wih h lows man prsisnc of accruals ( α + α ) 0 This suggss ha h accrual componns for financial insiuions may nd o b inrprd diffrnly. For xampl, invnory is no a prdicor of fuur arnings for his indusry.

23 in arnings forcasing ar Compurs, Machinry and Elcrical Equipmn. Th hr indusris wih h lows long-run man accrual-roe ( µ ) ar Exraciv indusris, Transporaion, and Uiliis, and wo of hs (Exraciv indusris, and Transporaion) hav amongs h hr highs long-run man cash-roes ( µ ). This suggss a ngaiv rlaionship bwn h longrun cash-roe and h long-run accrual-roe. 5. Th forcasing abiliy of h wo accouning informaion sysms Afr simaing h firm-yar informaion paramrs for ach indusry in boh h accouning sysms, I calcula h xpcd arnings and mark valu of quiy, E[ + ], E[ + ], MV and MV using quaions (7), (5), () and (9) for ach firm in ach yar. I hn compu h forcas rrors bwn h prdicd arnings/sock valus and h rpord arnings/obsrvd quiy valus. Finally I xamin h xplanaory powr of hs prdicd arnings and sock valus for h rpord arnings and h obsrvd quiy valus. To miiga h ffcs of oulirs, obsrvaions in h xrm prcnils of h informaion paramrs, including α, α, α, α, µ, µ, µ, δ and δ ar winsorisd. Obsrvaions in h xrm prcnils of MV and MV ar also winsorisd in h analysis. <Insr Tabl 4 abou hr> Panl A and Panl B of Tabl 4 compar arnings and sock valus rspcivly. Columns -4 show h abiliy of prdicions of arnings, E[ + ], and mark capialisaion, MV, drivd from h cash flows and accrual dynamics, o xplain h rpord arnings and obsrvd mark capialisaion (MV) on an indusry by indusry basis. Columns 5-7 show h quivaln rsuls for prdicions of arnings, E[ + ], and mark capialisaion, MV, drivd from h aggrga 3

24 arnings dynamics. Column 8 rpors Vuong Z-saisics from h arnings rgrssion quaions and from h valuaion rgrssion quaions in Panl A and Panl B rspcivly. Comparing Columns and 5 in Panl A of Tabl 4, on obsrvs ha h mans of absolu forcas rrors for arnings from h cash flow and accrual sysm ( MDE j ) ar smallr han hos from h aggrga arnings sysm ( MDE ) xcp in 4 ou of h 8 indusris. Th sam j columns in Panl B show ha h mans of absolu forcas rrors for mark valus from h cash flow and accrual sysm ( MDMV sysm ( MDMV ). j j ) ar all smallr han hos from h aggrga arnings Nx, I us wo-way clusr-robus sandard rrors o corrc for boh cross-scional and imsris dpndnc in a Mincr-Zarrowiz analysis (Prsn, 009; Gow al., 00). Columns 3 and 6 illusra ha, boh h mans and h mdians of h indusry cofficins ( γ and γ in quaions (8) and (9)) in h arnings rgrssions in Panl A ar clos o (wih man valus of.05 and.037 and mdian valus of.03 and.038 rspcivly) in h wo accouning sysms. Th man and mdian of indusry cofficins ( γ 3 and γ 4 in quaions (8) and (9)) in mark valu rgrssions in Panl B ar.377 and.49 rspcivly for h cash flow and accrual sysm, whil h corrsponding valus in h aggrga arnings sysm ar. and.35 rspcivly. As xpcd, h -saisics in h indusry-by-indusry rgrssions indica ha h man cofficin of γ ( i = - 4) is no significanly diffrn from on. In 4 ou of h 8 indusris h adjusd R-squards ( R accrual sysm ar highr han hos ( R i,, ) in h arnings rgrssions from h cash flow and ) in h aggrga arnings sysm as can b sn in Columns 4 and 7 in Panl A. Th quivaln numbr for h mark valu rgrssions is also 4 I hank Michll Prsn for h gnrous provision of som programming cod. 4

25 as can b sn in Columns 4 and 7 in Panl B. Th mans of h adjusd R-squards for arnings and mark valu rgrssions from h cash flow and accrual sysm ar 66.0% and 40.4% rspcivly. Ths ar largr han hos from h aggrga arnings sysm which ar 65.0% and 34.6% rspcivly. I hn s h null hypohsis ha h wo modls ar qually clos in xplaining h ru daa gnraing procss agains h alrnaiv ha on modl is closr using a Vuong s. Column 8 in Panl A of Tabl 4 shows ha hr ar 8 indusris wih saisically significan posiiv Z- saisics and only indusris wih ngaiv Z-saisic a h 5% lvl in h arnings rgrssions. Th sam column in Panl B shows ha hr ar 9 indusris wih saisically significan posiiv Z-saisics bu no ngaiv Z-saisic is significan a h 5% lvl in h mark valu rgrssions. Th -valus suggs ha h (posiiv) mans of hs Z-saisics ar saisically significanly diffrn from zro. Furhrmor, as shown in Panl C of Tabl 4, a paird -s of R mv, = mv, R has a -valu of.83, suggsing ha R is saisically mv, significanly diffrn from R mv,. Th sam s of R = R, has a -valu of.94, indicaing, ha R is also saisically significanly diffrn from, R., 5.3. Incrmnal conribuion from an alrnaiv accouning sysm I rpor rsuls on h wo ncompassing rgrssions as in quaions (0) and () on an indusry basis in Tabl 5. Again, I us wo-way clusr-robus sandard rrors o corrc for boh crossscional and im-sris corrlaion in h analysis. <Insr Tabl 5 abou hr> Panl A and Panl B of Tabl 5 show h rsuls for h arnings and sock valu rgrssions rspcivly. Columns -3 prsn h inrcp rms and hir -valus. In conras o h 5

26 inrcps in h arnings rgrssions whr only hr ar saisically significan a h 5% lvl, mos of h inrcps in h mark valu rgrssions ar significan. This is likly bcaus nonaccouning informaion, such as growh opions, may play an imporan rol in sock valuaions. Columns 4-5 in Panl A show ha 3 ou of h 8 cofficins ar significanly diffrn from zro a h 5% lvl wih an ovrall man of 0.73, whil Columns 6-7 show ha only 6 ou of h 8 cofficins ar significanly diffrn from zro wih an ovrall man of Th - saisics in h indusry-by-indusry rgrssions indica ha h man cofficin of γ 5 is no significanly diffrn from on. Howvr, ss rval ha h man cofficin of γ 5 is significanly lss han on and grar han zro. In ohr words, h cash flow and accrual sysm forcass domina h aggrga arnings sysm forcass for mos of h indusris in arnings forcasing. No ha for wo indusris (Elcrical quipmn and Compurs), nihr sysm forcass domina h ohr, so ha boh forcass conain usful informaion abou h ralisaion of arnings. Th poold sampl analysis shows ha h rgrssion cofficin of h forcass in h disaggrgad sysm is 0.83 (wih -valu 7.5) agains h rgrssion cofficin of h forcass 0.79 (wih -valu.73) in h aggrgad sysm. Similarly, Columns 4-5 in Panl B show ha 0 ou of h 8 cofficins ar significanly diffrn from zro a h 5% lvl wih an ovrall man of.43, whil Columns 6-7 show ha only 3 ou of h 8 cofficins ar significanly diffrn from zro wih an ovrall man of Again, h -saisics in h indusry-by-indusry rgrssions indica ha h man cofficin of γ 6 is no significanly diffrn from on, whil h man cofficin of γ 6 is no significanly diffrn from zro. No also ha for h Rail Indusry, h incrmnal informaion conaind in h prdicd mark valus from h aggrga sysm is xrmly infficin (wih significanly ngaiv cofficin) hough nihr sysm forcass domina h 6

27 ohr. In h poold sampl analysis, h cofficin of h prdicd valu in h disaggrgad sysm is 0.49 (wih -valu.) agains h corrsponding cofficin -0.0 (wih -valu -0.) in h aggrgad sysm. This confirms my finding abov ha h cash flow and accrual sysm forcass domina h aggrga arnings sysm forcass in mos indusris. Column 8 shows h adjusd R-squards for h rgrssions. Thy ar no much diffrn from hos in simpl Mincr-Zarrowiz rgrssions as rpord in Tabl 4. In summary, h analysis shows ha h disaggrgad accouning sysm largly ouprforms h aggrgad sysm alhough hr ar xcpions for a fw indusris Robusnss s For robusnss chcks I rpa h abov analysis for Dcmbr fiscal yar-nd firms only. This allows for h simaion of h rlaionship bwn mark valu and accouning fundamnals a h sam poin in im for ach firm-yar obsrvaion. I rsuls in 37,053 firm-yars obsrvaions. I summaris h main rsuls wihou abulaing h dails. I find ha h mans of absolu forcas rrors for arnings from h cash flow and accrual sysm ( MDE ) ar smallr han hos from h aggrga arnings sysm ( MDE ) xcp in 3 j ou of h 8 indusris. Th mans of absolu forcas rrors for mark valu from h cash flow and accrual sysm ( dynamic ( squards ( R MDMV j ) ar also smallr han hos from aggrga arnings MDMV j ) xcp for 3 indusris. For 4 ou of h 8 indusris h adjusd R-, han hos ( R, ) in h arnings rgrssions from h cash flow and accrual dynamics ar highr ) from h aggrga arnings sysm. Th quivaln numbr for h mark valu rgrssions is 3. Th mans of h adjusd R-squards for h arnings and h mark j 7

28 valu rgrssions from h cash flow and accrual dynamics ar 64.5% and 44.5% rspcivly. Ths ar largr han hos from h aggrga arnings dynamics, 63.% and 38.4% rspcivly. Finally, I run h wo ncompassing rgrssions as in quaions (0) and () on an indusry basis. Again, I us wo-way clusr-robus sandard rrors o corrc for boh cross-scional and im-sris dpndnc in h analysis. In conras o h inrcps in h arnings rgrssions whr only on is saisically significan, all bu hr inrcps in h mark valu rgrssions ar significan a h 5% lvl. ou of h 8 cofficins of E[ i, + ] ar significanly diffrn from zro a h 5% lvl wih an ovrall man of 0.79, whil only ou of h 8 cofficins E[ + ] ar significanly diffrn from zro wih an ovrall man of 0.0. Similarly, ou of i, of h 8 cofficins of prdicd mark valus, MV i,, ar significanly diffrn from zro a h 5% lvl wih an ovrall man of.54, whil only 4 ou of h 8 cofficins of MV i, ar significanly diffrn from zro wih an ovrall man of 0.. This confirms my arlir findings basd on h full sampl ha forcass basd on h cash flow and accrual sysm domina hos from h aggrga arnings sysm for mos of h indusris. 6. Conclusion Invsigaing h consquncs of dcomposing aggrga arnings ino cash flow and accrual componns for sock valuaion and h forcasing of arnings is imporan on boh horical and pracical grounds. This papr compars and conrass wo accouning informaion sysms on spcifying opraing cash flows and oal accruals h ohr aggrga arnings. Th modl focuss on h prsisnc of ach of aggrga arnings, cash flows and accruals, and h 8

29 xpcd long-run man accouning rurns on book quiy. Invsigaion of h propris of h informaion paramrs nabls an assssmn of h consisncy of hs wo informaion dynamics and an xploraion of h implicaions of incrmnal informaion conn for arnings forcass and sock valuaion. I find ha boh h prsisnc of arnings and ha of cash flows ar largr han h prsisnc of accruals in forcasing of arnings. I also find ha h xpcd long-run man aggrga ROE (in h aggrga sysm) is lss han h implid xpcd long-run man ROE in h disaggrgad sysm. Th vidnc shows ha h disaggrgad cash flow/accrual sysm gnrally ouprforms h aggrga arnings sysm in boh h forcasing of arnings and in sock valuaion. Spcifically, forcass of arnings and h prdicd mark valus from h cash flow and accrual sysm in gnral hav smallr rrors han hos from h aggrga arnings sysm rlaiv o h ralizaions of arnings and obsrvd mark valus. Th adjusd R- squards from h disaggrgad accouning sysm ar gnrally highr han hos from h aggrgad accouning sysm whn xamining h xplanaory powrs of h modls. Th rsuls also show ha h cash flow and accrual sysm forcass domina h aggrga arnings sysm forcass in h sns ha forcass of arnings and prdicd mark valus from h lar sysm provid no incrmnal informaion abou h ralisaions of arnings and obsrvd mark valus afr conrolling for forcass of rlvan valus from h formr sysm in a larg majoriy of indusris. Whil i is advanagous o dcompos arnings for h purpos of valuaion and forcasing, whhr, and h xn o which, h disaggrgad sysm ouprforms h aggrgad sysm rmains indusry-spcific. This sudy has implicaions for invsmn profssionals and horical rsarchrs. I is usful o bar in mind ha spliing arnings ino is componns is likly o yild mor prcis forcass 9

30 of fuur payoffs and hrfor br simas of quiy valu. Rsarchrs may modl arnings componns wih h sam noion proposd in his papr and driv a plausibl horical valu of quiy o xplor any mispricing. Th rsuls also appar o provid a basis for undrsanding som of h faurs of accouning pracic. Alhough h analysis is prsnd in rms of only wo arnings componns, h inuiion provids a raional for h mrgnc of daild lin im disclosurs in GAAP. Explici modlling of accrual and cash flow dynamics lads o h sablishmn of a rlaionship bwn sock rurn and accouning accruals. This may shd ligh on undrsanding h accrual anomaly socks wih high and low accruals ar mispricd givn hir risk. I lav his invsigaion for fuur rsarch. 30

31 Appndix A In his Appndix, I firs show how h mark valu of quiy in a no-arbirag conomy can b wrin as a linar combinaion of h currn book valu and h arnings componns rprsning cash flows from opraions and accruals { b, CFO, ACC }. I hn procd o idnify h mahmaical srucur of h cofficins in h linar valuaion modls as in quaions (9), (0) and () in h main x. Th dividnd discoun modl and h clan surplus rlaionship: d+ = CFO + + ACC + ( b + b ) nabl us o wri h mark valu of quiy MV in rms of h fuur valus of { b + τ, CFO + τ, ACC+ τ }, τ =,,.... Th hr rcurrnc quaions (), () and (8), spcifying h informaion dynamics for { b, CFO, ACC }, hn nabl us o xprss h mark valu of quiy in rms of hir currn valus. Hnc h mark valu of quiy, can b wrin in a linar combinaion of { b, CFO, ACC } as: MV, MV = ( + β ) b + β CFO + β ACC. (9) 0 Nx, w nd o show ha h firm spcific consans β ( i = 0,, ) can b xprssd in h form as in quaion sysm (0). Th no-arbirag condiion: E[ MV + + d+ ] = R MV implis ha i E [( + β ) b + β CFO + β ACC + d ] = R(( + β ) b + β CFO + β ACC ) Using h clan surplus accouning rlaionship o subsiu for d + in h abov, givs ( + β ) E [ CFO ] + ( + β ) E [ ACC ] + β E [ b ] + b = R(( + β ) b + β CFO + β ACC ) Whn w us h informaion dynamics (), () and (8) o limina h + rms, h abov quaion implis ha 3

32 ( + β )((( α ) µ α µ ) b + α CFO + α ACC ) + ( + β )(( α ) µ b + α ACC ) + ( + δβ ) b 0 = R( + β ) b + Rβ CFO + Rβ ACC. 0 Sinc his quaion mus hold for all for ach firm, by maching cofficins of CFO, ACC and b, w hav: CFO ACC : α ( + β ) Rβ = 0, : α ( + β ) + α ( + β ) Rβ = 0, b : ( + β )( α ) µ + (( + β )( α ) ( + β ) α ) µ + R + ( δ R) β = 0. 0 Solving for β0, β and β from h 3-quaion sysm abov, w g α ( α α α)( R ) β 0 = R( µ + µ ) + Rµ R +, R δ R α ( R α)( R α) α β =, R α α R α α ( ) R α α β = + = α. R α ( R α )( R α ) R α ( R α )( R α ) (0) Finally, if w dno α = α = α + α, and µ = µ + µ, w hav α α β 0 = Rµ R +, β = β =. R δ R α R α Th mark valu of quiy from h aggrga arnings sysm can now b wrin as α α MV = [ + ( Rµ R + )] b +. ( R δ ) R α R α () 3

33 Appndix B: Dfiniion of h Variabls wih h Rlvan Mnmonics MV: Mark valu of quiy b: book valu of quiy : n incom bfor xraordinary ims CFO: opraing cash flow ROE: rurn on quiy ROCF: cash rurn on laggd book valu of quiy ROACC: accrual rurn on laggd book valu of quiy ROE: arnings ovr book valu ROCF: cash flows ovr book valu ROACC: accruals ovr book valu MDE j : man of absolu % diffrnc in arnings for all firms ovr h sampl priod in indusry j from cash flow and accrual sysm MDE j : man of absolu % diffrnc in arnings for all firms ovr h sampl in indusry j from aggrga arnings sysm MDMV j : man of absolu % diffrnc in mark valus for all firms ovr h sampl in indusry j from cash flow and accrual sysm MDMV : man of absolu % diffrnc in mark valus for all firms ovr h sampl in j indusry j from aggrga arnings sysm E[ + ] : forcasd on priod ahad arnings from h cash flow and accrual sysm E[ + ]: forcasd on priod ahad arnings from h aggrga arnings sysm MV : prdicd mark valus from h cash flow and accrual sysm a im MV : prdicd mark valus from h aggrga sysm a im 33

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