Terminal Value Techniques in Equity Valuation - Implications of the Steady State Assumption

Transcription

1 Teminal Value Techniques in quiy Valuaion - Implicaions of he Seay Sae ssumpion Joaim Levin Pe Olsson SS/FI Woin Pape Seies in Business minisaion No 2:7 June 2 sac: This pape examines he coniions necessay fo calculain seay sae eminal values in equiy (company valuaion moels. We mae explici use of he fac ha a company s income saemens an alance shees can e moele as a sysem of iffeence equaions. Fom hese iffeence equaions, we eive coniions fo seay sae. The coniions ensue ha he company emains qualiaively simila yea y yea afe he valuaion hoizon an ha i has a sale evelopmen of eanins, fee cash flows, iviens an esiual income. We show how seay sae coniion violaions cause inenal inconsisencies in valuaion moels an how his can have a susanial impac on he value esimaes. Seay sae is fuhe a necessay coniion fo a fee cash flow valuaion, a ivien valuaion an a esiual income valuaion o yiel ienical esuls when eminal values ae use. The paamees of he moel ae common accounin an conol conceps, an he eive coniions have accounin meanin, linin soc vaiales in he alance shee wih he flow vaiales in (an elae o he income saemen. Key wos: equiy valuaion, eminal value, financial saemen analysis JL coes: G2, G3, M49 This pape has peviously een ciculae une he ile Hoizon Values in Company Valuaion. The helpful commens of Pee ason, Jennife Fancis, Føysein Gjesal, Pee Jenneen, Thoe Johnsen, Kenh Sosvi, Sefan Ya, an wo anonymous efeees as well as woshop paicipans a he UO Woin Goup on Financial Moellin, he Noweian School of conomics an Business minisaion, he Ohio Sae Univesiy, an he Socholm School of conomics ae aefully acnowlee. Financial suppo fom he conomic eseach Insiue an he Ban eseach Insiue, Socholm, Sween, is aefully acnowlee. Joaim Levin (cjl@hhs.se, Socholm School of conomics, P.O.Box 65, S-383 Socholm Coesponin auho Pe Olsson (polsson@us.wisc.eu, Univesiy of Wisconsin-Maison, 975 Univesiy venue, Maison, Wisconsin 5376

2 Inoucion This pape exploes seveal issues associae wih he calculaion of coninuin value fomulas use as hoizon values (o eminal values in company an equiy valuaion moels. Ou pimay focus is on claifyin he seay sae assumpion ha unelie he use of such hoizon values, an he coniions necessay o mae his assumpion opeaional. The eive coniions have inuiive accounin meanin an ae shown o uaanee inenal consisency in valuaion moels. The coniions fuhemoe uaanee ha popula equiy valuaion moels eive fom he PVD pinciple (pesen value of expece iviens, such as he esiual Income moel, he Fee Cash Flow moel an he Divien Discoun moel, yiel ienical esuls also when usin hoizon values. These moels ae heoeically equivalen, an ye lae-sample compaisons of he valuaion moels (Penman an Souiannis [998] an Fancis, Olsson an Oswal [2] show ha he moels yiel vasly iffeen esuls, even when hey ae ase on he same se of po foma financial saemens an all assumpions ae ienical. We show how his anomaly can e cause y seay sae coniion violaions. In equiy valuaion moels ase on foecase financial saemen aa (see, e.., Palepu, Bena an Healy [996] o Copelan, Kolle an Muin [994], one commonly foecass financial saemens fo a finie nume of yeas he explici foecas peio. Fo each yea a valuaion aiue (e.., fee cash flow o esiual income is calculae fom he financial saemen foecass. The hoizon value efes o he pesen value (a he hoizon of he valuaion aiue afe he explici foecas peio. Geneally, his valuaion appoach can e fomulae as: ( V V H s s PV V H s H ( ( whee: V is he esimae value (of a paicula valuaion concep a he valuaion ae H V is he hoizon (he las yea of he explici foecas peio is he valuaion aiue V PVH is he hoizon value is he iscoun ae Depenin on he valuaion aiue, fomula ( may nee a coecion o yiel he equiy value. So, fo example, will ne e an pefee soc e euce in he Fee Cash Flow moel, wheeas oo value of socholes equiy will e ae in he esiual Income moel. We will consie fou commonly use valuaion aiues: eanins, fee cash flows, iviens an esiual income. Fee cash flows, iviens an esiual income can e iecly use in valuaion moels ha ae fomally equivalen o he pinciple ha equiy value equals he pesen value of all fuue expece iviens. anins ae ofen use in less elaoae valuaion moels, someimes wih aiional assumpions (e.., an assume ivien payou aio. s Bealey an Myes [99, p.64] sues, he aionale fo usin a hoizon value is pamaic: Of couse, he [...] usiness will coninue afe he hoizon, u i s no pacical o foecas fee cash flow yea y yea o infiniy. The mos common meho of calculain hoizon values is o use a coninuin value fomula: V VH (2 PVH

3 whee: V PVH is he elevan hoizon value V is he valuaion aiue is he iscoun ae is he owh ae ( < To calculae (, one nees a foecas of V H ; his is ofen achieve y lein he valuaion aiue a ime H ow y, he owh ae: (3 PV V H ( V H When usin an expession such as (2 o (3 o calculae hoizon values, i is assume ha he valuaion aiue ows a a consan ae an ha he iscoun ae emains consan. The fac ha he hoizon value is ofen calculae usin a vey simple fomula oes no inicae ha i is unimpoan. On he conay, Copelan, Kolle, an Muin [994, p. 275] epo ypical values fo some inusies: fo a company in he oacco inusy he hoizon value accouns fo 56% of he oal company value, in he spoin oos inusy i is 8%, fo he ypical sin cae usiness he fiue is % an fo a hih ech company 25% (he fiues ae calculae usin a hoizon eih yeas ino he fuue fo he Fee Cash Flow moel. 2 The valuaion aiue eive fom he financial saemens fo yea H iscommonlyuseas numeao in he coninuin value (as in expession (3, someimes wih some ajusmens o nomalize he valuaion aiue o a level ha is eeme susainale in he pos-hoizon peio, possily wih owh. The level of heoeical jusificaion fo his vaies, u a eneal heme is a efeence o he seay sae concep in which he company emains qualiaively simila yea y yea afe he hoizon. Kaplan an uac [995, p. 64], e.., place a esicion on he eminal capial cash flow (hei valuaion aiue a he hoizon y sein epeciaion an amoizaion equal o capial expeniues, noin ha epeciaion an amoizaion canno excee capial expeniues in seay sae. The lae esicion visualizes, u oes no mae explici, ha hee is a lin eween he peceive easonailiy of he valuaion aiue a he hoizon an he unelyin funamenals as expesse in foecase financial saemens. jusmens mae (o no mae o he valuaion aiue use in he coninuin value calculaion can have a lae impac on he enie valuaion, so i is impoan how hese ajusmens ae mae. One can come up wih inuiive esicions, fo example he aove-menione coniion ha epeciaion an amoizaion no excee capial expeniues in seay sae; howeve, such inuiive esicions may e a-hoc an incomplee. Ou ojecive in his suy is o sues a moe sysemaic appoach, main explici use of popeies of he accounin sysem. In paicula we noe ha he ime seies of foecase financial saemens can e seen as a sysem of iffeence equaions. Seen in ha lih he seay sae concep can e mae opeaional y mahemaical analysis, whee all coniions necessay fo seay sae will e eive as iniial value coniions on he sysem of iffeence equaions. While he alea fo showin his may a imes e eious, he esul uns ou o e easy o implemen an, we hin, inuiively appealin. The inuiion is as follows: When a fim enes ino seay sae is qualiaive ehavio is expece o emain he same yea afe yea. Qualiaive ehavio can e mae opeaional y ecomposin i ino common accounin an conol conceps, such as pofi main, sales owh, pouciviy aios elain sales o capial, ec. The consancy of hese paamees ove ime is a necessay coniion fo seay sae 2

4 o pevail; i is no, howeve, sufficien. One also has o consie he ineacion of hese paamees, noin ha hei values canno e se inepenenly. Fuhemoe, paamee values mus e se such ha soc elaes o flow in a easonale manne in he foecase financial saemens. ll in all, hese ineepenencies quicly ecome complicae, an ou moelin can e seen as a way of ealin wih he complexiy. Ou analysis shows he elaions amon paamees an he associaions wih soc vaiales ha mus hol fo seay sae. Seay sae coniions mae in a echnical sense ecause hey ensue ha all implici assumpions ehin coninuin values ae fulfille. Moe funamenally, seay sae coniions ensue ha he foecase pefomance is sale. If seay sae coniions ae violae, he qualiaive ehavio of he company will chane afe he valuaion hoizon, an will eep chanin ove ime. Such chanes conaic he pemise fo usin a valuaion hoizon namely ha he company is expece o e sale a he hoizon, an hence eneae sale eanins, cash flows, ec. s we emonsae, even mino inenal inconsisencies can have a susanial impac on he final value esimae of a company. The seay sae coniions can also e useful in he pocess of eeminin a which poin in ime he hoizon iself shoul e se. The main esul is of a nomaive naue: all flows (income saemen an elae vaiales in he fis yea afe he hoizon shoul e ecie such ha coesponin socs (alance shee vaiales ow a he evenue owh ae. This ule ensues ha he company emains qualiaively simila houhou he pos-hoizon peio. This is also a necessay coniion fo eminal value calculaions in he Fee Cash Flow moel, he Divien Discoun moel an he esiual Income moel o yiel ienical esuls. Tha hese heoeically equivalen valuaion moels can yiel iffeen esuls even when hey ae ase on he same se of foecase financial saemens an all assumpions ae ienical is a souce of confusion oh in he lieaue an in he classoom. We show how seay sae coniion violaions can e he cause of such iffeences. Ou analysis povies a mehooloy ha is quie eneal an can e applie o any valuaion famewo ha involves foecass of fuue alance shee an income saemen aa. We o no claim ha all company valuaion moels mus inclue seay sae hoizon values. We o claim, howeve, ha he vas majoiy of valuaion exs an applicaions inclue his ype of hoizon values an ha i is heefoe of ea pacical impoance o have he seay sae issue hoouhly invesiae an implemenaion ouines fo seay sae evelope. The es of he pape is oanize as follows. In he nex secion, we escie ou mehooloy an selece moelin choices an efine he seay sae conceps associae wih each of he fou valuaion aiues we consie. Secion 3 eives he coniions necessay o achieve seay sae fo each aiue an fo he enie alance shee. Secion 4 aues he empiical impoance of he esuls, exemplifies y a case suy an iscusses some elae lae sample finins. Secion 5 explains he ansiion fom he explici foecas peio o seay sae an fuhe implemenaion issues. Secion 6 summaizes an conclues. 2 Teminoloy an Definiions We se up a valuaion moel fo he (seay sae peio, whee he company's qualiaive ehavio is expece o emain he same yea afe yea. We efine he company s alance shee an income saemen as follows: 3

5 sses Ne Woin Capial Ne Popey, Plan an quipmen De an quiy De Defee Taxes Goss PP ccumulae Dep. quiy evenues -Opeain xpenses -Depeciaion xpense -Inees expense -Taxes anins We fuhe efine he followin paamees. Many of hem ae aios, an he em aio analysis is someimesusealsooesciehisinofvaluaion: 3 a c i ne woin capial as % of evenues (sales oss PP as % of evenues (sales incease in efee axes as % of oss PP epeciaion expense as % of pecein yea s oss PP nominal owh ae, evenues (sales inees ae on e iscoun ae 4 p w opeain expenses as % of evenues (sales eiemens as % of pecein yea s oss PP ax ae e as % of alance shee oal (oo value The followin sae-vaiales ae also efine: evenues (sales in yea, 4

6 accumulaeepeciaionaheenofyea, T efee axes a he en of yea. We can now expess he alance shee an income saemen as funcions of he sae vaiales: sses Ne Woin Capial Ne Popey, Plan an quipmen a Goss PP ccumulae Dep. whee ( De an quiy De w a Defee Taxes quiy ( T c ( w( a T evenues -Opeain xpenses p -Depeciaion xpense -Inees xpense 5 iw a ( -Taxes 6 ( p iw( a anins ( ( p iw( a Some moelin choices ae saihfowa, such as efinin opeain expense as a pecenae of evenues. Ohes ae moe eaale in paicula he eeminaion of PP-elae iems, incluin epeciaion an eiemens, is no self-evien. The mehooloy in his pape lens iself o any specificaion, u o exemplify we have chosen a specificaion inene o esemle he veal exposiion in Copelan, Kolle an Muin [99, 994]. This has he avanae of iecly couplin ou analyical esuls o a valuaion oo well nown amon paciiones, suens an acaemics. Ou use of a sinle paamee o eemine ne woin capial implies ha all woin capial iems can e efine as a facion of evenues an, heefoe, ha hey in seay sae can e aeae ino ne woin capial, ovene y he same paamee. Goss PP is also eemine as a pecenae of evenues. I is hus assume ha i aes a sale amoun of woin capial an physical asses o eneae each olla of sales. ccumulae epeciaion is he pio peio s accumulae epeciaion plus he cuen peio s epeciaion expense minus he oo value of asses eie in he cuen peio. 5

7 Boo value of e is efine as a pecenae of he alance shee houh he paamee w, implyin ha he company ies o mainain a consan e-value aio in oo value ems. 7 ae leveae is a common assumpion in valuaion exs. mpiically, Fama an Fench [997] also show ha hee is a slow mean evesion o (fim-specific ae leveae. Hence, i seems easonale o moel leveae as consan in he seay sae peio. We ein y moelin his assumpion in oo-value ems, an lae eive he aiional coniions fo i o hol in mae value ems. Defee axes ae moele as a sepaae e iem. 8 Boo value of equiy is he esiual iem of he alance shee. To fuhe lin he income saemen wih he alance shee ove ime, we assume he clean suplus elaion hols. This means ha he chane in oo value of equiy equals eanins minus iviens, whee iviens ae efine ne of capial coniuions/wihawals. s menione aove, oo value of equiy is he esiual iem of he alance shee. Thouh he clean suplus elaion iviens ae efine o e he esiual iem of he enie equaions sysem, wih any excess capial isiue o equiy ownes. Fo simpliciy, he oo value of e is assume o equal is mae value. I shoul also e noe ha hee ae no excess maeale secuiies; we efine e as a ne financial iem. Cash neee o suppo opeaions is inclue in ne woin capial, howeve. The followin valuaion aiues can now e eive: anins, X : (4 ( ( p iw( a Fee cash flow, FCF : 9 (5 ( ( p ( T ( a a ( Diviens, DIV : (6 ( w( a T ( ( p iw( a (( w( a T esiual income, I : (7 ( ( p iw( a (( w( a T T We isinuish amon he followin ypes of seay sae: Paameic seay sae (PSS means ha he paamees esciin he company s evelopmen ae consan, e.., a consan evenue owh, a consan pofi main, ec. PSS is he weaes fom of seay sae, ecause no esicions ae place on he paamees ohe han ha hey emain consan. anins seay sae (SS means ha he company s peice eanins will ow a a consan ae. Moe pecisely, eanins in any yea aeesciey X ( X, whee is he consan evenue owh ae. Fee cash flow seay sae (FSS means ha he company s peice fee cash flow will ow a a consan ae : FCF ( FCF. 6

8 Divien seay sae (DSS means ha he company s peice iviens will ow a a consan ae : DIV ( DIV. esiual income seay sae (SS means ha he company s peice esiual income will ow a a consan ae : I ( I. Balance shee seay sae (BSS, finally, means ha all iems on he company s alance shee will ow a a consan ae. To oain seay sae in he valuaion aiues (SS, FSS, DSS, SS, i is no, mahemaically speain, a necessay coniion ha he company is in paameic seay sae. The evelopmen of he unelyin paamees may e shifin ove ime u in an offsein way so ha he valuaion aiue sill ows a a consan ae. We have neve seen such a moel popose neihe in exoos no in he eseach lieaue, howeve, so we will asac fom ha possiiliy an ea paameic seay sae as a necessay coniion. The inuiive inepeaion of seay sae as a company ha emains qualiaively simila yea y yea lens suppo, we hin, o his choice. The naue of he owh ae also eseves fuhe commen. Usin a coninuin value implies an infinie ime seies afe he hoizon. Hence i mus eally e he same owh ae in iffeen vaiales an aiues, an his owh ae mus e he evenue owh ae. If, e.., eanins wee o have a hihe owh ae han evenues, hen eanins woul afe a few yeas excee evenues. While his souns lie a fanasic usiness, i is haly ealisic. evese, if eanins ow slowe han evenues, hen pofiailiy will appoach zeo also no a ealisic seay sae scenaio fo a oin concen, since any aional owne woul eminae opeaions an ae he funs elsewhee. simila loic applies o he ohe aiues as well. 3 Seay Sae Developmen 3. Inoucion The company is expece o have eache a poin in ime whee he paamees ovenin he company s alance shees an income saemens ae consan, i.e. he paamees have eache hei seay sae values an he company is in paameic seay sae (PSS. In his secion, we aemp o invesiae une which coniions on he inpu paamees PSS will imply seay sae also fo he valuaion aiues (SS, DSS, FSS, SS. In Secion 2, hee sae vaiales wee efine fomin he followin sysem of iffeence equaions: (8 ( (evenues in yea (9 ( (accumulaeepeciaionaheenofyea ( T T c (efee axes a he en of yea By solvin he sysem, analyical expessions fo he sae vaiales can e oaine; fom hese, expessions fo he valuaion aiues will e eive. The soluion o he sysem of iffeence equaions is (see ppenix fo eails: ( ( (2 ( ( 7

9 (3 T T ( c, an T ae he iniial values of evenues, accumulae epeciaion an efee axes, especively. These iniial values fo he pos-hoizon peio ae iven y he foecass of complee financial saemens mae fo he explici foecas peio Seay sae in valuaion aiues anins seay sae (SS anins, ino (4 yiels: X, ae iven y expession (4. eaanin an susiuin expessions ( an (2 (4 X ( ( m z χ( γ wih he followin consans: X fo ( ( p m, ( iw a z X, χ ( iw, γ ( xpession (4 says ha fo SS o hol, eanins mus ow y. The exisence of he secon em in (4 implies ha eanins will no ow a he consan ae unless he secon em is zeo: (5 χ( γ O in ems of he oiinal paamees: (5a ( iw Two possiiliies fo coniion (5a o hol ae ule ou y assumpion: i (zeo inees ae an (% ax ae. This leaves wo possile coniions, one of which mus hol fo eanins o ow a he ae : (i all-equiy financin (w; o (ii (. The lef-han sie of coniion (ii is heowhinaccumulaeepeciaioninhefisyeaofheseaysae. Theih-hansieis epeciaion expense minus eiemens in he fis yea of he seay sae peio. Inuiively, his coniion esalishes he equie lin eween accumulae epeciaion (he soc vaiale an epeciaion-eiemens (he flows ha affec ha soc vaiale. We explain an elaoae on hese inepeaions a he en of his secion. Fee cash flow seay sae (FSS By susiuin expessions (8, ( an ( ino (5, he followin expession is oaine: 8

10 (6 FCF ( ( m z FCF fo wih he followin consans: ( ( p m, z FCF ( c a ( xpession (6 ells us ha fee cash flow seay sae is an immeiae consequence of he consancy of he inpu paamees; no fuhe paamee esicions ae equie. Compae o eanins, fee cash flow is hus consiealy less esice. 3 Divien seay sae (DSS eaanin expession (6, an susiuin expessions ( - 2 yiels: (7 DIV ( ( m z χ( γ wih he followin consans: DIV ( ( p, χ ( iw, ( γ m z DIV fo ( c a ( w a ( iw a The iviens expession (7 is simila o he eanins expession (4. This is no supisin, since iviens ae efine houh he clean suplus elaion. lhouh z iffes fo iviens vs. eanins, ha iffeence is ielevan fo puposes of esalishin seay sae; fo ivien seay sae o hol he same coniions as fo eanins seay sae apply. esiual income seay sae (SS Susiuin expessions ( - 3 ino expession (7 yiels he expession fo esiual income: (8 I ( ( m z ( χ ϑ( γ ( κ I wih he followin consans: ( ( p m, z I ( c κ, ( iw a ( w T ( γ, χ ( iw, ϑ ( w ( c a fo Fo esiual income o ow a a consan ae (SS, he followin coniion mus e fulfille: (9a ( χ ϑ( γ ( κ T O usin he oiinal paamees: 9

11 (9 (( iw ( w c (( iw ( w ( ( (( c T (( (( ( (( c T iw w We can now moe easily ienify a case whee (9 hols. sufficien coniion is: (9c ( an T ( c The fis coniion in (9c is he epeciaion lin seen fo eanins (an ivien seay sae. I ensues ha eanins ow a a consan ae. The secon esicion concens efee axes, an can e inepee as he aiional coniion neee o e ax efeals an oo value of equiy o ow a a consan ae. 4 Summay an inepeaions We can now summaize he seay sae coniions fo he iffeen valuaion aiues: T iue Fee cash flow Paamee esicion None anins ( o w Diviens ( o w esiual income (( (( ( (( c T iw w sufficien: ( an T ( c s soon as inpu paamees ae consan fee cash flow ows a a consan ae. Wih all-equiy financin, eanins an iviens equie no fuhe seay sae coniions. Fo esiual income, howeve, all-equiy financin is no sufficien fo seay sae. Mos companies have some e, so he moe eneal case (vali fo all financin policies is pehaps moe ineesin: (2a ( (2a T ( c fo eanins an iviens seay sae, aiional coniion sufficien fo esiual income seay sae. (accumulae epeciaion, (evenues an T (efee axes ae aleay iven (pincipally y he foecass fom he explici foecas peio. We conjecue ha one has some asis fo eciin on he value of he owh ae, wih a lowe seay sae oun ein expece inflaion. Fuhemoe, we fin i easonale ha one has an iea aou he amoun of fixe asses necessay o eneae a olla of sales, 5 poviin a value fo he PP-paamee. In expession (2a one is hen lef wih (,i.e. he epeciaion an eiemens paamees; in expession (2a he paamee ovenin efee axes, c, emains. Viewe in his manne, he coniions can e use o eemine paamees (such as o c

12 which may ohewise e elusive. The main impoance of he coniions, howeve, is moe inuiive. xpession (2a esalishes he seay sae epeciaion lin eween he alance shee an he income saemen. This ecomes cleae afe a efomulaion: (2 ( Insein expession (2 fo yiels: (2c The ih-han sie in (2c is he owh ae in accumulae epeciaion in yea. This owh ae mus e he same as he evenue owh ae. How his can e achieve is iven y expession (2a o (2: one can vay he foecas of epeciaion expense in yea ( an/o of eiemens in yea (. Opeaionally his can e one y vayin any of he paamees involve. This exemplifies a eneal feaue: The lef-han sie in (2a sans fo he owh in he soc vaiale in he fis pos-hoizon yea, i.e., he owh in accumulae epeciaion. The ih-han sie escies he elae flow vaiales, epeciaion expense ( an eiemens ( in he fis yea afe he hoizon. Similaly fo (2, he lef-han sie is he owh in efee axes, he owh in he soc vaiale, an he ih-han sie is he elae flow vaiale. In oh cases, he flows mus e ecie such ha he elae socs ow a he evenue owh ae. Noe ha he inuiion in ems of flows ein ecie o yiel a ceain owh ae fo he socs is quie eneal. Simila coniions will appea if we use iffeen moel specificaions Capial sucue issues In he pio secions we focuse on he seay sae coniions peainin o he valuaion aiue (he numeao in he coninuin value. The iscoun ae (which appeas in he enominao of (2 was no analyze, even houh he use of a coninuin value fomula also assumes ha he iscoun ae is consan. In eanins-ase valuaion moels, in he esiual Income moel an in he Divien Discoun moel he elevan iscoun ae is he cos of equiy, whichcanvaywihcapialsucue ecause of, e.., expece coss of financial isess an aency coss. 7 Cos of equiy also enes ino he weihe aveae cos of capial (wacc use in he Fee Cash Flow moel (whee in aiion he weihs fo he iffeen coss of capial ae iven y he capial sucue. Capial sucue is usually viewe o e in mae value ems. In accounin-ase valuaion moels we wo wih oo values, howeve, an i is heefoe of inees o examine he iffeence eween capial sucue in oo value ems an capial sucue in mae value ems. Hee, we will loo a he iffeence eween he oo value e aio an he mae value e aio. 8 ny iffeences eween he wo will e aiuale o iffeences eween he oo asse value an he mae asse value, since oo value of e equals mae value y assumpion. The mae value e aio in an aiay yea in he seay sae peio will hus e: (22a ω sses D (a mae value We nee an expession fo he mae value of he asse sie. The Fee Cash Flow moel povies his iecly. Since ou aim is o eive coniions fo a consan mae value capial sucue, i is appopiae o use a consan iscoun ae in he eivaion (in his case wacc:

13 (22 D ω sses ( w( a FCF ( ( m z w a WCC Susiuin expessions ( an (2 fo (22c ω w a an WCC FCF an eaanin: w ( ( m z FCF ( ( m z WCC WCC The fis of he wo ems in expession (22c is he seay-sae mae value e aio. The secon em is ime-epenen an oes o zeo only as ecomes lae. Thus we nee a paamee esicion o ensue ha he mae capial sucue is consan. Thee ae wo possiiliies: (i all-equiy financin (w; o (ii (. These ae exacly he same coniions ha wee eive in he pevious secion fo valuaion aiues ha inclue financin (i.e., all aiues excep FCF, so equiin a consan capial sucue will only impose fuhe coniions on he Fee Cash Flow moel he same coniions as we aleay ha fo eanins an iviens. No supisinly, hee is no escapin hese coniions whicheve moel one chooses o wo wih: wheeas FCF seay sae may equie fewe coniions, hose coniions will insea appea in he iscoun ae, he enominao in he hoizon value fomula. 3.4 Balance shee seay sae (BSS Fom he esuls in Secions 3.2 an 3.3, i is saihfowa o eemine he coniions neee o ensue ha each of he alance shee iems ows a a consan ae. This means ha he alance shee in elaive ems emains unchane. This woul e anohe inuiive seay sae efiniion. sses efiniion seay sae coniion Ne Woin Capial Ne Popey, Plan an quipmen Goss PP ccum. Depeciaion a whee ( FCF none ( De an quiy efiniion seay sae coniion De w a Defee Taxes quiy ( T c ( T c ( ( w( a T ( c ( T 2

14 If he paamees ae consan, i.e. he company is in paameic seay sae, i immeiaely follows ha: ne woin capial will ow a he consan ae, an oss popey, plan an equipmen will ow y. If coniion (2a hols (linin epeciaion soc an flow, hen: accumulae epeciaion will ow y ; ne popey, plan an equipmen will ow y ; e will ow y. If also coniion (2a hols (linin soc an flow of ax efeals, hen: efee axes will ow y, an oo value of equiy will ow y. To have BSS hee ae hus wo necessay coniions: ( an T ( c. These wo coniions have een iscusse ealie, an one can see ha hee is a uiin pinciple a wo: when esalishin a valuaion hoizon, one shoul foecas he flows so ha he coesponin soc vaiales ow a he evenue owh ae. One can also use his pinciple in evese: one shoul efine he valuaion hoizon as he poin in ime when i is eeme easonale ha he flows imply a owh ae in he soc vaiales equal o he evenue owh ae. This pinciple is quie eneal, an while we have shown i wih aios (he paamees hee, i woul e applicale also o ohe moels, whee one iecly foecass alance shee an income saemen iems wihou usin aios. The BSS concep is useful ecause i ensues ha he enie company emains simila yea afe yea, ha one has foecase an inenally consisen scenaio ha will pevail. In fac, we have a eneal seay sae whee he complee sysem of financial saemens is in seay sae: he valuaion aiues, he income saemen, an alance shee iems, as well as ohe elevan iems (lie capial expeniues an eiemens all ow a he same consan ae. 4 Does i all mae? We will now y o aue he empiical impoance of seay sae violaions houh a valuaion case suy an houh osevaions on empiical lae sample suies. The case suy, which is a nomal financial saemen analysis ype case, is he Sweish foesy company ssidomän B. The valuaion is mae as of Januay, 998. xplici foecass ae mae fo en yeas, wih each income saemen an alance shee iem foecase yea y yea. The ime afe ha (i.e. afe yea 28 is accoune fo houh a hoizon value. In his pape we concenae on he pa of he valuaion ha concens he issues involve in eeminin he hoizon value. Fom yea 28 an onwas he company is expece o have he followin seay sae paamee values: a5.%, 3.9%, c.26%, 4.7%, 4.%, i7.5%,.2%, p8%, 3.%, 28% an w25%. The foecass mae fo he explici foecas peio ive he iniial values of he sae vaiales: 43.5, 24.2 an T 3.9 (illion SK. We will efe o his as he ase case. The ase case paamee values fulfill coniions (2a an (2a, so we have a eneal seay sae (all alance shee iems ow a a consan ae as o all valuaion aiues. The equiy value of he company when enein seay sae a he en of yea 28 is 43.8 illion SK. 9 Now consie he eiemens paamee,. ssume ha one oes no use he seay sae easonin an coniion (2a o eemine i, u ahe loos a hisoical fiues fo he las few yeas. In he ssidomän case he hisoical fiue is.7% (compae o he seay sae fiue of 3.%. Hisoical fiues ae ofen suese as poxies fo he lon-em seay sae value of iffeen paamees, u sein.7% means ha he seay sae coniion (2a is violae. Is his hen of economic impoance in he valuaion? In ssidomän (wih.7%, usin he esiual Income moel wih a pepeuiy fomula yiels an equiy value of SK 44.2 illion a he hoizon. The Fee Cash Flow moel wih a pepeuiy yiels an equiy value of 55.9 illion a he hoizon, i.e. aoun 25% hihe. So he violaion of he seay sae coniion is no only a heoeical polem. I has non-ivial economic consequences, consequences ha ae iffeen fo iffeen valuaion moels. In his case, he violaion 3

15 has a much lae impac on he Fee Cash Flow moel han on he esiual Income moel, an he esiual Income moel is hus moe ous o his seay sae violaion. Thee ae wo easons fo his: Fis, he esiual Income moel places less eliance han he Fee Cash Flow moel on he eminal value, so eminal value polems cause y seay sae violaions will have less impac on he esiual Income moel. Secon, accual accounin places consains on he ehavio of esiual income, wheeas fee cash flows ae unconsaine y any epoin sysem. misae in foecasin he paamee will impac he capial expeniue foecas, an all of capial expeniues affec he FCF amoun use in he eminal value calculaion while only a poion (he epeciaion will affec he esiual income amoun. To fuhe illusae he effecs of seay sae violaion we can loo a ohe pefomance vaiales as well. Fiue has eun on (einnin-of-yea oo equiy, i.e., a measue of pofiailiy. Inuiively, one woul expec pofiailiy o e consan in seay sae. This is inee he case when 3.% (i.e. when coniion (2a is fulfille. No so when.7%, howeve: when seay sae is violae, hen he pefomance chanes afe he hoizon. n i is no only a one-ime chane; ahe chane ecomes he peominan feaue in he pos-hoizon peio. The.7% case ives a pofiailiy ha inceases fom he ase case level of 4.6% an appoaches 34.%. 2 eun on oo equiy 35.% 3.% 25.% 2.% 3.%.7% 5.%.% Yea Fiue - eun on oo equiy eun on oo equiy (O is a paiculaly oo inicao fo ou puposes. Inuiively, fuue pofiailiy is cenal o valuaion. Moe funamenally, O inclues he esiuals of he moele financial saemens: eanins (ne income is he enin iem in he income saemen an oo value of equiy is he enin iem in he moele alance shee. 2 n his is he ey: if he sysem (i.e., he moele financial saemens is in seay sae, hen he esiual of each financial saemen will e in seay sae, i.e. oh eanins an oo value of equiy will have he evenue owh ae. Consequenly, he aio eween eanins an oo value will e consan. One shoul also noe ha i is he accual accounin concep of eun on oo equiy ha seves as a chec on seay sae. Unoin he accuals (e.., o calculae FCF is no helpful in his espec. s we saw in secion 3.2 fee cash flow can ow a a consan ae even if seay sae is violae, an as we saw ealie in his secion he consequences of a seay sae violaion ae liely o e much moe sevee fo he Fee Cash Flow moel. 4

16 The esiual Income moel an he Fee Cash Flow moel ae oh heoeically equivalen o he Divien Discoun moel (iven clean suplus. Wih he fiues fom he example aove we have a siuaion whee fomally equivalen valuaion moels have he exac same inpu aa an assumpions. Bu he violaion of he seay sae coniion, inoucin a chanin pofiailiy, has iffeenial impac on he moels causin he moels o yiel iffeen values, in his case a iffeence of 25%. Thee is some confusion in he eae aou hese issues. On he one han mos papes an exoos aee ha he moels ae fomally equivalen. On he ohe han, empiical suies fin ha he moels yiel vasly iffeen value esimaes (see, e.., Penman an Souiannis [998] an Fancis, Olsson an Oswal [2]. 22 We claim ha one of he mos impoan an eneally uneconize easons fo such iffeences is he use of pepeuiy fomulas fo he hoizon value when seay sae equiemens ae violae. Consie Penman an Souiannis [998]. Thei sample is asically he enie populaion of fims on Compusa. Fuhemoe, hey use ealizaions o poxy fo foecass of iffeen accounin iems, which means ha he sample is y efiniion inenally consisen in he sense ha all valuaion aiues ae eive fom he same se of (ealize financial saemens. Ye he moels (usin coninuin-value ype hoizon values yiel compleely iffeen esuls. Usin an explici foecas peio of fou yeas, he esiual Income moel has an aveae oveesimaion of 6% of acual pice, wheeas he Fee Cash Flow moel on aveae uneesimaes pice y 76%. 23 Since he unelyin foecass ae ienical fo he valuaion moels (i.e. ealize financial saemen aa an he moels ae heoeically equivalen, he main eason fo he iffeences is he eaup of he infinie foecas hoizon ino an explici foecas peio an a hoizon value. s shown ealie, he moels will yiel ienical value esimaes only if he seay sae coniions hol a he hoizon. This is oviously no he case in Penman an Souiannis [998] (no in Fancis, Olsson an Oswal [2], so he esuls in lae sample empiical suies inicae ha seay sae violaions ae vey impoan. s in he excep fom he case suy epoe ealie in his secion, i seems ha he esiual Income moel is fa moe ous han he Fee Cash Flow moel o such violaions. 5 The Tansiion o Seay Sae We now move o he quesion of when seay sae is achieve. The analysis in Secion 3 pouce expessions fo he valuaion aiues an paamee esicions ha wee funcions of he iniial values of he sae vaiales,, an T. Tha analysis was a pue seay-sae analysis an as such was ecouple fom one vey impoan implemenaion issue: he ansiion o seay sae. xac eails aou how he iniial values of evenues, accumulae epeciaion an efee axes shoul e specifie wee omie. Inuiively, one woul lie o use he values of hese sae vaiales a H as iniial values, i.e. ae he values fom he financial saemens of he las yea in he explici foecas peio an se H, H an T T H. Unfounaely, he las in he moel complicae he issue somewha. To see why, consie accumulae epeciaion as example. ccumulae epeciaion in any yea is efine as he pecein yea s accumulae epeciaion plus he cuen peio s epeciaion expense minus he oo value of asses eie in he cuen peio. In ems of ou moel: (23 ( whee epesens oss PP a -. If, hen we nee oss PP a ime (- which in eneal canno e eemine as (, ecause in yea (-, which oes no elon o he PSS peio, he value of may iffe fom is seay sae value. Simila polems apply fo income saemen iems lie epeciaion expense an inees expense in fac, fo all iems ha ae moele usin lae values 5

17 of some vaiale. In ou moel he maximum la is one yea, so he polem can e aesse y efinin he hoizon H as follows: xplici foecass of full financial saemens ae mae unil an incluin yea H, whee yea H is he fis yea wih consan paamees. Fom he einnin of yea H an on, all paamees efinin he evelopmen of he company ae consan, i.e. he company is in paameic seay sae (PSS. yea H- yea H yea H H-2 H- H H valuaion hoizon ae explici foecas peio PSS peio (pepeuiy peio The iniial values ae hen efine as: (24 ( H H (25 H ( GH H (whee G H- is he foecase oss PP a he en of yea H- (26 T TH c TH Nex, consie he valuaion aiues. ememe ha hey in un conain lae values of he sae vaiales. s a consequence he seay sae expessions fo he valuaion aiues will only e vali fom ime H. This also means ha VH will eneally no equal ( VH an jus ain he valuaion aiue a he hoizon (yea H an insein i ino a hoizon value fomula (as in expession (3 can lea o sevee valuaion eos. 24 In summay, one yea las in oh he sae vaiales an in he valuaion aiues imply ha yea H is he appopiae ime fo measuin he inpus o he hoizon value fomula: V VH (2 PVH This means ha he foecasin moel (of financial saemens shoul inclue he fis wo yeas wih consan paamees (yeas H an H. Financial saemen analysis exoos eneally econize ha valuaion aiues ae lae funcions of he unelyin foecass of financial saemens (see, e.., Palepu, Bena an Healy [996, Ch. 6]. Howeve, he las in he sae vaiales epen on he paiculas of he foecasin moel an ae selom iscusse, even houh i is vey common in accounin-ase foecasin o moel a leas some of he ivin vaiales o inclue a la. I is ime o summaize he seay sae equiemens: (i he paamees shoul e consan fom ime H-, (ii he iniial value coniions shoul e fulfille a ime H, an (iii he hoizon value calculaion shoul e mae usin he valuaion aiue a ime H. Founaely, his is all easie one han sai: One nomally ses up foecass of all necessay iems in a speashee (income saemen, alance shee, pehaps FCF calculaions, ec.. If one uses aio foecass fo his as, hen he fis hin o ememe is ha he fis yea wih consan aios (paamees shoul e use as yea H, he hoizon, whee also he iniial value coniions mus e fulfille. This can easily e one houh, e.., he oal see funcion in xcel: he foecas of a aio ovenin an income saemen vaiale (o ohe flow iem shoul e mae such ha he coesponin soc vaiale (ypically in he alance shee ows a he evenue owh ae. The same pinciple applies also if one oes no use aios fo foecasin: hen he iec 6

18 foecass of income saemen iems shoul e mae such ha he coesponin alance shee iems ow a he evenue owh ae. If one oes no fin his a easonale assumpion, hen one shoul no use a hoizon value a ha ime, u ahe coninue o mae yea-y-yea foecass unil ealisic values fulfil he seay sae coniions. Thus, he seay sae coniions can e useful in eeminin he appopiae hoizon. The ohe hin o ememe is ha he aios shoul e consan fo wo yeas (one yea plus he maximum la in he valuaion moel efoe one uses a valuaion aiue as numeao in a coninuin value fomula. 6 Summay an Concluin emas This pape analyzes he ime-seies of foecase income saemens an alance shees as a sysem of iffeence equaions, an eives seay sae coniions ha oun he eminal value of he fim. The seay sae coniions ensue ha he company s foecase pefomance is sale afe he hoizon. The asic assumpion ehin he seay sae concep is ha he expece evelopmen of he company, as escie y he paamees, hols foeve (in infiniy. Inenally inconsisen paamee eeminaions may esul in an unealisic foecas of he company s pefomance afe he valuaion hoizon, which can sinificanly affec he value esimae calculae fo he fim. The seay sae coniions can hus seve oh as a chec aains inconsisencies eween paamee values, an as a ooli fo eeminin whee he hoizon shoul e se. n immeiae accounin inepeaion of he seay sae coniions is ha hey elae soc (alance shee o flow (income saemen an elae. The mehooloy use in his pape is eneal an can accommoae any foecasin moel ase on pojece financial saemens. The eneal pinciple is ha all flow iems in he pos-hoizon peio shoul e ecie so ha he coesponin soc iems ow a he consan evenue owh ae. This will yiel a eneal seay sae, which in un uaanees ha ey vaiales lie pofiailiy emain consan afe he valuaion hoizon. This is also a necessay coniion fo he Fee Cash Flow moel, he Divien Discoun moel an he esiual Income moel o yiel ienical esuls when implemenin hem wih hoizon values. 7

19 efeences Bealey,. an S. Myes. 99. Pinciples of Copoae Finance (4h eiion. New Yo: McGaw- Hill. Copelan, T., T. Kolle an J. Muin. 99 (994. Valuaion: Measuin an Manain he Value of Companies, s eiion (2 n eiion. New Yo: Wiley & Sons. Fama,. an K. Fench anins, Invesmen, Diviens, an De. Woin pape. Univesiy of Chicao an Yale Univesiy. Fancis, J., P. Olsson an D. Oswal. 2. Compain he ccuacy an xplainailiy of Divien, Fee Cash Flow an nomal anins quiy Value simaes. Jounal of ccounin eseach 38/, Kaplan, S., an. uac The Valuaion of Cash Flow Foecass: n mpiical nalysis. Jounal of Finance 5/4: Moiliani, F. an M. Mille The Cos of Capial, Copoaion Finance an he Theoy of Invesmen. meican conomic eview 48: Palepu, K., V. Bena an P. Healy Business nalysis an Valuaion: Usin Financial Saemens. Cincinai, Ohio: Souh-Wesen Collee Pulishin. Penman, S Synhesis of quiy Valuaion Techniques an he Teminal Value Calculaion fo he Divien Discoun Moel. Woin pape. Univesiy of Califonia a Beeley. Penman, S. an T. Souiannis Compaison of Divien, Cash Flow, an anins ppoaches o quiy Valuaion. Conempoay ccounin eseach 5: Zhan, X.-J Consevaive ccounin an quiy Valuaion. Woin pape. Univesiy of Califonia a Beeley. 8

20 9 ppenix - Deivaions Soluion o sysem of iffeence equaions ( ( In maix noaion: x x whee: x an ( The oos of he chaaceisic equaion ae λ an 2 λ. is iaonalize y P: ( P P P Susiuin u P x an u P x yiels he sysem u P P u, he soluion of which is: 2 ( c c u Susiuin ac yiels he soluion o he oiinal sysem: 2 2 ( ( ( ( ( c c c c c u P x an since he iniial values ae an, he complee soluion is: ( ( ( Inhesameway,hesoluionfoT is eive. Deivaion of eanins expession - equaion (4 The eanins expession (4 is oaine y eaanin equaion (4 an hen susiuin ( an (2 fo an -. Noe ha he expession is only efine fo (since i conains - values of sae vaiales ha ae efine wih iniial values a ime zeo. X ( ( [ ] iw a p

21 ( ( p ( ( iw( a ( iw ( ( p ( ( iw( a ( ( ( iw ( ( p ( ( ( iw( a ( iw ( ( iw ( ( ( p ( ( iw a ( ( iw This yiels equaion (4 fo : (4 X ( ( m z χ( γ wih he followin consans: X ( ( p m, ( iw a z X χ ( iw, γ ( Deivaion of fee cash flow expession - equaion (6 The eivaion is caie ou y eaanin expession (5 an main susequen use of expessions (8 an (: FCF ( ( p ( T T ( a a ( [( ( p a ] [ a ( ] T T ( ( a a ( ( ( p c ( ( p ( c a ( By usin expession (, we oain expession (6 fo : (6 FCF ( ( m z wih he followin consans: ( ( p m, FCF z FCF ( c a ( 2

22 Deivaion of ivien expession - equaion (7 The ivien expession (7 is eive y eaanin expession (6, an usin expessions (, ( an (2: DIV ( w( a T ( ( p iw( a [( w( a T ] [( ( p ( w( a ] [( w( a ( ( iw( a ] ( w [ ( iw ( w ] T T ( ( p ( ( [ w( a ] [( w( a ( ( iw( a ] ( w [ ( iw ( w ] c ( ( p ( ( [ w( a c] [( w( a ( ( iw( a ] ( w [ ( iw ( w ] ( ( p ( ( c ( w( a ( iw( a ( ( ( ( w ( w ( ( p ( [( iw ( w ] [( iw ( w ] ( ( c ( w( a ( iw( a ( ( w ( ( [( ( ] ( iw w [( iw] ( iw ( ( p ( ( c ( w( a ( iw( a ( ( ( ( w [( iw ( w ] ( ( ( p [( iw] ( iw ( ( [( ( ] ( ( [ ( ( ] ( c w a iw a w iw ( ( iw 2

23 22 xpession (7 is oaine fo : (7 ( ( ( z m DIV DIV γ χ wih he followin consans: ( ( p m ( ( ( a iw a w a c z DIV ( iw χ, ( γ Deivaion of esiual income expession - equaion (8 The esiual income expession (8 is oaine y eaanin equaion (7 an hen susiuin expessions (, (2 an (3: I ( ( [ ] ( ( [ ] T a w iw a p ( ( ( ( ( [ ]( [ ] ( ( [ ] T w iw a w iw p ( ( ( ( ( ( ( a w iw a p ( ( [ ] ( ( c c c T w iw ( ( ( ( ( ( ( c a w a iw p ( ( [ ] ( ( T c w iw This yiels equaion (8 fo : (8 ( ( I z m I ( ( ( T κ γ ϑ χ wih he followin consans: ( ( p m ( ( ( c a w a iw z I ( iw χ, ( w ϑ, ( γ, ( c κ

24 ppenix 2 - Seay sae coniions fo alenaive moel specificaions This appenix povies seay sae coniions fo wo alenaive moel specificaions ha have een suese in he lieaue. The alenaive specificaions iffe fom he one use in he main ex in how he invesmens in PP ae moele. Peviously, oss PP has een moele as a consan pecenae of evenues, enoe y he paamee (as in Copelan, Kolle an Muin [99]. In he fis alenaive hee, followin Palepu, Bena an Healy [996] an Copelan, Kolle an Muin [994], i is ne PP ha is insea moele as a pecenae of evenues, n. The secon alenaive, also suese in Copelan, Kolle an Muin [994], moels he capial expeniues as a pecenae of evenues, e. Fo hese alenaives he followin iffes fom he oiinal moelin in secion 2: lenaive (Palepu, Bena an Healy [996], Copelan, Kolle an Muin [994]: Ne Popey, Plan an quipmen: n Goss Popey, Plan an quipmen n ccumulae Depeciaion: ( ( n Defee axes: T T c( n lenaive 2 (Copelan, Kolle an Muin [994]: -- G, oss PP, is an aiional sae vaiale -- Ne Popey, Plan an quipmen: G Goss Popey, Plan an quipmen G G e G ccumulae Depeciaion: ( G Defee axes: T cg T By usin he same line of easonin as fo he oiinal specificaion, we e he followin coniions fo he alenaive specificaions: lenaive : iue Paamee esicion Fee cash flow ( ( n anins ( ( n Diviens ( ( n esiual income ( ( n an T ( c( n 23

25 lenaive 2: iue Paamee esicion Fee cash flow 25 ( G e( G e( G anins Diviens esiual income ( e ( e ( ( ( ( ( ( e an T ( ( ( ( ce In oh alenaive cases, no even FCF ows a a consan ae, unless an iniial value coniion is fulfille. Moeove, all-equiy financin is no lone a sufficien coniion fo havin a consan owh in eanins an iviens. In fac, oh hese specificaions (which ae he avocae y he mos ecen exoos in he aea ae aneous in his espec: coninuin value calculaions (ealess of which valuaion moel is use will e incoec, unless he iniial value coniion is fulfille. Tain capial sucue ino consieaion, hus complein he valuaion moels, he aove ales ive he coec coniions, excep fo FCF in lenaive 2, whee oh ( G e( an ( ( e have o e fulfille. ( Penman (997 povies a hoizon value appoach focusin on he measuemen eo of he accounin, whee fomula (2 aises as special case. The unelyin equiemen is ha he owh ae of he measuemen eo is consan eween any susequen se of S yeas (eyon H. In pacice, he polem is o eemine his S-yea owh ae. I can e infee fom he pojece consan owh ae of esiual income eyon he hoizon; he appoach sill equies seay sae assumpions. In his pape we sic o he sana applicaion wih -yea peio lenh (an -yea owh aes, u noe ha he analysis coul e pefome usin S-yea cycles insea wihou any effec on he inuiion of ou esuls. 2 Hoizon value polems ae liely o e mos sevee in valuaion moels ha place he laes weih on he hoizon values. Fo a iven company, he fee cash flow hoizon value is eneally lae han he iviens (o eanins hoizon value, which in un is lae han he esiual income hoizon value. 3 The paamees ae iniially esice as follows: >; c [, ]; (, ]; (, ; i>; >; p (, ; (, ]; [, ; w [,. Ne woin capial is hus unesice. Goss PP mus e posiive. The chane in efee axes can e zeo u no neaive in he pepeuiy peio, also new ax efeals uin a yea canno excee oss PP. leas some facion of he pio yea s physical capial mus e epeciae, u epeciaion canno excee %. The owh ae mus e posiive u smalle han he iscoun ae (since he company value woul ohewise e infinie. The inees ae is posiive, as is he iscoun ae. The opeain pofi main is posiive u less han %. Some facion of pecein yea s physical asses mus e eie, u one canno eie moe han %. The ax ae can e zeo u mus e smalle han %. De can e zeo, u he company is no allowe o e % e finance. 4 Cos of equiy,, fo iviens, eanins an esiual income; weihe aveae cos of capial (wacc fo fee cash flow. 5 Inees expense is calculae ase on einnin-of-yea e. 24

26 6 Noe ha a company canno mae losses in pepeuiy, so eanins efoe axes ae non-neaive in seay sae. This maes he moellin of axes saihfowa. 7 Defee axes ae explicily exclue fom he e ovene y w. The eason is ha ax efeals ae line o he fims opeaions an hus no eally an iem inclue in financin ecisions. Concepually, one may even hin aou efee axes as a neaive iem on he asse sie. 8 Moellin efee axes may seem somehin of an oveill in a sylize moel lie his. They seve a special pupose, howeve. In many counies ax accounin is isinc fom GP accounin in some aspecs. Thus we wan o moel he iffeence eween he povision fo axes in he (GP income saemen an acual axes pai. In a paicula yea his iffeence equals he chane in efee axes on he alance shee. xacly how his chane shoul e specifie epens on a couny s ax ules. Hee, we moel efee axes as hey ae efine in Copelan, Kolle an Muin [99], noin ha much moe exac couny-specific moels can e applie. 9 ( ax ae (evenues op. exp. ep ep chane in ef. axes chane in ne woin cap. capial expeniues. esiual income equals eanins minus he cos of capial imes he lae oo value of equiy. Palepu, Bena an Healy [996] iscuss owh ae assumpions, i.e., he value of in ou moel. In paicula, hey aue he insensiiviy of company value o sales owh assumpions if one assumes a compeiive equiliium. Noe, howeve, ha alhouh he company value may in some cicumsances e insensiive o he exac value of he owh ae, i will sill e necessay o have he same owh ae,, fo he iffeen aiues. 2 s menione in he inoucion, he ypical siuaion is ha full financial saemens ae moele explicily fo a limie nume of yeas, he explici foecas peio. The values of vaiales a he en of his peio a he hoizon ae in essence he iniial values of he pos-hoizon peio (see Secion 5 fo moe exac implemenaion eails. 3 Because fee cash flow is y efiniion inepenen of financin, he all-equiy financin esicion is ielevan. Fee cash flow also oes no inclue epeciaion, so epeciaion issues ecome ielevan (excep fo hei influence on axes pai, u ha effec is inclue in he z FCF consan. 4 Fo eanins seay sae an alenaive sufficien coniion was all-equiy financin (w. This will no suffice fo esiual income o ow a a consan ae, howeve. Wih all-equiy financin expession (9 euces o: ( ( c T. 5 Base on he analys s nowlee of he company, compaale companies, ec. 6 See ppenix 2 fo he esulin coniions fo wo alenaive moel specificaions fom he lieaue. 7 ven in a Moiliani an Mille [958] wol he cos of equiy is a funcion of leveae (while he weihe aveae cos of capial is consan. In a sein wih copoae axes, oh he cos of equiy an he weihe aveae cos of capial can vay wih leveae. 8 Thee is no pefee soc in he moel, so we nee only loo a he e aio (since he equiy aio is simply one minus he e aio. 9 Calculae usin, e.., he esiual Income moel: quiy value Boo equiy I / ( / usin he esiual income expession (7 / / ( (illion SK. Since he seay sae coniions ae fulfille, he Fee Cash Flow moel an he Divien Discoun moel ive exacly he same esul. See, e.., Zhan [998] fo an analyical poof. Noe ha while ha pape poins o he impoance of he seay sae concep in his espec, he pupose of ou pape is o evelop a eneal mehooloy o mae seay sae opeaional. 25

27 2 Fiue is eive y usin he iniial values of, an T as iven fom he explici foecas peio an usin he consan paamees o eive all income saemen an alance shee vaiales yea y yea afe he hoizon. This in un maes i possile o calculae O yea y yea. 2 ememe ha while in acual, ealize, financial saemens hese hins ae efine simulaneously houh oule-eny ooeepin, in valuaion we eal wih foecass of oh income saemen an alance shee, whee eanins ae he esiual iem of he income saemen an oo value of equiy is he esiual iem of he alance shee. 22 We sess ha his is no a ciicism. Boh Penman an Souiannis [998] an Fancis, Olsson an Oswal [2] ae pefecly epesenaive of common pacice in his ea (which is also hei pupose. 23 Penman an Souiannis [998, ale ]. The iffeences ae vas ealess of he lenh of he explici foecas peio. 24 In he ssidomän B case, his woul lea o an ovepicin y aoun 22%. 25 The inepeaion of his coniion is ha capial expeniues ( e ( minus eiemens ( G in he fis yea of he seay sae peio mus e ecie such ha oss PP ows a he evenue owh ae. 26