he Value Relevance of Alernaive Mehods of Accouning for Employee Sock Opions Wayne R. Landsman, Ken Peasnell, 2 Peer F. Pope 2 and Shu Yeh 3 April 24. Kenan-Flagler Business School, Universiy of Norh Carolina a Chapel Hill, Chapel Hill, NC 27599. 2. he Managemen School, Lancaser Universiy, Lancaser, LA 4YX, UK. 3. Deparmen of Accouning, Naional aiwan Universiy, aipei, aiwan, R.O.C. We are graeful o Jack Ciesielski of R.G. Associaes, Inc., for providing employee sock opion daa used in his sudy, and o he Cener for Finance and Accouning Research, Universiy of Norh Carolina, and he Financial Services Exchange for providing financial suppor. We also hank workshop paricipans a he 24 European Accouning Associaion Congress, he Universiy of Norh Carolina, and he Ohio Sae Universiy for helpful commens. Corresponding auhor: Wayne Landsman, Kenan-Flagler Business School, Universiy of Norh Carolina, Chapel Hill, NC 27599-349, 99-962-322, wayne_landsman@unc.edu.
he Value Relevance of Alernaive Mehods of Accouning for Employee Sock Opions Absrac We use he residual income valuaion framework o compare four approaches o employee sock opions (ESOs) accouning proposed by regulaors. Only an exension of he IASB s ED-2 mehod reaing he fair value of ESOs as a liabiliy and employing mark-o-marke accouning, resuls in accouning numbers ha accuraely reflec he diluion effecs of ESOs on curren shareholder value. he oher accouning mehods (APB-25, FASB Exposure Draf and SFAS- 23) lead o oversaemen of curren equiy value. Empirical value-relevance resuls are consisen wih wo predicions. Firs, esimaing equaions for mehods ha do no accoun for ESO diluion effecs are beer specified afer conrolling for opion fair value. Second, SFAS-23 accouning numbers have relaively low explanaory power for equiy values, when compared wih APB-25 and Exposure Draf specificaions including opion fair value and an IFRS 2 exension specificaion where he valuaion weigh on he change in he ESO liabiliy differs from oher income componens.
. Inroducion Curren accouning rules for employee sock opions (ESOs) for firms filing in he U.S. are governed by Saemen of Financial Accouning Sandards No. 23: Accouning for Sock- Based Compensaion (FASB 995, hereafer, SFAS 23). SFAS 23 requires firms o disclose in foonoes o he financial saemens he pro forma effecs on earnings of employee compensaion expense aribuable o amorizing he fair value of employee sock opions a he gran dae. If firms were required o recognize ESO expense, Credi Suisse Firs Boson (24) repors ha for S&P 5 firms dilued EPS including he effecs of fair value of ESO grans is 8%, 9% and 2% lower han repored EPS in 23, 22, and 2, respecively. he sheer magniude of his effec on income, as well as he recen poliical fallou associaed wih corporae managers cashing in on heir employee sock opions before large price declines, has raised he quesion of wheher firms should be required o recognize ESO expense o ensure ha invesors ge a rue picure of corporae performance. he pressure on he FASB in he U.S. o revisi SFAS 23 and o consider mandaing recogniion of ESO expense in income has been largely driven by he Inernaional Accouning Sandards Board (IASB), which issued in February 24 Inernaional Financial Reporing Sandard No. 2, Share Based Paymen (IASB, 24). IFRS 2 requires recogniion of employee sock opion expense using gran dae fair value. Alhough here are some minor differences beween IFRS 2 and SFAS 23, he key poin is ha all adopers of IAS (e.g., all European Union firms beginning in 25) would be required o expense employee sock opions using gran dae fair value beginning on January, 25. One monh afer passage of IFRS 2, he FASB issued SFAS 23 permis firms o use Accouning Principles Board Opinion 25: Accouning for Sock Issued o Employees (AICPA 972, hereafer APB 25), which allows firms o avoid recognizing employee sock compensaion expense if he opions ha are graned have a zero inrinsic value a he dae of gran.
an Exposure Draf, Share Based Paymen (FASB, 24), ha closely parallels he inernaional sandard. If he Exposure Draf is enaced as a sandard, i will require recogniion of employee sock opion expense using gran dae fair value. Corporae preparers, paricularly hose in high ech indusries ha use sock opions as a major componen of heir compensaion packages, are no keen on he requiremen o expense ESOs. hey raise wo poenially valid criicisms. Firs, firms ha issue employee sock opions do so because hey ge somehing in reurn, an inangible asse, in he form of he employees inellecual capial. 2 his asse is recognized neiher under SFAS 23 nor IFRS 2. he FASB acknowledged his in he exposure draf ha preceded SFAS 23, Exposure Draf: Accouning for Sock-Based Compensaion (FASB, 993, hereafer, Exposure Draf). he Exposure Draf would have required employers o recognize as an inangible asse he fair value of sock opions a he gran dae, o amorize his asse, and o record he asse s amorizaion as employee compensaion expense. In effec, SFAS 23 and IFRS 2 recognize an expense ha relaes o an off-balance shee asse, which creaes he impression ha ESOs impose a cos wihou providing any aendan benefi o he firm. Criics conend ha a more appropriae accouning reamen would be o record an asse a gran dae, as is he case in he Exposure Draf. Second, criics argue ha he oal compensaion expense recognized using gran dae ESO fair value may bear no relaion o he firm s oal economic deb o is employees a dae of exercise, i.e., he difference beween he cash proceeds, if any, and he cash he firm would receive if he shares were issued a marke price. Similarly, if he opions lapse unexercised, he curren shareholders enjoy a gain a he expense of he opion holders ha is no recognized in SFAS 23 and IFRS 2. An accouning policy ha () recognizes a gran dae he firm s 2 Consisen wih his, Hanlon, Rajgopal, and Shevlin (23) find a posiive empirical relaion beween ESO grans o he firm s op five execuives and fuure earnings. 2
obligaion o is employees as a liabiliy, raher han as a componen of equiy, and (2) includes he effecs of changes in a firm s obligaion o employees afer gran dae, would beer capure he economic impac of ESOs on a firm s equiy-holders. Alhough marking-o-marke his obligaion appears o be a odds wih he ways in which oher liabiliies are reaed in financial saemens, his is exacly he way he IASB in IFRS 2 and FASB in he March 24 Exposure Draf rea he liabiliy when ESO selemen akes he form of cash raher han he issuance of sock. I is also commonplace in accouning regularly o updae he amouns shown for long-erm liabiliies, such as sie resoraion coss. he purpose of his sudy is o examine how hese subsanially differen approaches o accouning for employee sock opions reflec he economic effecs of employee sock opions on curren equiy marke value. Firs, we explicily model he diluion effecs on shareholder value associaed wih employee sock opions using a dividend discoun model. We hen use he residual income framework o derive he implied equiy values in erms of accouning variables associaed wih four ESO accouning mehods. he mehods we examine reflec variaions of curren and proposed accouning sandards, i.e., APB 25, SFAS 23, he Exposure Draf, and an exension of IFRS 2 (hereafer he IFRS 2 exension) ha recognizes an ESO asse and an ESO liabiliy a gran dae, and changes in he fair value of he ESO liabiliy afer gran dae. Findings from he modeling analysis indicae ha only he IFRS 2 exension resuls in recognized balance shee and ne income amouns ha accuraely reflec he economic diluion effecs of ESOs on curren shareholder equiy value. he reason for his resul is ha of he four mehods, only he IFRS 2 exension adops wha Chrisensen and Felham (23, ch. 9) refer o as super clean surplus accouning, whereby income reflecs all gains and losses aribuable o exising shareholders. he findings also indicae ha he APB 25 and Exposure Draf mehods 3
resul in balance shee and ne income amouns ha oversae he value of curren shareholder equiy value. In paricular, hese wo mehods resul in accouning measures ha reflec he sum of curren equiy marke value and he value of he sock opions graned o employees. Alhough boh mehods saisfy clean surplus in ha all gains and losses arising from ransacions no involving equiy claimans pass hrough income, Chrisensen and Felham label hese mehods as mixed surplus accouning because he accouning amouns reflec he value of he claims of boh exising and poenial fuure equiy holders. Finally, we find ha he SFAS 23 mehod resuls in balance shee and ne income amouns ha when used in valuaion would also lead o he equiy value of exising shareholders being oversaed, alhough o a lesser exen han in he cases of he APB 25 and Exposure Draf mehods. he reason for his is ha SFAS 23 accouning amouns reflec he value of he claims of exising shareholders and a fracion of he claim of poenial fuure equiy holders. We es he value relevance of he four accouning mehods by esimaing wo separae cross-secional equiy valuaion models for each accouning mehod in which he measures of equiy book value and residual income are adjused o reflec he applicable accouning reamen. Boh equaions wihin each pair have equiy marke value as he dependen variable, bu he second adjused equaion includes opion fair value as an explanaory variable wih he resricion ha is coefficien equals negaive one. he effec of his resricion is o resae he dependen variable as he sum of equiy marke value and opion fair value. Based on our modeling, we make wo predicions. Firs, we make predicions concerning he imporance of including opion fair value in he adjused equaion. For he wo mixed surplus accouning mehods, APB 25 and Exposure Draf, we predic ha he adjused equaion will be beer specified han he unadjused model i.e., he one ha excludes opion fair value because a 4
valuaion based on equiy book value and residual income should equal equiy value of curren shareholders plus opion fair value. We canno make a similar predicion for he SFAS 23 mehod, because analysis shows ha a valuaion based on equiy book value and residual income should equal equiy value of curren shareholders plus a fracion of opion value. Finally, under he IFRS 2 exension mehod, because a valuaion based on equiy book value and residual income should equal equiy value of curren shareholders, here is no reason o expec he adjused equaion will be beer specified han he unadjused equaion. Second, we predic ha he esimaing equaion based on SFAS 23 equiy book value and residual income amouns should be less well specified han he adjused esimaing equaion for he APB 25 and Exposure Draf mehods, and he unadjused esimaing equaion for he IFRS 2 exension mehod. his predicion is based on our valuaion modeling showing ha he gradual recogniion of equiy under SFAS 23 gives rise o measures of equiy book value and residual income ha do no combine o correcly value eiher equiy marke value or he sum of equiy marke value and opion fair value. We es our predicions using a sample of S&P 5 firms wih available daa from 997-2, and esimae annual cross-secional valuaion models and pooled models wih year fixedeffecs. We esimae opion fair value using he Black-Scholes (973) opion pricing formula. o address he endogeneiy problem arising from regressing sock prices on opion fair values (Aboody, 996), we esimae opion fair value using an insrumen for equiy marke value consruced from a wo-sage regression. he resuls from our ess are consisen wih our predicions. In paricular, we find ha he adjused esimaing equaions are beer specified han he unadjused ones for he APB 25 and Exposure Draf models, bu here is no difference in relaive explanaory power beween he adjused and unadjused IFRS 2 exension esimaing 5
equaions. In addiion, he SFAS 23 esimaing equaion exhibis less relaive explanaory power han hose associaed wih he oher hree appropriaely adjused mehods. Our sudy builds on prior research examining he relaion beween ESO expenses and equiy marke values. Using an esimae of ESO fair values in he period before SFAS 23, Aboody (996) shows a negaive relaion beween his esimae and equiy marke values. Chamberlain and Hseih (999) and Aboody, Barh, and Kasznik (24) find a negaive relaion beween ESO expense and equiy marke values, where he former is based on SFAS 23 disclosures. A sudy ha relaes more closely o he curren one, Bell, Landsman, Miller and Yeh (22), compares he value relevance of accouning amouns based on wo accouning mehods, SFAS 23 and APB 25, for a sample of compuer sofware firms. In a concurren sudy, Li (22) exends he work of Chamberlain and Hseih (999) and Aboody, Barh, and Kasznik (24) by incorporaing he diluion effecs of employee sock opion grans, boh curren and expeced fuure, and provides empirical evidence of a negaive associaion beween equiy marke values and boh ousanding ESOs and expeced fuure ESO expenses. In anoher concurren sudy, Li and Wong (23) esimae equiy valuaion equaions, including an esimae of ESO fair value as a regressor in addiion o equiy book value and residual income, each of which is based on repored book amouns. he sudy finds ha equiy marke value reflecs he diluion of ESOs, providing evidence ha invesors ake ino accoun ha such opions dilue he claim o fuure dividends of curren shareholders. However, neiher Li (22) nor Li and Wong (23) addresses how curren and proposed ESO accouning mehods reflec ESO diluion effecs. he remainder of his paper is organized as follows. Secion 2 presens analysis of how he four differen mehods of accouning for employee sock opions affec he relaion beween 6
marke values and fuure accouning numbers. Secion 3 describes he empirical esimaing equaions. Secion 4 describes he sample daa. Secion 5 presens he empirical findings. Finally, secion 6 summarizes and concludes he sudy. 2. Analysis 2. Accouning for ESOs here are a leas four ways of accouning for ESOs: 3. APB 25 mehod: ignore hem, i.e., measure hem a inrinsic value. If he opions are exercised, paid-in capial is credied wih he cash received. 2. SFAS 23 mehod: credi paid-in capial employee sock opions (PIC opions) as and when ESO expense is recognized. Add he balance on his accoun o he cash received and include in paid-in capial as when he opion is exercised. If he opions are no exercised, leave he balance in PIC opions as a diry surplus componen of equiy. 3. 993 FASB Exposure Draf mehod: recognize an asse a gran dae equal o he fair value of he ESOs graned and amorize he asse over he vesing period as ESO expense. PIC opions is se equal o he value shown for he asse (pre-paid compensaion) and lef unchanged hereafer. As wih he SFAS 23 mehod, he balance on PIC opions is added o he cash received and included in paid-in capial as and when he opion is exercised and if no exercised lef as a componen of equiy. 4. Opions as a liabiliy (IFRS 2 exension) mehod: as under mehod 3, recognize an asse and amorize i bu rea he recognized fair value of he opion as a liabiliy. Mark-o- 3 Mos ESOs are graned a-he-money. Wha follows ignores he issue of wheher he opions have an exercise price ha is differen o he marke value of he underlying shares a gran dae since incorporaing his possibiliy merely complicaes he analysis wihou adding anyhing significan. 7
marke he liabiliy wih he value adjusmens being included in income. If he opion is exercised, he value of he opion plus he cash proceeds will equal he fair value of he equiy issued o employees. Eiher way, he liabiliy will be exinguished. Figure shows he accouning journal enries under each of he four mehods. Mehod conforms o he clean surplus principle, since all recognized gains and losses pass hrough income. Mehod 4 shares his propery. However, gain and loss recogniion differs under he wo mehods. Mehod is an example of wha Chrisensen and Felham (23, ch. 9) label mixed surplus accouning, whereby gains and losses are accouned for from he perspecive of he aggregae equiy claims including exising and prospecive equiy holders. Mehod 4 is accouned for on wha Chrisensen and Felham call a super-clean surplus basis. Under his mehod, income reflecs all gains and losses aribuable only o exising shareholders. We now develop a model showing he consequences of he alernaive accouning reamens of ESO s and he relaed implicaions for accouning-based valuaion. 2.2 Model 2.2. Model seup Consider a firm ha has graned an ESO o a manager a dae ha is exercisable a dae on paymen of he exercise price, X. No furher ESO conracs are expeced o be graned in he fuure. 4 A gran dae, he ne incomes in fuure periods, NI, =,2,, are uncerain, bu he marke s ne income forecass incorporae he anicipaed moivaional and reenion benefis ha led he firm o choose he manager s compensaion conrac. Dividends in fuure periods =,2,, will be shared beween exising shareholders (e) and he manager (m), 4 We make his assumpion o simplify he exposiion. Since none of he accouning mehods under consideraion involves immediae recogniion of opions ha migh be graned in he fuure, nohing is gained by inroducing such complicaions. We reurn o he valuaion implicaions of his simplificaion a he end of sub-secion 2.2.2. 8
wih he exising shareholders receiving e m d = d + d, () e d and he manager geing m d. Unil dae +, all he e dividends flow o he exising shareholders, i.e., d = d,,2,...,. If he ESO subsequenly = lapses unexercised, he manager ges nohing, i.e., d m =, = +, + 2,... We assume ha he value of he firm and he claims of e and m do no depend on he exercise price, X. 5 Cash flows and non-eso componens of accouning accruals are assumed o be unaffeced by he choice of accouning reamen of he ESO. he manager s ne ESO compensaion a exercise dae is max( MV m m m X,) = MV min( MV, X ), (2) where he (currenly uncerain) marke value of he shares ha migh be issued o m a ha dae is where E [.] m m = E [ d + ] MV, (3) = ( + r) is he expecaions operaor evaluaed using risk-neural probabiliies based on informaion available a dae and r is he (assumed consan) risk-free rae of ineres. he value of he ESO a gran dae a dae, OPV, can be expressed in erms of he discouned expeced value of (2): OPV = = E[ MV X MV m m min( MV ( + r) m m df( MV ) X ( + r), X )] X df( MV m ), (4) 5 he exercise proceeds are a source of capial o he firm. o avoid irrelevan complicaions, we make he sandard Modigliani-Miller ype of assumpion ha he firm is following an opimal invesmen sraegy such ha an addiional dollar of X resuls in a dollar increase in dividends, leaving he oal value of he firm unchanged. We make an equivalen assumpion regarding m s employmen conrac. An increase in X will resul in he ESO being worh less o m, bu we assume ha his would be offse by an increase in sraigh salary such ha boh m s uiliy and he value of e s shares are unchanged. 9
m where F( MV ) is he cumulaive risk-neural probabiliy densiy funcion associaed wih m MV. By he law of ieraed expecaions, we can use (3) o rewrie (4) as OPV m = = + E[ d ] E[ X ], ( + r) ( + r) (5) where X m E [ X ] = X df( MV ) is he exercise price muliplied by he probabiliy of he opion being exercised. As long as here is some probabiliy ha he opion will be exercised, he ESO will have a posiive value, i.e., OPV >. 2.2.2 Dividend-based valuaion he dae value of he exising shareholders claim can be expressed as: e e [ ] = E d MV. (6) = ( + r) Consisen wih Chrisensen and Felham (23), expression (6) can be redefined, using () and (3), in erms of he aggregae dividend flow expeced o accrue o boh curren and fuure shareholders, adjused for he diluion effec associaed wih he ESO gran. he ESO will only be exercised by m if MV m > X and he economic cos incurred by e will exceed X, he cash proceeds received by he firm from he exercise of opions. he correc diluion adjusmen is he expeced marke value of any shares subsequenly issued o employees. his can be capured explicily by wriing e MV in erms of oal dividends expeced o be paid o e and m, recognizing ha he subsequen issuance of new shares o m will dilue he claim of e by an amoun equal o m he expeced marke value of hose shares, i.e., by E [ MV ]: MV E[ d ] E[ MV ( + r) ( + r) m e = = ]. (7)
e Value per share can be compued by dividing MV by he number of curren shares ousanding, wihou any furher adjusmen for he diluion effecs of he ESO. shareholders, A measure of equiy value ha mixes or combines he claims of exising and fuure c MV, can also be derived. his measure discouns he projeced ne dividend flow beween he firm and all curren and prospecive equiy claimans, reaing new capial conribuions as negaive dividends: MV E[ d ] E[ X ]. ( + r) ( + r) c = = (8) I follows from () and (5) ha his combined value is equal o he sum of he marke values of exising shares and he ESO: MV c e m E[ d ] E[ d ] E[ X ] = + = ( + r) = + ( + r) ( + r) (9) = MV e + OPV. he valuaion expression equaion (9) can be used o obain an indirec esimae of by valuing boh e MV, c MV and OPV and aking he difference, bu his is a cumbersome procedure. Anoher way is o compue value on a dilued per share basis. However, he applicable diluion correcion o be used in per share calculaions is equivalen o assuming ha he proporion of e new shares o be issued under he ESO relaive o exising shares is equal o OPV / MV. 6 he direc mehod of valuing exising shares in equaion (7) requires subsequen share issues o hird paries, in his case m, o be measured a fair value. he indirec mehod of equaion (8) does no 6 Le e n and m n denoe he number of shares held by exising shareholders and employee shareholders, respecively, upon exercise of he ESOs. We can see from equaion (9) ha his requires his implies ha n n m e OPV =. MV e MV MV + OPV n n + n e e =. e e m
disinguish beween he value of equiy in issue and possible new shareholders in he fuure. Any such share issues are herefore measured a he resources flowing o he enerprise a ime of issue, i.e., he exercise price, X. Equaions (7) and (8) reveal he imporance of clariy in he reamen of fuure diluion in he valuaion of curren equiy claims. We show below ha he issue of idenifying he appropriae ne dividend sream has implicaions for he choice of ESO accouning mehod. Our analysis assumes ha no new ESO conracs will be issued in he fuure. However, fuure ESO grans a daes can easily be accommodaed in our analysis. o see his, assume he firm is expeced o issue addiional ESOs a daes i ( i =,2,...), wih projeced values fuure m E OPV i ]. Dividends payable o non-curren shareholders, d, will be shared beween he [ holders of he curren and fuure ESOs. Suppose he valuaion is carried ou as in equaion (8), based on he forecas ne cash flows o and from all equiy claimans., I can be shown by inducion ha he value of ha dividend sream will equal he presen value of all claims, including hose no ye wrien, i.e., [ ] fuure c e E OPV MV = MV + OPV +. () ( + r) One reason we ignore his aspec of valuaion is ha no proposed ESO accouning mehod involves recogniion of fuure ESOs. We rea fuure opion grans as an unmodeled source of i oher informaion in he empirical analysis, omiing he fuure E[ OPV ]. ( + r) i erm in (), since all our esimaing equaions based on he differen accouning reamens for ESOs are similarly affeced by his omied variable. In he remainder of our modeling, we herefore coninue o assume ha no furher ESO conracs will be wrien. 2
2.3 Residual income valuaion he residual income valuaion model allows he value of he firm o be wrien in erms of accouning fundamenals relaed o he creaion of shareholder wealh raher han dividends, which reflec he disribuion of wealh (Preinreich, 938; Edwards and Bell, 96; Peasnell, 982; Ohlson, 995). If he clean surplus accouning relaion holds hen he dividend discoun model can be expressed in erms of curren equiy book value and fuure residual incomes, as follows: where i BV and + i i i E[ RI ] MV = BV () = ( + r) i RI are he book value of equiy a ime and he residual income for period, respecively, using ESO accouning mehod i. Residual income is a random variable, defined as RI = NI rbv. i i i i NI is ne income for period using accouning mehod i. If accouning violaes he clean surplus relaion, fuure residual income flows would have o be adjused by expeced diry surplus flows in order o ensure ariculaion beween equaion () and he relevan dividend discoun model. he four alernaive accouning mehods described in secion 2. esablish differen measures for (componens of) equiy book value and accrued ESO-relaed expenses. We now consider he implicaions of applying he residual income valuaion model o iems measured under he accouning alernaives. Specifically, given ha he alernaive accouning reamens adop differen perspecives on he inclusion of ESO-relaed accouning iems, we consider he relaion beween value esimaes based on he residual income valuaion model and he value of 3
he underlying claims of owners and managers. his analysis has implicaions for he specificaion of he empirical ess ha follow in secion 3. Differences in residual income-based value esimaes may arise because of differences in he magniude of recognized equiy book value, or differences in he iming or magniude of income, or boh. Opion expense is no charged in arriving a ne income under mehod. Opion expense under accouning mehods 2, 3 and 4 is based on he fair value of he ESO a gran dae ( OPV ) apporioned over he -year vesing period. We assume opion expense is compued on OPV a sraigh-line basis, wih being allocaed o each period. Equiy book value differences arise depending on wheher he accouning mehod recognizes an ESO-relaed pre-paid compensaion asse and because of differences in he classificaion of he associaed opion as an equiy accoun or a liabiliy. No asse or opion credi is recognized a dae under mehod 2 (SFAS 23), in conras o mehods 3 and 4 (Exposure Draf and IFRS exension). he amoun iniially recognized as a pre-paid compensaion asse under mehods 3 and 4 equals OPV. he corresponding credi is reaed as equiy under mehod 3 and as a liabiliy under mehod 4. here are several implicaions for he residual income model of he differen ways of accouning for ESOs. In mehods 3 and 4, he impac of he recogniion of an asse ha is subsequenly amorized is sraighforward. he recogniion of he pre-paid compensaion asse simply changes he balance beween curren book value and fuure residual income. Under mehod 4, he credi arising from recogniion of he asse a gran dae is reaed as a liabiliy, implying ha equiy book value a ha dae is idenical o mehod (APB 25), where no asse or liabiliy is recognized. he difference beween he wo mehods appears in he sreams of fuure residual incomes and (we shall see laer) in he resuling presen values. Mehods 2 and 3, on he 4
oher hand, rea he opion accoun as a form of paid-in capial. he only difference beween he wo mehods is ha he equiy builds up slowly under mehod 2 (wih nohing being recognized a gran dae), whereas i is all recognized a gran dae under mehod 3. herefore, equiy book value under mehods 2 and 3 differ a gran dae from he equiy book value amouns repored under mehods and 4. We now examine he consequences of applying he residual income valuaion model () o equiy book value and projeced residual income flows obained under he four accouning alernaives. Our main objecive in his secion is o show how esimaed value obained from he residual income model relaes o he value of curren equiy ousanding. Mehod Mehod is he benchmark model where he accouning sysem recognizes no ESO expense, asse or liabiliy, i.e., APB 25. he oher hree accouning alernaives can be relaed o he relevan accouning numbers obained under mehod. We assume ha he ne income flows are linked o he underlying dividend flows and equiy book values by assuming ha he clean surplus relaion holds in his base accouning sysem, i.e., changes in equiy book value equal ne income less dividends paid. However, noe ha for valuaion purposes dividend policy irrelevance is assumed o hold. Any exogenous change in he iming of dividend paymens will no affec he value of he firm because he firm and equiy claimans are assumed o be able o borrow and lend a he same cos of capial. he value of he firm obained by applying expression () o he residual income flows under mehod is as follows: + E[ RI ] MV = BV (2) = ( + r) 5
where ( d X ) + ( BV BV for = RI = NI rbv and NI =. Subsiuing he ne d + ( BV BV for income and equiy book value values for mehod ino equaion (2) and canceling and collecing erms gives: MV E ( + r) = = [ d ] E [ X ] ( + r). (3) Valuaion expression (3) is idenical o he value obained using he mixed surplus dividend discoun model in equaion (8). We herefore know from (9) ha MV = MV = MV + OPV. Since OPV mus be posiive, applying he residual income valuaion model o accouning numbers prepared under mehod over-esimaes he value of curren equiy. his is obvious, given ha mehod ignores sock opions in recognized ne income and equiy book value. Noe ha mehod applies wha Chrisensen and Felham (23, p.294) label as mixed surplus because he accouning reflecs dividends flowing o exising and poenial fuure equiy holders. c e Mehod 2 In he firs periods, ne income under mehod 2 differs from ne income under mehod by an amoun equal o he recognized opion expense. However, as can be seen in Figure, he credi associaed wih he opion expense is included in paid-in capial. he wo enries herefore cancel and he equiy book value under mehod 2 is always he same as equiy book value under mehod,i.e., BV = ( =,, ). his implies ha he capial charge levied o arrive a 2 BV residual income is he same under he wo mehods. I herefore follows ha mehod 2 residual 6
incomes will be less han heir mehod counerpars by an amoun equal o he opion expense: RI =. As a resul, use of ESO mehod 2 accouning numbers in () yields: 2 RI OPV MV 2 = MV = MV e = OPV ( + r) ( + r) + r OPV. (4) ESO accouning mehod 2 recognizes opion equiy over ime, as a by-produc of recognizing opion expense. Generally, he resuling valuaion provides an esimae of neiher he e MV nor MV e + OPV. Only in he special case where r = will MV 2 e = For r >, MV > MV. 2 e MV. More generally, 2 2 MV is an increasing funcion of boh r ( MV / r ) and ( MV / ) 2 > > e 2 e and falls wihin he range, MV MV < MV + OPV.. he boundary o which 2 MV is closes will vary from case o case. However, for opion grans where = 5 (a ypical opion gran vesing period), 2 MV will be closer o e MV han o OPV MV e + as long as r is less han 28.6%. hus, empirically we expec mehod 2 o yield a value esimae closer o e MV. Mehod 3 Ne income under mehod 3, he Exposure Draf mehod, is he same as under mehod 2. On he oher hand, he immediae recogniion of an asse gives rise o a credi ha is reaed as equiy under mehod 3, hus giving rise o a difference in equiy book value a dae under he 3 2 wo mehods, i.e., BV = BV + OPV = BV. his difference in book values diminishes wih 3 + ime, as he ESO asse is amorized, such ha BV = BV + OPV ( ). A ime, he asse is 7
3 fully amorized and BV =. he residual income sream reflecs boh he amorizaion BV charges and he exra (bu diminishing) equiy book value. Applying valuaion expression () o he equiy book value and residual income flows, yields: MV 3 2 OPV + = MV r = ( + r) ( + r) ( + r) = MV + OPV r r = MV. OPV 3 he resul is he same as wih mehod, i.e., MV = MV e + OPV. Mehod 3 resuls in an overesimae of he value of exising equiy bu correcly values he oal of he claims of e and m. As wih mehod, mehod 3 is a form of mixed surplus accouning because i reflecs dividends flowing o exising and poenial fuure equiy holders. (5) Mehod 4 Under mehod 4, he IFRS 2 exension mehod, an asse is recognized immediaely and he associaed credi is reaed as a liabiliy. As a consequence, dae equiy book value is he same as under mehod because he asse and liabiliy fully offse each oher. he asse is amorized in he same way as under mehod 3, bu ne income also includes gains and losses on marking-omarke he liabiliy: NI 4 + ( BV 4 4 = d BV = NI OPV ) OPV, (6) 8
where OPV = OPV OPV represens he change in he marke value of he liabiliy. he equiy book values of mehods and 4 diverge during he vesing period by he accumulaed charges agains ne income: 4 BV = BV OPV OPVs, =,2,,-. (7) s = As shown in Figure, a dae, he marked-o-marke book value of he ESO liabiliy plus he exercise proceeds will equal he marke value of he shares issued o m: MV m = OPV = OPV + = OPV. (8) I can be seen from (7) and (8) ha equiy book values under mehods and 4 are equal a vesing dae and hereafer: BV 4 + s m = BV + s OPV OPV + MV = s =,, (9) = BV + s. he residual income valuaion rule can be applied, using equaions (6), (7) and (9), as follows: MV 4 = BV = BV + 4 = + + + = = 4 E[ RI ] ( + r) E [ RI E[ RI ]. ( + r) OPV ] OPV r OPV ( OPV ( + r) OPV ) (2) Collecing erms in (2), we know from our resuls for mehod ha 9
MV 4 = BV = = + = E[ RI ] OPV ( + r) E[ d ] OPV. ( + r) (2) Insigh ino his resul can be obained by recalling ha all he ESO expenses and gains and losses on he ESO liabiliy are accouned for on wha Chrisensen and Felham (23) refer o as he super-clean surplus accouning basis, whereby he accouning reflecs dividends flowing only o exising equiy holders. In which case, i follows ha mehod 4 will yield an esimae of value ha is a funcion of d and 4 e MV. Equaion (2) implies ha MV = MV. m Mehod 4 is he only one of he four accouning mehods considered ha provides an unbiased esimae of he value of exising equiy. Equiy is recognized if (and only if) new shares are issued, and hese are hen accouned for a marke value. Such super-clean accouning guaranees ha residual income is on a proprieary basis relevan o he valuaion of shares in issue. 3. Empirical Specificaion and Predicions 3. Esimaing Equaions he residual income valuaion models in secion 2 sugges ha for models and 3, equiy marke valuaion equaions based solely on equiy book value and residual income applicable o each mehod will be incorrecly specified unless an esimae of he opion fair value is added o equiy marke value. he adjusmen for mehod 2 is more complex, since a valuaion based on equiy book value and residual income should equal equiy marke value plus a fracion of opion value, rendering a precise predicion difficul. Because a valuaion based on equiy book value 2
and residual income should equal equiy marke value under mehod 4, no adjusmen should be necessary. o es hese predicions, we esimae he following four pairs of equaions, and compare he relaive explanaory power of each se of regressors using an F-es because each of he pairwise comparisons is beween nesed models. Following he sandard residual income valuaion framework, each esimaing equaion includes a measure of equiy book value and curren period residual income applicable o he relevan ESO accouning mehod. 7 For model, based on accouning for ESOs under APB 25, we have he following empirical models: MVE i = α + α RI + α BV + ε (22) i 2 i i MVE i ' i 2 i i i = α + α RI + α BV OPV + ε, (22 * ) where RI is abnormal earnings under model and equals NI i rbve ; NIi equals ne income before exraordinary iems and disconinued operaions for fiscal year ; 8 of common equiy a he end of fiscal year ; ousanding a he end of fiscal year ; BVEi is he book value MVEi is he marke value of common shares OPV i is an esimae of ESO opion fair value (described ' below) a he end of fiscal year ; and ε i and ε i are error erms; and he i and subscrips denoe 7 Because our primary concern is wih he relaive explanaory power of regressors associaed wih differen mehods of accouning for ESOs, we make no predicions regarding he magniudes of equiy book value and residual coefficiens across he various specificaions. However, in our discussion of he resuls, we assess heir reasonableness, including heir signs, and compare heir magniudes wih hose from exan research. We noe ha he Ohlson residual income valuaion model suggess ha oher informaion will generally be relevan in explaining equiy values when prices lead earnings. 8 Bell, Landsman, Miller, and Yeh (22) poin ou ha alhough defining residual income based on ne income before exraordinary iems and disconinued operaions violaes he clean surplus assumpion in Ohlson (995), i eliminaes poenially confounding effecs of large one-ime iems and is consisen wih prior empirical research (e.g., Barh e al. 999, 2; Dechow e al. 999; Hand and Landsman, 2). Ohlson (999, 6) concludes ha his approach is jusified in empirical work because one-ime iems are likely o have limied forecasing abiliy. 2
firms and years, respecively. 9 Following Dechow e al. (999), Barh, Beaver, Hand, and Landsman (999), and Bell, Landsman, Miller, and Yeh (22), we se he expeced rae of reurn on book value of common equiy, r, a 2 percen, he long-erm reurn on equiies, in hese and all subsequen valuaion equaions. he error erms reflec oher informaion as well as random error. For ease of exposiion, we use he same noaion for coefficiens across alernaive pairs of valuaion equaions. Noe ha by resricing he coefficien on OPV o be in equaion (2 * ) he dependen variable in ha equaion is implicily he sum of MVE and OPV. Based on he residual income valuaion in secion 2.3, we predic ha equaion (22 * ) will be beer specified han equaion (22) because equiy book value and residual income equal equiy value of curren shareholders plus opion fair value. For accouning mehod 2, based on he SFAS 23 mehod of ESO accouning, we have: MVE i = α + α RI + α BV + ε (23) 2 2 2 i 2 i i MVE i 2 2 2' = α + α RI + α BV OPV + ε, (23 * ) i 2 i i i 2 2 where BV = and RI = RI OPIONEXPENSE. Similar o oher earnings componens, BV OPIONEXPENSE is an afer-ax measure of ESO expenses, measured as NI less afer-ax SFAS 23 Pro Forma Earnings, which is aken from he SFAS 23 disclosures. OPIONEXPENSE corresponds o OPV in he model. As in equaion (22 * ), he coefficien on OPV is resriced o be in equaion (23 * ), and he dependen variable in ha equaion is implicily he sum of MVE and OPV. Based on he residual income valuaion in secion 2.3, we hesiae o predic wheher equaion (23 * ) will be beer specified han equaion (23). 9 Following prior research (e.g., Barh, Beaver, Hand, and Landsman, 999), each valuaion equaion we consider includes inerceps and error erms o allow for he valuaion effecs of unmodeled oher informaion. 22
equaions: For model 3, based on he FASB Exposure Draf, we have he following esimaing MVE i = α + α RI + α BV + ε (24) 3 3 3 i 2 i i MVE i 3 3 3' i 2 i i i = α + α RI + α BV OPV + ε, (24 * ) where 3 BV = BV OPIONEXPENSE + OPIONEQUIY, s= s 3 = s s= RI RI OPIONEXPENSE r( OPIONEQUIY OPIONEXPENSE ). s= OPIONEXPENSE is he accumulaed amorizaion of he ESO asse a ime and r( OPIONEQUIY OPIONEXPENSE ) is he addiional capial charge arising from he s= s unamorized ESO asse. OPIONEQUI Y is he sum of amouns credied o equiy as of ime resuling from ESO grans. Noe ha OPIONEQUIY is fixed a dae of gran and is, herefore, measured a hisorical cos. In conras, OPV is marked-o-marke every accouning period. As in equaions (22 * ) and (23 * ), he coefficien on OPV is resriced o be in equaion (24 * ), and he dependen variable in ha equaion is implicily he sum of MVE and OPV. Based on he residual income valuaion in secion 2.3, we predic ha equaion (24 * ) will be beer specified han equaion (24) because equiy value of curren shareholders plus opion fair value depend on equiy book value and residual income. Finally, for model 4, based on he IFRS 2 exension mehod of ESO accouning, we have, MVE i = α + α RI + α BV + ε (25) 4 4 4 i 2 i i MVE i 4 4 4' i 2 i i i = α + α RI + α BV OPV + ε, (25 * ) 23
where 4 s Σ s s s= s= BV = BV OPIONEXPENSE ( OPIONLIAB OPIONLIAB ) + s= ( FV _ ESO OPIONS _ EXERCISED ), s s RI 4 RI OPIONEXPENSE ( OPIONLIAB OPIONLIAB ) = and r[ OPIONEXPENSEs Σ( OPIONLIABs OPIONLIABs )], s= s= OPIONLIAB is he sum of amouns recognized as liabiliies as of ime resuling from ESO grans. Noe ha OPIONLIABis simply OPV; we adop he convenion of referring o i as a liabiliy o reinforce he noion ha under he IFRS 2 exension mehod, he credi a gran dae is o a liabiliy accoun, and he liabiliy is hen marked-o-marke. he amoun OPIONLIABs s OPIONLIAB is a gain or loss iem resuling from changes in he fair values of ESO liabiliy subsequen o he gran dae. FV _ ESOs is he weighed average fair value of ESOs exercised a ime s, and OPIONS _ EXERCISEDs is he number of ESOs exercised a ime s. When ESOs are exercised, equiy book value under Mehod 4 increases by he fair marke value of he shares issued, which equals he balance of OPIONLIAB and he cash received (which is already included in mehod equiy book value). In conras o he firs hree models, including OPV as on an explanaory variable in equaion (25 * ) should no improve upon he correc residual income specificaion given by equaion (25) and could lead o a deerioraion in specificaion by adding noise o he esimaing equaion. hus, we predic no difference in model explanaory power beween equaions (25) and (25 * ). I is imporan o noe ha: BV 4 = BV 3 OPIONLIAB. (26) 24
his follows because, prior o exercise, amoun of he sum of he changes in when ESO are exercised or expire, OPIONLIAB and OPIONEQUI Y differ by he OPIONLIAB ha are included in income under Mehod 4; OPIONLIAB is closed ino book equiy and equaion (24) sill holds. hus, equaion (26) permis measuremen of equiy book value under Mehod 4 wihou having o calculae all of is componens, paricularly he number of opions exercised or expired. In addiion o he pairwise comparisons of he esimaing equaions corresponding o each of he four mehods for accouning for ESOs, we make he furher predicion ha he esimaing equaion based on SFAS 23 should be dominaed by each of he oher hree mehods, appropriaely adjused o reflec wheher opion fair value should be included as an implici addiion o he dependen variable, MVE. his predicion is based on he observaion in our residual income valuaion modeling which shows ha he gradual recogniion of equiy under SFAS 23 gives rise o measures of equiy book value and residual income ha equal neiher MVE nor MVE plus OPV. hus, we also predic ha equaions (22 * ), (24 * ) and (25) will each be beer specified han eiher equaion associaed wih model 2, equaions (23) and (23 * ). o es hese predicions, we compare he relaive explanaory power of each se of regressors based on he Vuong (989) likelihood raio es, which permis comparison of he explanaory power of wo alernaive non-nesed models, wihou assuming under he null ha eiher model is he correc model. We esimae cross-secional regressions for equaions (22) hrough (25) for 997 hrough 2, as well as pooled regressions for each equaion using year fixed-effecs. We repor regression -saisics using Whie- (98) correced sandard errors and consider -saisics wih associaed wo-sided p-values less han.5 as saisically significan. We do no repor 25
consans from eiher he pooled fixed-effecs or he annual regressions. All equaions are esimaed using unscaled daa (Barh and Kallapur, 996). 3.2 Measuremen issues Unlike OPIONEXPE NSE, which can be deduced as he ne of repored ne income and SFAS 23 pro forma ne income, he oher opion value-based variables, OPV (OPIONLIAB) and OPIONEQUI Y, mus be esimaed. OPIONEQUI Y is he sum of gran dae ESO fair values, compued as he accumulaion since 995 of he number of ESOs graned in each year muliplied by he weighed-average fair value per share a gran dae. A complicaion is ha SFAS 23 pro forma ESO expenses and relaed disclosures are based on ESOs graned from 995 and forward bu he disclosures do no provide separae oals for he number of opions ousanding arising from grans before and afer 995. Because we esimae he opion valuebased variables using he oal number of opions graned and ousanding as of a paricular balance shee dae, here is an inconsisency beween measuremen of he income saemen variable, 4. OPIONEXPE NSE, and he measuremen of equiy book value under mehods 3 and Alhough Barh and Kallapur (996) provide convincing reasons o esimae cross-secional equiy valuaion models similar o ours using unscaled daa, here are several addiional reasons o avoid esimaing our equaions on a per share basis. Firs, our heoreical analysis suggess ha equaions using differen accouning mehods for ESOs require differen share amouns as scalars. his would amoun o hrowing away he baby wih he bah waer in ha we could no longer carry ou any meaningful ess of he valuaion effecs of differen mehods of accouning for ESOs. Second, as noed in foonoe 3, deflaion for all bu mehod 4 would require esimaing addiional shares relaing o ESOs based on OPV. his would needlessly inroduce he poenial of addiional measuremen error in he affeced models. here are wo addiional inconsisencies in he measuremen of equiy book value and residual income for all bu Mehods and 2. he firs arises from he fac ha OPIONEXPENSE is on an afer-ax basis, and we ignore income effecs in our measuremen of equiy book value under Mehods 3 and 4. In principle, equiy book value under hese wo mehods should reflec accumulaed he same before-ax OPIONEXPENSE charge. he second is ha OPIONEXPENSE reflecs adjusmens for anicipaed forfeiures, bu book equiy under Mehods 3 and 4 canno be adjused appropriaely because we do no have deails of he forfeiures. We do no expec hese sources 26
We use he Black-Scholes (973) opion pricing model o esimae fair value of ESOs ousanding a each balance shee dae so ha we can consruc OPV (OPIONLIAB) using disclosed parameer amouns aken from he SFAS 23 disclosures. he relaed parameers we use are:. Exercise price of he opion: he curren year s weighed exercise price for all ousanding ESOs. 2. Expeced sock-reurn volailiy: repored expeced sock-reurn volailiy for opions issued in he curren year, aken from he SFAS 23 disclosures. 3. Risk-free ineres rae: repored risk-free ineres rae for opions issued in he curren year, aken from he SFAS 23 disclosures. 4. Expeced dividend yield: repored expeced dividend yield for opions issued in he curren year, aken from SFAS 23 disclosures. 5. ime o mauriy: repored expeced life for opions issued in he curren year, adjused for he ime lapses since issuance by using half of expeced life of newly graned opions. 2 Because he SFAS 23 disclosures do no provide deail on hese inpu variables for differen ranches of opions, we assume he opion grans are issued evenly across years, and no opions are exercised before he end of heir expeced lives. hus, he average life for all opions ousanding is equal o half of expeced life of newly graned opions. In addiion, for firm years wih missing inpu daa, we subsiue he average values from he available years. he final key parameer used as an inpu o he Black-Scholes opion pricing model is he price of he underlying sock. Opion pricing heory would sugges ha we use he sock price a of measuremen error o have a maerial affecs on inferences concerning he validiy of our predicions because all he relevan models are affeced similarly. 2 Because we do no have he daa relaed o all opions ousanding, we use he curren year s. We are currenly conducing sensiiviy ess using he simple average of individual years daa. 27
fiscal year end. However, Aboody (996) noes ha because ESO values increase wih prices of underlying socks, regressing sock prices on ESO values creaes an endogeneiy problem as sock price would appear in boh he dependen and independen variables. hus, failure o ake accoun of his endogeneiy would resul in esimaed ESO values ha are posiively correlaed wih regression error erms, and he resuling coefficiens on he opion fair value-based variables would be biased. In paricular, conrary o he predicions of our heoreical analysis, findings from unabulaed regressions relaing o Mehod reveal a posiive relaion beween OPV and equiy marke value. o address he endogeneiy problem, we esimae OPV andopionliabusing he prediced sock price from he benchmark residual income valuaion model (on a per share basis) ha excludes all ESO-relaed measures, i.e., equaion (2). By consrucion, he esimaed ESO fair values obained from his firs-sage procedure are no correlaed wih he error erms in he second-sage valuaion equaion (2). When prediced sock prices from he firs-sage regression are negaive, we se hem o zero. 4. Sample and Daa he sample comprises,354 firm-year observaions drawn from he S&P Indusrial Index. he sample period includes fiscal years 996-2, wih 996 being he firs year for which SFAS 23 daa are available and 2 being he mos recen available sample year. he poenial sample for use in our cross-secional regression is 2,5 observaions, which reflecs he fac ha lagged equiy book value is used o compue abnormal earnings. We require firms o have earnings, equiy marke value, (non-negaive) equiy book value, and employee sock opion daa necessary o esimae equiy book value and residual income under all four ESO accouning 28
mehods. 3 o miigae he effecs of ouliers, for each variable appearing in he esimaing equaions, by year, we rea as missing observaions ha are in he exreme op and boom one percenile (Kohari and Zimmerman, 995; Collins, Maydew and Weiss, 997; Fama and French; 998; Barh, Beaver, Hand, and Landsman, 999). Afer imposing his requiremen bu before imposing he ESO daa availabiliy requiremen on a per share basis, he poenial sample ranges from a low of 44 firm-year observaions in 996 o a high of 467 in 2. Earnings, equiy book value and equiy marke value daa are drawn from he Compusa daabase, and employee sock opion daa are from a daabase provided o us by Jack Ciesielski of R.G. Associaes, Inc. able, panels A and B, presens sample descripive saisics and correlaions. Panel A reveals ha, on average, equiy marke value far exceeds equiy book value for all four ESO accouning mehods, wih mean (median) raios of he wo amouns of roughly 4.5 (3.5). In addiion, mean and median residual income for all four mehods are posiive. Alhough he posiive median residual income conrass wih findings in prior research, e.g., Barh, Beaver, Hand, and Landsman (999), he earlier sudy s sample period ends in 997 our firs sample year and he remaining sample years were highly profiable for large U.S. firms. he sample mean and median amouns for he opion liabiliy under mehod 4 (OPV) are of same order of magniude as residual income. Panel B reveals ha all of he variables are correlaed wih each oher. Noably, equiy marke value is highly correlaed wih each of he equiy book value and residual income amouns, as well as wih OPV. able 2 presens regression summary saisics corresponding o he firs-sage equiy valuaion equaion used o esimae prediced sock price, which is an inpu o he Black-Scholes formula-based esimae of opion fair value. As described in secion 3, he esimaing equaion is essenially he same as ha associaed wih APB 25 in 3 Following Bell, Landsman, Miller, and Yeh (22), we require posiive beginning owner s equiy o ensure ha he firm s cos of capial in calculaing abnormal earnings (rbve ) is posiive. 29