Employee Stock Option Accounting in a Residual Income Valuation Framework

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1 Employee Sock Opion Accouning in a Residual Income Valuaion Framework Wayne R. Landsman Kenan-Flagler Business School Universiy of Norh Carolina a Chapel Hill Chapel Hill, NC 7599 Ken Peasnell Managemen School Lancaser Universiy Lancaser, LA 4YX England Peer Pope Managemen School Lancaser Universiy Lancaser, LA 4YX England Shu Yeh Deparmen of Accouning Naional Taiwan Universiy Taipei, Taiwan, R.O.C. Sepember 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. Corresponding auhor: Wayne R. Landsman, Kenan-Flagler Business School, Universiy of Norh Carolina a Chapel Hill, Chapel Hill, NC , (99) 96-, wayne_landsman@unc.edu

2 Employee Sock Opion Accouning in a Residual Income Valuaion Framework Absrac We use he Ohlson (995, 999) valuaion framework o compare he exen o which four alernaive approaches o accouning for employee sock opions (ESOs) ha reflec variaions of curren and proposed accouning sandards bes capure he economic effecs of employee sock opions on curren equiy marke value. The ESO accouning mehods are APB 5, he FASB s 99 Exposure Draf, SFAS, and an exension of he IASB s ED-. We explicily model he diluion effecs on shareholder value of employee sock opions using a dividend discoun model and hen use he Ohlson residual income framework o derive he implied equiy value amouns associaed wih each ESO accouning mehod. Findings from he modeling indicae ha only he ED- exension mehod resuls in recognized balance shee amouns ha accuraely reflec he economic diluion effecs of ESOs on curren shareholder equiy value by recognizing an ESO asse and liabiliy a gran dae, and subsequenly recognizing gains and losses on he liabiliy in income. Tha is, only he ED- exension employs super clean surplus accouning, whereby income reflecs all gains and losses aribuable o exising shareholders. The oher accouning mehods all resul in balance shee amouns ha oversae he value of curren shareholder equiy. Based on he modeling analysis and employing cross-secional valuaion equaions we hen es wo predicions. Firs, for he APB 5 and Exposure Draf mehods, we predic and find ha he equaion is beer specified, in erms of relaive explanaory power, when he esimaing equaion is adjused by including opion fair value as a regressor, resricing is coefficien o be, because a valuaion based on equiy book value and residual income should equal equiy value of curren shareholders plus opion fair value. Alhough we have no clear predicion for he SFAS mehod, we find he similarly adjused equaion is also beer specified. We also predic and find ha he SFAS esimaing equaion exhibis lower relaive explanaory power han ha associaed wih he adjused APB 5 and Exposure Draf mehods and he ED- exension mehod, alhough he resul only obains for he ED- exension when we permi he change in he ESO liabiliy o have a differen coefficien from ha on oher aggregae income componens.

3 . 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. : Accouning for Sock-Based Compensaion (FASB 995, hereafer, SFAS ). SFAS 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, Bear Searns (Accouning Issues, July ) repors ha dilued EPS for S&P 5 including effec of fair value of ESO grans is % lower han repored EPS. The 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. The pressure on he FASB in he U.S. o revisi SFAS wih a look a mandaing recogniion of ESO expense in income is being largely driven by he Inernaional Accouning Sandards Board (IASB), who recenly issued an exposure draf, ED-, Share Based Paymen (IASB, ) mandaing recogniion of employee sock opion expense using gran dae fair value. Alhough here are some minor differences beween ED- and SFAS, he key poin is ha all European Union firms would be required o expense employee sock opions using gran dae fair value if, as is likely o be he case, he ED is adoped as a sandard. 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 SFAS permis firms o use Accouning Principles Board Opinion 5: Accouning for Sock Issued o Employees (AICPA 97, hereafer APB 5), 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.

4 expense ESOs. They raise wo poenially valid criicisms. Firs, firms ha issue sock opions o heir employees do so because hey ge somehing in reurn, an inangible asse, in he form of he employees inellecual capial, ha is no recognized under SFAS nor ED-. The FASB acknowledged his in heir exposure draf ha preceded SFAS, Exposure Draf: Accouning for Sock-Based Compensaion (FASB, 99, hereafer, Exposure Draf). The 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. Second, 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. Thus, accouning ha reas he firm s obligaion o is employees as an offseing liabiliy o he inangible asse a gran dae, and includes he effecs of changes in he firm s obligaion o employees afer gran dae beer capures he economic impac of ESOs on he firms 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 and FASB propose o rea he liabiliy when selemen akes he form of cash raher han he issuance of sock. I is also commonplace in accouning o regularly updae he amouns shown for long-erm liabiliies, such as sie resoraion coss. The purpose of his sudy is o use he Ohlson (995, 999) valuaion framework o compare he exen o which he various approaches o accouning for employee sock opions bes reflec he economic effecs of employee sock opions on curren equiy marke value. We do his in wo seps. Firs, we explicily model he diluion effecs on shareholder value of employee sock opions using a dividend discoun model. Then, using he Ohlson residual income framework, we derive he implied equiy value amouns associaed wih four ESO accouning mehods ha reflec variaions of curren and proposed accouning sandards, viz.

5 APB 5, SFAS, he Exposure Draf, and an exension of ED- (hereafer he ED- exension) ha recognizes changes in he fair value of firm s obligaion o employees afer gran dae. Findings from he modeling analysis indicae ha only he ED- exension resuls in recognized balance shee amouns ha accuraely reflec he economic diluion effecs of ESOs on curren shareholder equiy value. The reason for his resul is ha of he four mehods, only he ED- exension adops wha Chrisensen and Felham (, ch. 9) refer o as super clean surplus accouning, whereby income reflecs all gains and losses aribuable o exising shareholders. The findings also indicae ha he APB 5 and Exposure Draf resul in balance shee amouns ha oversae he value of curren shareholder equiy value. In paricular, hese wo mehods resul in balance shee 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 exising and fuure equiy holders. Finally, we find ha he SFAS accouning mehod resuls in balance shee amouns ha also oversae he equiy value of exising shareholders, alhough he oversaemen is less han ha associaed wih he APB 5 and he Exposure Draf. The reason for his is ha he SFAS accouning mehod is neiher super-clean nor mixed. We es he empirical validiy of our residual income valuaion models by esimaing wo separae cross-secional equiy valuaion models relaing o each accouning mehod in which equiy book value and residual income are adjused o reflec he accouning reamen applicable o each of he four mehods. Boh equaions wihin each pair have equiy marke value as he dependen variable, bu he second adjused equaion includes opion fair value

6 as an explanaory variable wih he resricion ha is coefficien equals negaive one. The 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, for he APB 5 and Exposure Draf mehods, 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 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 mehod, because a valuaion based on equiy book value and residual income should equal equiy value of curren shareholders plus a fracion of opion value. Finally, because a valuaion based on equiy book value and residual income should equal equiy value of curren shareholders under he ED- exension mehod, here is no reason o expec he adjused equaion will be beer specified han he unadjused equaion. We es our predicions by assessing each model s relaive goodness-of-fi using he Vuong (989) Chisquare es. Second, we predic ha he esimaing equaion based on SFAS equiy book value and residual income amouns should be dominaed by each of he oher hree models, appropriaely adjused o reflec wheher opion fair value should be included as an implici addiion o equiy marke value. This predicion is based on he observaion in our residual income valuaion modeling which shows ha he gradual recogniion of equiy under SFAS gives rise o measures of equiy book value and residual income ha equal neiher equiy marke value nor he sum of equiy marke value an opion fair value. We es our predicions using a sample of S&P 5 firms wih available daa from 996-, and esimae annual cross-secional valuaion models and pooled models wih year fixed-effecs. We esimae opion fair value using he Black-Scholes opion pricing formula. However, because of he endogeneiy problem arising from regressing sock prices 4

7 on opion fair values (Aboody, 996), we esimae our opion fair value measure using an insrumen for equiy marke value consruced from a wo-sage regression. The 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 5 and Exposure Draf models, bu here is no difference in relaive explanaory power beween he adjused and unadjused ED- exension esimaing equaions. In addiion, he SFAS esimaing equaion exhibis less relaive explanaory power han hose associaed wih he oher hree mehods. The remainder of his paper is organized as follows. Secion derives how he four differen mehods of accouning for employee sock opions affec he relaion beween marke values and fuure accouning numbers. Secion describes he empirical esimaing equaions, secion 4 discusses sample daa, and secion 5 presens he empirical findings. Secion 6 summarizes and concludes he sudy.. Accouning for ESOs There are a leas four ways of accouning for ESOs:. APB 5 mehod: ignore i, i.e. measure a inrinsic value. If he opion is exercised, paidin capial is credied wih he cash received.. SFAS 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 In a relaed sudy, Li () also models he diluion effecs of employee sock opions, and provides empirical evidence ha he fair value of ousanding ESOs is negaively associaed wih equiy marke value. However, he paper does no address how curren and proposed ESO accouning mehods reflec ESO diluion effecs. In anoher relaed sudy, Li and Wong () 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. The 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, as wih Li (), Li and Wong () does no address accouning for he effecs of ESO diluion. 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. 5

8 received and include in paid-in capial as when he opion is exercised. If no exercised, leave balance on PIC opions as a diry surplus componen of equiy.. 99 FASB ED rejeced mehod: recognize asse a gran dae equal o he fair value of he ESO and amorize 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 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 mehod: as under mehod, recognize asse and amorize i bu rea he recognized fair value of he opion as a liabiliy. Mark-o-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. Mehods and 4 conform wih clean surplus in ha all gains and losses pass hrough income. Mehod is an example of wha Chrisensen and Felham (, ch. 9) label mixed surplus accouning. Mehod 4 is accouned for on wha hey call a super-clean surplus basis. Income reflecs all gains and losses aribuable o exising shareholders. Mehods and appear o conain an elemen of diry surplus accouning absen from mehods and 4, since if he opions are no exercised, a gain o exising shareholders bypasses income. There are several implicaions for he residual income model of he differen ways of accouning for ESOs. The impac, in mehods and 4, of he recogniion of an asse ha is subsequenly amorized is sraighforward. Ignoring for he momen he reamen of he associaed credi enry, he recogniion of he pre-paid compensaion asse simply changes he balance beween curren book value and fuure residual income. All we need o ensure, as is 6

9 done in Bell, Landsman, Miller and Yeh (), is ha he wo componens are reaed consisenly. Under mehod 4, he credi arising from recogniion of he asse a gran is reaed as a liabiliy accoun, meaning ha he book value of equiy a ha dae is he same as under mehod, where nohing is recognized. The difference beween he wo mehods appears in he sreams of fuure residual incomes and (we shall see) in heir resulan presen values. Mehods and, on he oher hand, rea he opion accoun as a form of paid-in capial. The only difference beween he wo mehods is ha he equiy builds up slowly under mehod (wih nohing being recognized a gran dae) whereas i is all recognized a gran dae under mehod. Therefore, he book value of equiy differs a gran dae from he book value under mehods and 4, reflecing he fac ha fuure incomes are o be shared beween exising and new (i.e. opion holding) shareholders. Under cerain (no-exercise) saes of naure, gains will arise o exising shareholders ha will no be recognized unil he firm is dissolved.. Example To gain furher insigh, i is helpful o consider a very simple hree-period scenario. A firm issues an ESO a ime exercisable afer wo periods on paymen of X. No new informaion appears in period. 4 A ime, he exising shareholders ge all of he (cerain) dividend ( d e = d ). A ime, he sae of naure is revealed. Payoffs in period are condiional on he sae of naure a ime and he firm is liquidaed a ime. As in period, he exising shareholders ge all he dividends in period ( e d s ds = ), regardless of wheher he sae is good (s = g) or bad (s = b). If s = g, he opion is exercised because he presen value of he new shares exceeds he srike price: MV n g > X. In ha case, exising 4 This exra period is included in he model simply in order o have wo periods over which opion expense can be charged in mehods -4. 7

10 shareholders would receive e d g in period and he new shareholders would ge n d g such ha e n d g dg + dg =. Conversely, if s = b, he opion would lapse unexercised because he new shares would be worh less han he employees would have o pay for hem: MV n b < X. In e b b ha case, he exising shareholders would ge all he dividends in period : d = d. All agree ha he probabiliy of a good sae a = is p and of a bad one is p. We assume ha employees and invesors alike are risk-neural. All expecaions of dividends are afer incorporaion of incenive effecs arising from he compensaion conrac. 5 The fair value of he ESO a = is OPV = n p( MVg X ) = ( + r) n dg p ( + r) X ( + r) () where r is he riskless rae of ineres. 6 The marke value of exising shares can be herefore be wrien as MV e e e e d E[ d ] E[ d ] = r ( + r) ( + r) d E[ d ] E[ d d = r ( + r) ( + r) n ] () d d g = + p + r ( + r) n dg d + ( + r) g d b + ( p) ( + r) db + ( + r) Making use of (), () can be re-arranged and redefined in erms of dividends accruing o curren and fuure shareholders adjused for he expeced marke value of any shares subsequenly issued o employees (he diluion effec): 5 The simple hree period model ignores he effecs of opions ha migh be graned in fuure periods. Such complicaions are ignored since consideraion of hese poenial effecs adds no obvious valuaion or accouning insighs and canno be modeled empirically. In paricular, in conras o Li () and Li and Wong (), we rea fuure opion grans as an unmodeled source of oher informaion in he empirical analysis, since all esimaing equaions based on he differen accouning reamens of ESOs are similarly affeced by his omied variable. 8

11 MV e n d E[ d ] E[ MV ] E[ d ] = + + () + r ( + r) ( + r) n n [ g where E MV ] = pmv. Consisen wih Chrisensen and Felham, he period ne dividends is arrived a afer deducing he fair value of any new shares expeced o be issued in he fuure, no he cash proceeds, X, received by he firm from he exercise of opions. A price per share can be compued by dividing by curren shares in issue, wihou any adjusmen for he exisence of poenially diluive securiies. This is imporan when working wih super-clean surplus residual incomes. A measure of equiy value can also be derived ha mixes ogeher he claims of exising and fuure shareholders: MV m d E[ d X ] E[ d ] = r ( + r) ( + r) d E[ d = + + r = MV e + OPV ] + OPV ( + r) ( + r). E [ MV n ] E[ d ] + ( + r) (4) Equaions () and (4) reveal ha he way fuure diluion is measured affecs direcly he valuaion of curren claims. Furhermore, idenifying he appropriae ne dividend sream is cenral o he choice of a suiable residual income concep. The direc mehod of valuing exising shares requires subsequen share issues o hird paries (in his case, employees) o be measured a fair value. The indirec mehod does no 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. These wo bases correspond o he super-clean and mixed bases for accouning purposes. 6 The assumpion of risk neuraliy is made simply o avoid having o specify risk-neural probabiliies, wih he problems hey enail for empirical work. 9

12 . Residual Income Valuaion Le i BV s represen he book value of equiy using mehod i a ime under sae s. 7 Under mehods, and 4, opion expense will be based on he fair value of he opion a gran dae ( OPV ), o be spread over he wo-year vesing period, wih δopv o be charged in period and ( δ ) OPV in period. No asse or opion credi is iniially recognized a ime under mehod, whereas i is under mehods and 4. The amoun iniially recognized as asse value under mehods and 4 equals OPV, wih he corresponding credi reaed as equiy under mehod and as a liabiliy under mehod 4. Mehod Ne incomes wih his (base-case) mehod are: NI NI NI NI g b s = d = ( d = d = d g b s + BV X ) + BV + BV BV BV b s g BV BV ( s = g, b). The value obained by convering hese incomes o residual incomes, RI NI rbv = and (5) RI s = NI rbv, and discouning is s, s 7 The sae subscrip is suppressed in wha follows eiher when only one sae can occur or when dealing wih probabiliy-weighed expecaions.

13 MV = BV = BV RI RI g + + p + r ( + r) NI rbv + + r NI b rbv ( p) ( + r) RI g RI b + ( ) + p ( + r) ( + r) NI g rbv + p ( + r) NI b rbv + ( + r) b. NI g rbv + ( + r) RI b + ( + r) g + (6) Subsiuing (5) ino (6), canceling and collecing erms yields: MV d E[ d X ] E[ d] = + +, (7) + r ( + r) ( + r) which is exacly he same value obained using he mixed surplus dividend model given by equaion (4): m e MV = MV = MV + OPV. (8) Since OPV mus be posiive, he use of mehod will resul in an over-esimae of he value of curren equiy. Mehod The iniial book value of equiy under mehod is he same as under mehod : BV = BV. Mehod ne income conains a charge for opion expense in he firs wo periods, bu i is he same in period, regardless of he sae: NI NI NI s s = NI = NI = NI s s δopv ( δ ) OPV. (9) However, since he credi associaed wih he opion expense is included in paid-in capial, he wo enries cancel and he equiy book value under mehod is always he same as equiy book value under mehod : BV = BV and s BV s BV = ( =,; s = g,b). This means ha he capial charge levied o arrive a residual income is he same under he wo mehods. I herefore follows ha mehod residual incomes will be less han heir mehod counerpars

14 by an amoun equal o he opion expense: RI = RI δopv and RI s = RIs ( δ ) δopv. The residual income-based value obained by mehod mus herefore equal MV = MV = MV = MV e e δ δ + OPV r ( r) + + δ δ + OPV r ( r) δr + ( + r) OPV. () Mehod recognizes opion equiy slowly, as a by-produc of recognizing opion expense. The resul is a measure of equiy value ha is neiher super-clean nor mixed. For e r =, MV = MV, i.e., he equiy value per model equals ha of curren equiy holders. e For r >, MV > MV. Moreover, for any feasible amorizaion rae, < δ, MV is closer o e MV han o OPV MV e + since ( + r) δ > r. Mehod Ne incomes are he same as under mehod : NI = NI ; s NI s NI = ( =,; s = g,b). On he oher hand, he recogniion of an asse immediaely gives rise o a credi ha is reaed as equiy under mehod such ha = BV + OPV = BV OPV. BV + A ime, he exra opening equiy is reduced by he addiional period expense o give BV = BV + ( δ ) OPV.

15 s s A ime, a furher amorizaion charge will have ensured ha BV = BV, regardless of he sae of naure. In oher words, all he addiional opion equiy, OPV, recognized a he ouse will by now have been compleely offse hrough he compleion of he amorizaion of he corresponding asse. The residual income sream will incorporae boh he amorizaion charges and he exra (bu diminishing) equiy. In period, he full effecs are fel: RI = NI = NI = RI rbv δ OPV r( BV + OPV ) (a) ( δ + r) OPV. In period, he capial charge diminishes regardless of he sae of naure (s = g,b): RI s = NI = NI = RI s s s rbv ( δ ) OPV r[ BV ( + r)( δ ) OPV. + ( δ ) OPV ] (b) Finally, in period here are no addiional expenses and he capial charge is he same as under mehod (regardless of sae): RI s = NI = NI = RI s s s. rbv rbv s (c) Puing his alogeher, we have: MV = BV RI E[ RI ] E[ RI ] r ( + r) ( + r) E[ RI ( δ + r) OPV ] = ( BV + OPV ) + + r E[ RI ( + r)( δ ) OPV ] E[ RI ] + +. ( + r) ( + r) () Collecing erms, we have:

16 MV = MV = MV = MV δ + r ( + r)( δ ) + OPV + r ( + r) e + OPV. () The resul is he same as wih mehod. Mehod provides an over-esimae of he value of exising equiy. Mehod 4 Under mehod 4, an asse is recognized immediaely bu he associaed credi is 4 reaed as deb. Opening equiy is herefore he same as i is under mehod : BV = BV. The asse is amorized in he same way as under mehod. However, here are wo differences in he way incomes are calculaed: ne income conains gains and losses on marking-o-marke he opion liabiliy; and since accumulaed prior valuaion adjusmens are included in beginning-of-period equiy, capial charges differ accordingly. Afer period, no uncerainy has been resolved and he opion is now worh OPV = OPV ( + r), resuling in OPV = ropv being charged o income. In he nex period, if he good sae occurs, he n g g X opion will increase in value o OPV = MV, he opion will be exercised and here n g will be a furher charge of OPV = MV X OPV. In he bad sae, he opion will lapse unexercised and a gain will be recorded of OPV b = OPV. g Combining hese amorizaion charges and fair value adjusmens, 8 he residual income in he firs period is: RI 4 = RI = RI δopv OPV ( δ + r) OPV. (4) 4

17 If he good sae follows, he mehod 4 residual income conains an amorizaion charge, a gain in he value of he opion liabiliy and an adjusmen o he capial charge o in period : RI 4 g = RI = RI g g ( δ ) OPV + ( + r)( δ + r) OPV OPV g ( MV + r( δ + r) OPV n g X ). (5) The book value of equiy a he beginning of (good) period includes opion expenses and pricing adjusmens from he wo previous periods, plus he new share capial ha has been issued (recorded a marke value): BV 4 g g = BV [ δopv + ( δ ) OPV [ OPV = BV g. + OPV g ] + [ MV n g ] X ] (6) 4 g g The final period residual income is herefore unchanged: RI = RI. If he bad sae occurs, period residual income will be: RI 4 b = RI = RI b b ( δ ) OPV + ( + r)( δ + r) OPV + OPV. b + r( δ + r) OPV (7) 4 b b Again, RI = RI. As wih he oher cases, we can define mehod 4 value by reference o mehod value: MV 4 ( δ + r) OPV = MV + r ( + r)( δ + r) OPV ( MV + p ( + r) ( + r)( δ + r) OPV + ( p) ( + r). n g X ) (8) Using (), his simplifies o 8 Since opening equiy is he same as under mehod, here is no incremenal capial charge in period. 5

18 MV 4 = MV = MV e OPV. (9) Mehod 4 is he only one 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 recorded in he books a marke value. Such super-clean accouning guaranees ha residual income is on a proprieary basis relevan o he valuaion of shares in issue. 9. Empirical Specificaion and Predicions. Esimaing Equaions The residual income valuaion models in secion sugges ha for models and, 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. The adjusmen for mehod is more complex, since a valuaion based on equiy book value and residual income should equal equiy marke value and a fracion of opion value, rendering i difficul o make any clear predicion. Because a valuaion based on equiy book value and residual income should equal equiy marke value under mehod 4, no adjusmen should be necessary. To es hese predicions, we esimae he following four pairs of equaions, and 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 9 An ineresing aside is ha our modeling provides a clear answer o he quesion of how bes o reflec he diluion effecs of poenial shareholders in he compuaion of earnings per share, EPS. Procedures ha rejec super clean surplus accouning for ESOs in favor of mixed surplus accouning will missae dilued EPS unless adjusmens are made o he denominaor so ha i reflecs he fair value of opions ousanding. In paricular, EPS compued using mehods and will equal EPS compued using mehod 4 only by seing he denominaor equal o he number of exising shares plus a muliple, φ, imes he maximum number of poenial new shares arising from exercise of ESOs ousanding. By comparing equaions () and (9), i is sraighforward o show ha he addiional shares, φ m, mus equal ( OPV / MV e ) n, where n is he number of exising shares, and m is he number of possible new shares. Curren GAAP accouning for EPS makes an adjusmen based on opion inrinsic values insead of heir fair values. As a resul, EPS fully dilued will be biased upwards. Core, Guay, and Kohari () make a similar observaion. The same basic observaion applies o mehod, excep ha he funcion for he addiional new shares is more complicaed in ha i is based on he rae a which ESOs are amorized. 6

19 non-nesed models wihou assuming under he null ha eiher model is he correc model. Following he sandard Ohlson framework, each esimaing equaion includes a measure of equiy book value and curren period residual income applicable o each mehod of accouning for ESOs. For model, ha based on accouning for ESOs under APB 5, we have: MVE i = α + α RI + α BV + ε () i i i MVE i = α + α RI + α BV OPV + ε ( ) ' i i i i where RI is abnormal earnings under model and equals NI i rbve ; NI i equals ne income before exraordinary iems and disconinued operaions for fiscal year ; book value of common equiy a he end of fiscal year ; common shares ousanding a he end of fiscal year ; MVEi is he marke value of BVEi is he OPVi 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 firms and years, respecively. Following Dechow e al. (999), Barh, Beaver, Hand, and Landsman (999), and Bell, Landsman, Miller, and Yeh (), we se he expeced rae of reurn on book value of common equiy, r, a percen, he longerm reurn on equiies, in hese and all subsequen valuaion equaions. The 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 Our primary concern is wih he relaive explanaory power of regressors associaed wih differen mehods of accouning for ESOs Alhough we expec he equiy book value and residual income coefficiens o be posiive, we make no predicions regarding he magniudes of heir coefficiens across he various specificaions. Bell, Landsman, Miller, and Yeh () 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, ; Dechow e al. 999; Hand and Landsman, ). Ohlson (999, 6) concludes ha his approach is jusified in empirical work because one-ime iems are likely o have limied forecasing abiliy. 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. 7

20 resricing he coefficien on OPV o be in equaion ( ), he dependen variable in ha equaion is implicily he sum of MVE and OPV. Based on he residual income valuaion in secion., we predic ha equaion ( ) will be beer specified han equaion () because a valuaion based on equiy book value and residual income should equal equiy value of curren shareholders plus opion fair value. have: For model, which is based on he SFAS mehod of accouning for ESOs, we MVE i = α + α RI + α BV + ε () i i i MVE i ' = α + α RI + α BV OPV + ε, ( ) i i i i where BV = BV and RI = RI OPTIONEXPENSE. Similar o oher earnings componens, OPTIONEXPENSE is an afer-ax measure of ESO expenses, measured as NI less afer-ax SFAS Pro Forma Earnings, which is aken from he SFAS disclosures. OPTIONEXPE NSE corresponds o δ OPV in equaion (). As in equaion ( ), he coefficien on OPV is resriced o be in equaion ( ), and he dependen variable in ha equaion is implicily he sum of MVE and OPV. Based on he residual income valuaion in secion., we hesiae o predic wheher equaion ( ) will be beer specified han equaion (). For model, which is based on he FASB Exposure Draf, we have, MVE i = α + α RI + α BV + ε () i i i MVE i = α + α RI + α BV OPV + ε ( ) ' i i i i where BV = BV OPTIONEXPENSE + OPTIONEQUITY, s= RI = RI OPTIONEXPENSE r( OPTIONEQUITY s OPTIONEXPENSE ). s= s 8

21 s= OPTIONEXPENSE is he accumulaed amorizaions of he ESO asse a ime and r( OPTIONEQUITY OPTIONEXPENSE ) is he addiional capial charge arising from s s= amorizing he ESO asse. OPTIONEQUI TY is he sum of amouns credied o equiy as of ime resuling from ESO grans. Noe ha OPTIONEQUITY is fixed a dae of gran and is herefore measured a hisorical cos, whereas OPV is marked-o-marke every accouning period. As in equaion ( ), he coefficien on OPV is resriced o be in equaion ( ), and he dependen variable in ha equaion is implicily he sum of MVE and OPV. Based on he residual income valuaion in secion., we predic ha equaion ( ) will be beer specified han equaion () because a valuaion based on equiy book value and residual income should equal equiy value of curren shareholders plus opion fair value. Finally, for model 4, which is based on he ED- exension mehod of accouning for ESOs, we have, MVE i = α + α RI + α BV + ε () i i i MVE i = α + α RI + α BV OPV + ε ( ) 4 4 4' i i i i where BV 4 = BV OPTIONEXPENSE s= s= ( FV _ ESO s s Σ s= ( OPTIONLIAB OPTIONS _ EXERCISED ) s OPTIONLIAB s s ) + and RI ( OPTIONLIAB OPTIONLIAB ) 4 = RI OPTIONEXPENSE [ s s= s= r OPTIONEXPENSE Σ( OPTIONLIABs OPTIONLIABs )], 9

22 OPTIONLIAB is he sum of amouns recognized as liabiliies as of ime resuling from ESO grans. Noe ha OPTIONLIAB is simply OPV; we adop he convenion of referring o i as a liabiliy o reinforce he noion ha under he ED- exension mehod, he credi a gran dae is o a liabiliy accoun, and he liabiliy is hen marked-o-marke. The amoun OPTIONLIABs s OPTIONLIAB 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 OPTIONS _ EXERCISEDs is he number of ESOs exercised a ime s. When ESOs are exercised, equiy book value under Mehod 4 increases by fair marke value of he shares issued, which equals he balance of OPTIONLIAB 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 ( ) should no improve upon he correc residual income specificaion given by equaion (). In fac, i may worsen hings by adding noise o he esimaing equaions. Thus, we predic no difference in model explanaory power beween equaions () and ( ). I is imporan o noe ha BV 4 = BV OPTIONLIAB. (4) This follows because, prior o exercise, amoun of he sum of he changes in Mehod 4; when ESOs are exercised or expire, OPTIONLIAB and OPTIONEQUI TY differ by he OPTIONLIAB ha are included in income under OPTIONLIAB is closed ino book equiy and equaion (4) sill holds. Thus, equaion (4) 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

23 esimaing equaion based on SFAS 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. This predicion is based on he observaion in our residual income valuaion modeling which shows ha he gradual recogniion of equiy under SFAS gives rise o measures of equiy book value and residual income ha equal neiher MVE nor MVE plus OPV. Thus, we also predic ha equaions ( ), ( ), and () will each be beer specified han eiher equaion associaed wih model, equaions () and ( ). We esimae cross-secional regressions for equaions () hrough () for 997 hrough, 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 consans from eiher he pooled fixed-effecs or he annual regressions. All equaions are esimaed using unscaled daa (Barh and Kallapur (996)).. Measuremen issues Unlike OPTIONEXPE NSE, which can be deduced as he ne of repored ne income and SFAS pro forma ne income, he oher opion value-based variables, OPV (OPTIONLIAB) and OPTIONEQUI TY, mus be esimaed. OPTIONEQUI TY is he sum of gran dae ESO fair values, which is 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 pro forma ESO expenses and relaed 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. This 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 9, deflaion for all bu mehod 4 would require esimaing addiional shares relaing o ESOs based on OPV. This would needlessly inroduce he poenial of addiional measuremen error in he affeced models.

24 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 value-based 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, measuremen of equiy book value under Mehods and 4. 4 OPTIONEXPE NSE, and he We use he Black-Scholes (97) opion pricing model o esimae fair value of ESOs ousanding a each balance shee dae so ha we can consruc OPV (OPTIONLIAB) using disclosed parameer amouns aken from he SFAS disclosures. The relaed parameers we use are:. Exercise price of he opion: he curren year s weighed exercise price for all ousanding ESOs.. Expeced sock-reurn volailiy: repored expeced sock-reurn volailiy for opions issued in he curren year, aken from he SFAS disclosures.. Risk-free ineres rae: repored risk-free ineres rae for opions issued in he curren year, aken from he SFAS disclosures. 4. Expeced dividend yield: repored expeced dividend yield for opions issued in he curren year, aken from SFAS disclosures. 4 There are wo addiional inconsisencies in he measuremen of equiy book value and residual income for all bu Mehods and. The firs arises from he fac ha OPTIONEXPENSE is on an afer-ax basis, and we ignore income effecs in our measuremen of equiy book value under Mehods and 4. In principle, equiy book value under hese wo mehods should reflec accumulaed he same before-ax OPTIONEXPENSE charge. The second is ha OPTIONEXPENSE reflecs adjusmens for anicipaed forfeiures, bu book equiy under Mehods and 4 canno be adjused appropriaely because we do no have deails of he forfeiures. We do no expec hese sources of measuremen error o have a maerial affecs on inferences concerning he validiy of our predicions because all he relevan models are affeced similarly.

25 5. Time 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. 5 Because he SFAS 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. Thus, 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. The 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 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. Thus, 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 4 reveal a posiive relaion beween OPTIONLIAB and equiy marke value. To address he endogeneiy problem, we esimae OPV andoptionliab using he prediced sock price from he benchmark Ohlson model (on a per share basis) ha excludes all ESOrelaed measures, i.e., equaion (). 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 equaions () hrough (). When prediced sock prices from he firs-sage regression are negaive, we se hem o zero. 5 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.

26 4. Sample and Daa The sample comprises,54 firm-year observaions drawn from he S&P Indusrial Index. The sample period includes fiscal years 996-, wih 996 being he firs year for which SFAS daa are available and being he mos recen available sample year. The poenial sample for use in our cross-secional regression is,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 mehods. 6 To 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, he poenial sample ranges from a low of 44 firm-year observaions in 996 o a high of 467 in. 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. Table, 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 (.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. 4

27 firms. The sample mean and median amouns for he opion liabiliy under mehod 4 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 he ESO liabiliy. Table 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, he esimaing equaion is essenially he same as ha associaed wih APB 5 in which equiy book value and residual income are repored amouns ha exclude effecs of ESOs alhough he equaion is esimaed on a per share basis so ha he fied value from he regression can be used direcly in he opion valuaion formula. Table reveals ha equiy book value and residual income are significan regressors in every sample year, and produce high R values. 5. Resuls Panels A and B of Tables hrough 6 presen regression summary saisics corresponding o he equiy valuaion equaions for each of he four ESO accouning mehods, i.e., equaions () hrough ( ). Panel A (panel B) in each able corresponds o he equaion ha excludes (includes) opion fair value as an addiional regressor whose coefficien is resriced o equal negaive one. Each panel includes pooled fixed effecs coefficiens, -saisics and adjused R values, mean coefficiens, -saisics and adjused R values from he five annual cross-secional esimaions, maximum and minimum coefficiens, number significanly posiive coefficiens, and Z and Z saisics based on he annual 6 Following Bell, Landsman, Miller, and Yeh (), we require posiive beginning owner s equiy o ensure ha he firm s cos of capial in calculaing abnormal earnings ( rbve ) is posiive. 5

28 regressions. 7 The overall picure provided by he four ables is very similar. All eigh models have high R values, and all unresriced regressor coefficiens are significan posiive in he pooled and in all five annual esimaions. For example, Table, panel A, which repors he findings relaing o he APB 5 mehod of accouning for ESOs (i.e., mehod ) reveals R values exceed, 8 percen, on average, and mean across years residual income and equiy book value coefficiens of 6. and., respecively. Inspecion of he remaining ables suggess ha differen mehods of accouning for ESOs resuls in equiy coefficiens book value and residual coefficiens of similar magniudes. Table 7 summarizes he key resuls of he sudy. Panel A presens he Vuong - saisics corresponding o he pairwise comparisons, for any given mehod of accouning for ESOs, of model explanaory power for equaions ha do or do no include opion fair value as a regressor, i.e., hose beween equaions () and ( ), () and ( ), () and ( ), and () and ( ). Panel B presens he Vuong -saisics corresponding o he comparisons of model explanaory power beween hose relaing o he SFAS mehod of accouning for ESOs and hose relaing o he hree ESO accouning mehods. Alhough, based on our predicions, comparisons should be limied o beween equaion () and equaions ( ), ( ) and (), we abulae saisics comparing esimaions for mehods,, and 4 o boh esimaions for mehod. Panel A reveals findings consisen wih our predicions. In paricular, he Vuong - saisic comparing equaions () and ( ) for he APB 5 accouning mehod is.8, 7 Throughou we use a five percen level of significance level under a wo-sided alernaive. Mean -saisics for regression parameers from he year esimaions are simple year averages and are included for descripive purposes. Two Z-saisics, Z and Z, are used o es for significance of he -saisics from he five annual esimaions. Z equals / N N j = j / k j /( k j ), where j is he -saisic for year j, k j is he degrees of freedom, and N is he number of years. Z, which equals /( sddev( ) / ( N ), correcs for poenial upward bias in Z arising from lack of independence of parameers across years. See Barh (994) for furher deails. 6

29 indicaing ha he equaion including opion fair value as an implici par of he dependen variable is beer specified. Similarly, he Vuong -saisic comparing equaions () and ( ) for he Exposure Draf accouning mehod is.5, also indicaing ha he equaion including opion fair value as an implici par of he dependen variable is beer specified. We predic and find ha he wo esimaing equaions corresponding o he ED- exension ESO accouning mehod are saisically equivalen in erms of explanaory power (-saisic =.64). Finally, alhough we have no predicions for he SFAS equaions, he -saisic of.8 suggess ha he model ha includes opion fair value is beer specified, which is consisen wih he fracion of opion value (see equaion ()) being closer o one han o zero. 8 Panel B reveals ha, as prediced, he relevan esimaing equaions corresponding o he APB 5 and Exposure Draf mehods of accouning for ESOs, i.e., equaions ( ) and ( ), are beer specified han he one relaing o SFAS, equaion (). The Vuong - saisics are 5.87 and 5., respecively. However, he Vuong -saisic of. relaing o comparison of explanaory power of equaions () and () suggess ha he equaion for he ED- exension mehod of accouning for ESOs is no significanly beer specified han ha for he SFAS mehod. One explanaion for his null resul is ha equaion () is empirically misspecified in ha he change in opion value, which is implicily a negaive componen of residual income, is resriced o have he same coefficien as he oher componens of income. I is likely ha change in opion value is enirely ransiory because sock prices follow a random walk, which suggess i should have a coefficien of negaive 8 One alernaive and simple explanaion for he superioriy in erms of model specificaion of he adjused models for mehods, and is he fac ha an imporan variable, opion fair value, is included as an addiional regressor. To es his conjecure direcly, we re-esimaed each of he adjused equaions ( ) hrough ( ) wih opion fair value bu wihou imposing he resricion ha is coefficien equals. Unabulaed findings indicae ha for all four accouning mehods, he adjused and unadjused equaions have saisically indisinguishable model explanaory power. This finding refues he alernaive explanaion and provides addiional suppor for he inclusion of opion liabiliy bu wih he coefficien resricion implied by our heory. 7

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