Lancaser Universiy Managemen School Working Paper 1996/004 An Earnings-Based Valuaion Model in he Presence of Susained Compeiive Advanage John O''Hanlon The Deparmen of Accouning and Finance Lancaser Universiy Managemen School Lancaser LA1 4YX UK John O''Hanlon All righs reserved. Shor secions of ex, no o exceed wo paragraphs, may be quoed wihou explici permission, provided ha full acknowledgemen is given. The LUMS Working Papers series can be accessed a hp://www.lums.lancs.ac.uk LUMS home page: hp://www.lums.lancs.ac.uk/
AN EARNINGS-BASED VALUATION MODEL IN THE PRESENCE OF SUSTAINED COMPETITIVE ADVANTAGE John O Hanlon Deparmen of Accouning and Finance Lancaser Universiy Lancaser LA1 4YX U.K. Telephone:(44) (0)1524-593631 e-mail: J.O hanlon@lancaser.ac.uk 29 Sepember 1997 Acknowledgemens The commens of Harold Bierman, Richard Brief, Colin Clubb, Gerald Felham, Suresh Govindaraj, Richard Heaney, Yu Hon Lui, Jamie Munro, Ken Peasnell, Peer Pope, Andrew Sark and Paul Taylor are graefully acknowledged.
An earnings-based valuaion model in he presence of susained compeiive advanage Absrac In his paper, he process which generaes a company s economic value and is accouning numbers is represened in erms of he company s invesmen in, and uilisaion of, compeiive advanage. Wihin his represenaion, i is shown ha a company which earns normal economic reurns migh plausibly generae perpeual exponenial growh in posiive ne presen value projecs, in unrecorded goodwill and in residual income. Since exponenial growh in residual income may make i impracicable o consruc earnings-based valuaion models which employ he ime-series properies of unscaled residual income (or of unscaled earnings), i is argued ha earnings-based valuaion models should employ he imeseries properies of scaled residual income (or of scaled earnings). A model which incorporaes such properies is hen derived. In a cerainy seing in which here are no shocks o he economic reurn series, economic value is a funcion of normal profiabiliy and of normal book value growh; in a seing in which shocks o he economic reurn series occur, i is necessary o add a erm which reflecs ransiory abnormal profiabiliy and a erm which reflecs ransiory abnormal book value growh. The imporance of he abnormal profiabiliy erm is deermined by persisence in abnormal profiabiliy; he imporance of he abnormal book value growh erm is deermined by he normal marke-o-book raio.
1. Inroducion This paper represens he join evoluion of a company s economic value and accouning numbers in erms of he company s invesmen in, and uilisaion of, compeiive advanage. In such a seing, he company migh plausibly experience persisen exponenial growh in posiive ne presen value (NPV) projecs, in unrecorded goodwill and in residual income. Since such growh in residual income may make i impracicable o consruc earnings-based valuaion models which employ he ime-series properies of unscaled residual income (or of unscaled earnings), i is argued ha earnings-based valuaion models should employ he ime-series properies of scaled residual income (or of scaled earnings). A model which incorporaes such properies is hen derived. I is well known ha economic value can be expressed as he sum of accouning book value and he presen values of all expeced fuure residual incomes (Edwards and Bell, 1961; Edey, 1962; Peasnell, 1982): he residual income componen of he expression represens unrecorded goodwill. Ohlson (1995) provided an imporan impeus o he modelling of he links beween economic value and accouning numbers by developing his residual income-based valuaion relaionship. Making he assumpions ha accouning book value is an unbiased esimaor of economic value and ha residual income is generaed by a zero-mean saionary ime-series process, he derived a model in which economic value is parly expressed as a weighed average of (i) book value and (ii) an ex-div earnings muliple. The model provided an imporan illusraion of how a heoreically suppored accouningbased valuaion model could incorporae knowledge of he ime-series properies of earnings. The unrealisic assumpion of unbiased accouning ha was made in Ohlson (1995) was relaxed in Felham and Ohlson (1995) and in Felham and Ohlson (1996). Felham and Ohlson (1996) allowed persisen unrecorded goodwill o arise from wo sources which accounans migh recognise inuiively: (i) depreciaion errors and (ii) he exisence of a persisenly growing sream of posiive NPV projecs, of which he full value is no immediaely capured by he balance shee. Accouning-based valuaion models, such as ha derived in Felham and Ohlson (1996), which allow for he observable phenomenon of persisen exponenial growh in unrecorded goodwill o resul from he observable phenomenon of 1
persisen sreams of posiive NPV projecs, are aracive as poenial bases for he pracical ask of valuaion and for he empirical research designs of marke-based accouning researchers. However, here is an apparen problem in modelling persisen growh in unrecorded goodwill in erms of persisen growh in posiive NPV projecs: i is no clear how i can be expeced ha a persisenly growing sream of posiive NPV projecs will be generaed in a compeiive environmen. Rappapor (1986) made he poin ha compeiion should evenually eliminae he availabiliy of posiive NPV projecs. This poin was echoed in sudies by Bernard (1993) and by Ou and Penman (1993) which suggesed ha compeiion is likely o eliminae posiive NPV projecs wihin a finie horizon and ha, herefore, one of he main poenial causes of unrecorded goodwill and of posiive residual income is likely o be eliminaed wihin such a horizon. This paper addresses his issue by demonsraing ha, even in a seing in which a company does no earn abnormal economic reurns, i is plausible ha he company migh be generaing persisenly growing sreams of posiive NPV projecs, of unrecorded goodwill and of residual income. This demonsraion ress upon a represenaion of he economic value and accouning numbers of a going concern company as oupus of a process in which he company coninually invess in, and uilises, compeiive advanage. The accouning depreciaion is correc in he sense ha he rae maches he rae of decline in projec cash flows bu i is wrong in he sense ha i ignores he value of he compeiive advanage ha is embedded wihin projecs. This represenaion provides indicaions as o he impac of he acquisiion and uilisaion of compeiive advanage upon he normal level of profiabiliy and upon he normal level of he marke-o-book raio. This represenaion is hen developed in order o derive an earnings-based valuaion model which incorporaes he ime-series properies of scaled earnings ha migh be observed in he seing described. Iniially, he derivaion is effeced in a cerainy seing: he resulan model is similar o one which has appeared in he shareholder value analysis lieraure, in which economic value is expressed in erms of normal profiabiliy and he normal book value growh rae. Subsequenly, shocks o he economic reurn series are incorporaed: in he resulan model, economic value is expressed in erms of normal profiabiliy, 2
he normal book value growh rae, ransiory abnormal profiabiliy and he ransiory abnormal book value growh rae. The model, ogeher wih he underlying analysis, has a number of ineresing feaures. Firs, i expresses he cenral roles of he predicion of profiabiliy and of he predicion of growh in he ask of fundamenal analysis. 1 Second, i suggess a focus for lieraure ha is concerned wih he finie-horizon properies of accouning numbers: i suggess ha abnormal profiabiliy and he abnormal book value growh rae migh plausibly be expeced o approximae o zero wihin a finie horizon. Third, alhough he analysis in his paper does no employ he echnology of opions heory, he represenaion developed here provides some insigh ino he impac of real opions (Dixi and Pindyck, 1994; Trigeorgis, 1996) on iems, such as profiabiliy and he marke-o-book raio, which are of ineres o financial saemen analyss. Fourh, he analysis gives indicaions of he effec of he acquisiion and uilisaion of compeiive advanage in deermining he normal level of profiabiliy. This is relevan for hose concerned wih he use of managerial performance measures based on varians of residual income such as Economic Profi (Copeland, Koller and Murrin, 1995; McTaggar, Kones and Mankins, 1994) and Economic Value Added (EVA ) 2 (Sern, Sewar and Chew, 1995). The remainder of his paper is organised as follows: secion 2 shows ha, wihin a seing in which he company coninually invess in compeiive advanage, i is possible o accommodae a persisen sream of posiive NPV projecs, wih consequen exponenial growh in unrecorded goodwill and in residual income, wihou requiring ha he company as a whole should earn abnormal economic reurns; secion 3 derives an earnings-based valuaion model which allows for such growh in unrecorded goodwill and in residual income; secion 4 concludes he paper. 2. Posiive ne presen value projecs, unrecorded goodwill, accouning rae of reurn and residual income where payoffs from projecs arise parly in he form of compeiive advanage 1 The imporance aached by analyss o he predicion of profiabiliy and growh is evidenced by an accoun of he aiudes of successful analyss which was published by he London Sunday Times on 1 June 1997 (page 3 of he Money secion). 2 EVA is a service mark of Sern Sewar & Co. in he Unied Saes, he Unied Kingdom, and oher counries of he world. 3
The analysis in his secion of he paper is carried ou in a no-arbirage cerainy seing in which he company as a whole earns normal economic reurns. Unrecorded goodwill, he accouning rae of reurn (ARR) and residual income are represened as oupus of a process in which he going concern company coninually makes invesmens in compeiive advanage which is embedded wihin projecs. The company makes an iniial invesmen in a zero NPV firs generaion projec of which he payoffs accrue parly in he form of direc cash receips and parly in he form of compeiive advanage. This compeiive advanage is realised as posiive NPV second generaion projecs. Invesmen in hese second generaion projecs iself resuls in subsequen payoffs which accrue parly as direc cash receips and parly as posiive NPV hird generaion projecs. This process coninues indefiniely, wih he company coninually cashing in previously acquired compeiive advanage hrough invesmen in posiive NPV projecs which hemselves deliver compeiive advanage which will bring abou subsequen posiive NPV projecs. The accouning sysem depreciaes he compeiive advanage along wih he projecs in which i is embedded. I is shown ha, wihin he framework represened here, persisen exponenial growh in posiive NPV invesmens, in unrecorded goodwill and in residual income migh plausibly arise even in he absence of abnormal economic reurns for he company as a whole. I is also shown ha he asympoic levels of ARR and of he marke-o-book raio are funcions of parameers which capure (i) he proporion of oal projec value ha is represened by invesmen in compeiive advanage and (ii) he proporion of he cos of new projecs ha is represened by he cashing in of previously acquired compeiive advanage. The following assumpions are made regarding he analysis in his secion: i. A incorporaion (ime 0), he company makes an iniial issue of equiy capial which is wholly invesed in he company's firs generaion projec. The amoun of equiy capial raised is he opening book value of he company (y 0 ). Abnormal economic reurns for he company are precluded from his par of he analysis, so he firs generaion projec has zero NPV: he economic value of he company a ime 0 (P 0 ) is equal o y 0. (If he firs generaion projec is allowed o have a non-zero NPV, his does no change he asympoic resuls derived below.) 4
ii. The periodic payoffs from he firs generaion zero NPV projec each accrue parly in he form of cash receips direcly aribuable o ha projec and parly in he form of posiive NPV second generaion projecs which resul from compeiive advanage acquired hrough invesmen in ha firs generaion projec. These second generaion projecs parly consis of an invesmen in compeiive advanage. The payoffs from he second generaion projecs herefore also accrue parly in he form of cash receips and parly in he form of hird generaion posiive NPV projecs: he process coninues indefiniely. This process is characerisic of a company which is in he going concern phase of is exisence. Tha par of he oal period payoff of he company which accrues in he form of cash a period is denoed by C ; ha par of he period payoff which accrues in he form of posiive NPV projecs a period is denoed by N. The proporion of oal payoffs which accrues in he form of cash receips is denoed by F. F is assumed o be consan across all projecs and across ime. Some, bu no all, of projec payoffs are assumed o arise as cash receips: herefore, 0 < F < 1. For all, F= C /( C + N ). (1) The proporion of oal projec payoffs which accrues as posiive NPV projecs arising from earlier invesmen in compeiive advanage is (1-F). Thus, (1-F) represens he proporion of he value of projecs which is made up of he invesmen in compeiive advanage. iii. The oal cash cos of buying ino all of he second and subsequen generaion projecs ha arise a period is denoed by I. The raio of cash cos o presen value of such new projecs is denoed by H. As wih F, H is assumed o be consan across all projecs and across ime. All second and subsequen generaion projecs are assumed o be posiive NPV projecs wih an iniial cash cos of greaer han 0: herefore, 0 < H < 1. (1-H) represens he raio of NPV o presen value of second generaion and subsequen projecs. H/(1-H) herefore represens he raio of cash cos o NPV of such projecs. Consequenly for all : I = N H. (2) 1 H 5
Where he company as a whole is earning normal economic reurns, (1-H) represens he proporion of he oal value of second generaion and subsequen projecs ha is conribued by he uilisaion of compeiive advanage embedded wihin earlier projecs. iv. Each projec generaes a sream of oal periodic payoffs (i.e. C plus N) which accrues in he form of a declining perpeuiy, where he rae of decline is B per period. 0 < B 1. The use of his assumed payoff paern is convenien because i produces a relaively simple analysis. However, here is empirical evidence o suppor he use of such a paern. As will become apparen laer, his declining payoff paern gives rise o a profiabiliy persisence parameer in he form of he auoregressive coefficien of an auoregressive process of order 1 (AR(1) process): empirical evidence in O Hanlon (1996) suggess ha, of various sandard imeseries generaing processes, AR(1) is he one which bes characerises ARR series in he U.K. v. There are no financial asses, financial liabiliies or working capial a any period end. The dividend for period, denoed by d, is he excess of he cash receips from projecs for ha period over he cash cos of invesmen in new projecs for ha period: vi. d = C I. (3) Each projec is recorded in he balance shee a is hisoric cash cos less accumulaed accouning depreciaion. The accouning depreciaion rae for all projecs is deermined by he rae of decline in he projecs' cash payoff sream. The rae is herefore B per period on a declining balance basis. The depreciaion is correc in ha he rae maches he rae of decline in projec cash flows bu is wrong in ha i ignores he value of he compeiive advanage embedded wihin projecs: 3 he invesmen in his compeiive advanage is depreciaed as par of he projecs wihin which i is embedded, raher han being capialised in anicipaion of he subsequen posiive NPV projecs o which i will give rise. This non-recogniion ( overdepreciaion ) by he accouning sysem of he valuable compeiive advanage gives rise o a marke-o-book premium. 3 A furher complicaion could be inroduced by allowing he depreciaion rae o differ from he rae of decline in cash flows: his complicaion is no inroduced here. 6
vii. Accouning obeys he clean surplus relaionship: y = y 1 + x d, (4) where y (y -1 ) is he accouning book value a period end (-1) and x is accouning earnings for period, where x = C - y -1 B. Before proceeding wih he analysis, wo poins are made. Firs, given he no-arbirage cerainy seing, he dollar reurn is as follows for all : ( R 1) P 1 = P P 1 + d = P P 1 + C I, (5) where R is one plus he cos of equiy, which is assumed o be consan, and P (P -1 ) is he economic value of equiy capial a period-end (-1). P can be wrien as he presen value a period-end of he projecs which made up P -1 plus he presen value of new projecs arising a period : P = P ( B ) + N + I. (6) 1 1 Combining (5) and (6), he dollar reurn for period can be wrien as he period oal payoff (C plus N ) less he decline during period in he presen value of he projecs which made up P -1 : ( R 1) P 1= N + C P 1 B. (7) Second, i is imporan o commen on he erm posiive NPV which is used above and in he following analysis. If he definiion of cos is amplified o include he value of he previously acquired compeiive advanage ha is being cashed in o provide posiive NPV projecs, hese projecs are no posiive NPV a all: hey jus appear o be posiive NPV because sandard capial budgeing procedures ignore he value of he compeiive advanage ha is being uilised. The impression ha hese projecs have posiive NPV is reinforced by he accouning depreciaion procedure which over-depreciaes he invesmen in compeiive advanage, wih he consequence ha he book value of second and subsequen generaion projecs is less han heir presen value. In his seing, he sandard capial budgeing procedures and he sandard accouning depreciaion procedures conspire ogeher o make projecs look as hough heir presen value exceeds heir cos. Such a process is likely o be presen in he reurn-earnings generaing process of any going concern business and is a he hear of he 7
subsequen exposiion. For he sake of erminological convenience, and o be consisen wih oher sudies which allow for such processes (e.g. Felham and Ohlson (1996)), I will coninue o use he erm posiive NPV in he exposiion. In order o faciliae undersanding of he seing described above, Table 1 presens a numerical example of he evoluion of economic value and accouning numbers in ha seing. In his example, R = 1.20, F = 0.70, H = 0.667 and B = of 1.00. Making B equal o 1.00, gives a paricularly simple example. Table 1 conains he following noaion no previously defined in he ex: A (= x /y -1 ) denoes he ARR for period, x a (= x - (R-1)y -1 ) denoes residual income for period and χ a denoes he rae of residual income for period ( = x a / y -1 ). (INSERT TABLE 1 ABOUT HERE) The subsequen analysis wihin his secion is presened in he form of hree proposiions. Proposiion 1 suggess ha, in he seing described above, economic value and invesmen in posiive NPV projecs migh plausibly grow exponenially. I is shown ha he rae of growh is a funcion of R, F, B and H. Proposiion 2 saes ha he asympoic rae of growh in book value and in unrecorded goodwill is he same as he rae of growh in economic value defined in Proposiion 1. I is shown ha he asympoic marke-o-book raio is he reciprocal of H. Finally, Proposiion 3 saes ha unscaled residual income grows exponenially a he rae of growh in book value defined in Proposiion 2. On he basis of hese hree proposiions, i is argued ha earnings-based valuaion models incorporaing imeseries properies of earnings should reflec he exponenial growh propery of accouning numbers ha is likely o be observed in he presence of coninual invesmen in compeiive advanage. 8
Proposiion 1: In he absence of abnormal economic reurns, he rae of growh in economic value and in new invesmen in posiive NPV projecs is a weighed average of (R-1) and (-B), where he weighs reflec he relaive proximiy of F o 1 and H respecively. If dividends are posiive, posiive exponenial growh in economic value and in new invesmen in posiive NPV projecs occurs if (R-1)(1-F)/(F-H) exceeds B. Such growh does no depend upon he presence of abnormal economic reurns. Proof: From (2) and (3), he dividend yield a period (= d /P -1 ), denoed by D, is D C N( H /( 1 H)) =. P 1 (8) Subsiuion of (1) ino (7) gives C = P ( R 1+ B) F 1 N = P ( R 1+ B)( 1 F). 1 (9) Subsiuion of (9) ino (8) gives D P 1( R 1+ B) F P 1( R 1+ B)( 1 F)( H/( 1 H)) = P R B F = + H ( 1 ). 1 H 1 (10) R, B, F and H are consan, so D (hereafer D) is consan. (Noe here ha posiive dividends require F > H.) The rae of growh in economic value, denoed by g, is consan a 1 F g = R D = R B F H ( 1) ( 1). 1 H 1 H (11) From (11), g is a weighed average of (R-1) and (-B), where he weighs reflec he relaive proximiy of F o 1 and H respecively. 4 If dividends are posiive (i.e. if F > H), posiive exponenial growh in P occurs if (R-1)(1-F)/(F-H) > B. From (9), N is proporional o P -1. Therefore, such growh in N also occurs if (R-1)(1-F)/(F-H) > B. Posiive exponenial growh in P and in N does no depend upon he exisence of abnormal economic reurns. 4 Noe ha as F approaches 1, lile of he payoff from projecs accrues as compeiive advanage, reenions approach zero and g approaches -B; as F falls owards H, he proporion of payoffs ha accrues in he form of cash falls owards he proporion of new projec value ha is made up of cash cos: payou approaches zero and g approaches (R-1). 9
Proposiion 2: The asympoic rae of growh in book value and in unrecorded goodwill is equal o he rae of growh in economic value, g. Proof: Subracion of accouning depreciaion (y -1 B) from he expression for cash payoffs for period gives accouning earnings for period, as x = C y B= P ( R 1+ B) F y B. (12) 1 1 1 The period earnings which is reained, denoed by x r, is r x = P (( R 1+ B) F D) y B. 1 1 Using his expression for x r, book value evolves as follows (recall ha P 0 = y 0 ): y = P (( 1 B) + ( R 1+ B) F D) 1 0 y = P (( 1 B) + (( R 1+ B) F D)( 1 B) + (( R D)( R 1+ B) F D)) 2 0 2 (( R 1+ B) F D)(( R D) ( 1 B) ) y = P0 ( 1 B) +. ( R D) ( 1 B) Since (1-B) < 1, as y P0 (( R 1 + B) F D) ( R D) ) ( R D) ( 1 B). (13) The consan rae o which he book value growh rae asympoes is herefore g = (R-D-1). Since P is equal o P 0 (R-D) for all, he asympoic marke-o-book raio, denoed by M, is ( M R D ) ( 1 = B ), ( R 1+ B) F D which by subsiuion of (10) is ( R 1+ B) ( R 1+ B)( F H) /( 1 H) 1 M = =. ( R 1+ B) F ( R 1+ B)( F H) /( 1 H) H (14) The marke-o-book raio herefore asympoes o he consan value of 1/H. A he asympoe, for H < 1, unrecorded goodwill ( = P y = ( M 1) y 1) is posiive and grows exponenially a he rae of g per period. 10
Proposiion 3: For (R-1) > 0 and B > 0 and F H, he asympoic rae of residual income differs from zero and he sign and magniude of he difference depend upon he sign and magniude of he difference beween F and H. The asympoic rae of growh in unscaled residual income is equal o he rae of growh in book value, g. Proof: Using (12), ARR, for period, denoed by A, is A x = = y 1 P 1( R 1 + B) F y 1B. y 1 As, since he marke-o-book raio 1/H, A P 1( R 1+ B) F P 1HB F = ( P H H R 1+ B ) B 1 F H R B F = + H ( 1) = A, H (15) where A is he asympoic ARR. Residual income for period, denoed by x a, is a x = x ( R 1) y 1. (16) The rae of residual income (i.e. ARR less he cos of equiy) is denoed by χ a, and is defined as: χ a a x x ( R 1) y = = y y 1 1 1 = A ( R 1). (17) The asympoic rae of residual income, denoed by χ a, is χ a F A R H R B F H = ( 1) = ( 1) + ( R 1) H = R + B F H ( 1 ). H (18) For (R-1) > 0 and B > 0 and F H, χ a differs from zero and he sign and magniude of he difference depend upon he size and magniude of he difference beween F and H. (Noe ha, if dividends are posiive, F > H and χ a > 0.) A he asympoe, unscaled residual income a a = ( x ( χ y 1 )) grows exponenially a he rae of growh in book value, g. 11
The proposiions ha have been developed in his secion sugges how residual income migh be expeced o evolve hrough ime in he case of a going concern company which is coninually invesing in compeiive advanage. Even in a siuaion in which he company as a whole is earning normal economic reurns only, one migh expec o observe exponenial growh in economic value, in posiive NPV projecs, in book value, in unrecorded goodwill and in residual income. The process by which invesmen in one projec generaes compeiive advanage ha can be exploied hrough invesmen in subsequen projecs is a fundamenal deerminan of he way in which going concern companies evolve. ( Learning by doing is an example of a phenomenon which resuls in invesmen in compeiive advanage being bundled up wih oher oulays and expensed in he going concern company.) This process is herefore likely o be a fundamenal deerminan of he join evoluion of economic value, book value and accouning earnings. Aemps o analyse he join evoluion of economic value, book value and accouning earnings migh herefore benefi from an accouning-based valuaion model ha explicily allows for he behaviour of accouning numbers ha is likely o be observed in he presence of coninual invesmen in compeiive advanage. The following secion develops an earnings-based valuaion model which allows for he exponenial growh in residual income ha migh be observed in he presence of such susained compeiive advanage. Before proceeding furher wih he analysis, i is insrucive o dwell briefly on some of he implicaions of expressions (15) and (18). These expressions sugges ha, in he presence of susained compeiive advanage, where accouning depreciaion does no separaely recognise invesmen in ha compeiive advanage, normal profiabiliy and normal excess profiabiliy are a funcion of he invesmen in, and uilisaion of, compeiive advanage: for F > H, he normal excess of profiabiliy over he cos of equiy is a posiive funcion of R, B and F and is a negaive funcion of H. This resul has implicaions in wo relaed conexs. Firs, alhough he analysis in his paper does no employ he echnology of opions heory, he acquisiion and uilisaion of compeiive advanage is essenially abou he acquisiion and uilisaion of real opions. The represenaion ha is developed here provides an indicaion of how he acquisiion and uilisaion of real opions (Dixi and Pindyck, 1994; Trigeorgis, 12
1996) migh impac on iems, such as profiabiliy and he marke-o-book raio, which are of ineres in financial saemen analysis. Second, he analysis is relevan for hose concerned wih he implemenaion of managerial performance measuremen sysems based on varians of residual income. Such varians include Economic Profi (Copeland, Koller and Murrin, 1995; McTaggar, Kones and Mankins, 1994) and Economic Value Added (EVA ) (Sern, Sewar and Chew, 1995). Economic Profi and EVA are varians of residual income in which cerain accouning disorions are correced: he inenion is ha he resuling adjused residual income measure can be used such ha posiive (negaive) residual income indicaes superior (inferior) economic performance. As can be seen from expressions (15) and (18), he ineracion of F and H can produce a normal rae of residual income of greaer han zero. To he exen ha he accouning correcions do no deal wih he phenomenon represened here, posiive residual income may no necessarily be an indicaor of superior economic performance: i may be incorrec o regard a posiive or negaive value for residual income as an indicaion of posiive or negaive abnormal performance. 5 3. An earnings-based valuaion model where payoffs from projecs accrue parly in he form of compeiive advanage Secion 2 shows ha unscaled residual income migh plausibly grow exponenially a he book value growh rae. Sandard auoregressive, inegraed moving average (ARIMA) ime-series modelling echniques involve he ransformaion hrough differencing of a series o a saionary series and hen he esimaion of he auoregressive and moving average parameers for he appropriaely differenced series. If he series exhibis exponenial growh, differencing may fail o achieve saionariy. Aemps o use ARIMA-based approaches for he esimaion of residual income persisence (or, for similar reasons, for he esimaion of earnings persisence) on he basis of unscaled daa may fail or may resul in he idenificaion of generaing processes wih unnecessarily high orders of differencing. For reasons relaed 5 The need o se benchmarks of oher han zero for residual income and is varians is recognised by Sern Sewar & Co., who marke he EVA varian of residual income. In seing EVA benchmarks, he difference beween marke value and (adjused) book value is someimes used as a basis for impuing expecaions of fuure (non-zero) EVA. I am graeful o Joel Sern for his informaion. 13
o hose oulined in Secion 2, sock price changes are also likely o exhibi exponenial growh. However, whils he Finance lieraure has long acknowledged ha work involving he ime-series properies of sock price changes should focus on scaled changes, i is no widely acknowledged ha work on he ime-series properies of accouning flows should focus on he ime-series properies of he scaled flows. On he basis of he analysis in secion 2, i is argued ha heoreical or empirical earningsbased valuaion models which incorporae he ime-series properies of residual income should focus on scaled residual income and ha, since he driver of growh in residual income is book value, he appropriae scaling iem is book value. The remainder of his secion is concerned wih he consrucion of a model based on residual income scaled by book value. Peasnell (1982) showed ha, if accouning obeys he clean surplus relaionship, he dividend capialisaion model, τ P = E ( d+ τ ) R, τ= 1 (19) where E (.) is an expecaions operaor, can be re-wrien as P y E x a τ = + ( + τ ) R. τ= 1 (20) Appendix 1 shows ha, in a cerainy seing where here have been no shocks o he economic rae of reurn series and where x a and y will grow a he consan rae of (R-D-1) = g, (20) can be re-wrien as P = y 1 A g, (M.1) γ 1 where γ = R /( 1 + g). This is a no-shock accouning-based valuaion model, conaining a normal ARR erm and a normal book value growh rae erm. (M.1) can also be wrien as P = y A g, ( R 1) g which is described as he equiy spread model in a shareholder value analysis ex by McTaggar, Kones and Mankins (1994). 14
The effec of pas and curren shocks o he economic rae of reurn series is now overlaid upon he no-shock accouning-based valuaion model, (M.1). (M.1) is wrien in erms of normal profiabiliy and he normal book value growh rae: allowance for shocks requires he addiion of erms which deal wih ransiory abnormal profiabiliy and he ransiory abnormal book value growh rae. In permiing shocks o he economic rae of reurn series, he analysis is moving from a cerainy seing o an uncerainy seing. In such a seing, he values of he fuure payoffs (C plus N) from projecs are expeced values raher han cerain values. The invesmen of I a period becomes an invesmen in he cash payoffs from a group of projecs plus an invesmen in a baske of opions embedded wihin ha group of projecs. The presen value a period-end of he expeced cash payoffs from ha group of projecs and of he expeced expiraion values of he embedded opions, aken ogeher, is I / H (i.e. he cash cos of he projecs imes he raio of presen value o cos). In developing (M.1) o allow for presen and pas shocks, i is assumed ha he company has reached is asympoic values of ARR ( A ), marke-o-book raio ( M ) and book value growh rae ( g ) and has previously encounered no shocks o is economic reurn series. I hen experiences a shock o is economic reurn series which represens he effec of a revision concerning he oal payoffs (i.e. C plus N) expeced o accrue from he company s exising projecs. The changes o he expeced payoffs which represen he shock are capialised as a declining perpeuiy. Such a shock causes he economic rae of reurn o diverge from (R-1) in he period in which he shock arises. Marke efficiency is assumed: consequenly, he economic rae of reurn is expeced o be (R-1) in all periods subsequen o he period in which he shock arises. The parameers, F, B and H, are assumed o remain consan in he afermah of he shock, as is he cos of equiy, (R-1). Furhermore, i is assumed ha he accouning depreciaion policy does no change in response o he shock: consequenly, i akes ime for he impac of he economic income shock o be capured by he accouning sysem and here resuls ime-series dependence (persisence) in he ARR series. Accouning coninues o obey he clean surplus relaionship. In Appendix 2 i is shown ha his se of circumsances gives rise o he following accouning-based valuaion model: 15
P = y A g M + A A + g g γ 1 ( ) ω γ ω γ ω ( ) γ ω, (M.2) 1 where ( A A) is he ransiory abnormal ARR, g is now defined o be he normal book value growh rae, ( g g) is he ransiory abnormal book value growh rae and ω is he asympoic persisence parameer for abnormal ARR, for he abnormal rae of residual income and for he abnormal book value growh rae. As saed in Appendix 2, he persisence parameer, ω, akes he form of he auoregressive coefficien ha would be esimaed in an auoregressive model of order 1 (AR(1) model) for each of hese iems. The definiion of he persisence parameer in erms of an AR(1) coefficien resuls from he underlying assumpion ha payoffs ake he form of a declining perpeuiy. 6 (M.2) is consisen wih a version of equaion (3.a) from Felham and Ohlson (1996) in which cash flow decline is se equal o he reducing balance depreciaion rae. 7 According o (M.2), he value of equiy is obained by adjusing he seady sae model (M.1), which conains a normal ARR erm and a normal book value growh rae erm, by a erm reflecing emporary divergence from normal ARR and by a erm reflecing emporary divergence from he normal book value growh rae. The muliplier on he abnormal ARR erm comprises he growh adjused discoun facor and he asympoic ARR persisence parameer, ω : as ω approaches zero, he muliplier on abnormal ARR approaches zero. The muliplier on he abnormal book value growh rae erm also includes hese wo erms bu he key componen of his muliplier is he asympoic marke-o-book raio M (=1/H, where H < 1). As H (= he raio of cos o presen value of new projecs) falls, he muliplier on he abnormal book value growh rae diverges posiively from one. (M.2) does no include an oher informaion erm, such as ha included in he Ohlson (1995) analysis, which capures he effec on he economic value of he company of ha informaion which has no ye impaced on accouning numbers and which is no capured by persisence mulipliers applied o 6 As was menioned earlier, empirical evidence in O Hanlon (1996) suggess ha, of various sandard ime series processes, AR(1) is he one which bes characerises ARR series in he U.K.. 7 The lenghy bu sraighforward demonsraion of he consisency is no reproduced here bu is available on reques from he auhor. 16
curren accouning numbers. In an empirical seing, his consideraion may be imporan bu no aemp is made here o include such a erm. Such a erm would be compound funcion of he sochasic properies of accouning numbers and of he sochasic properies of oher informaion : 8 i is no clear ha he precise form of such a erm would add significanly o he insighs afforded by his analysis and, consequenly, i is omied. As well as suggesing how he ime-series properies of earnings migh be incorporaed ino earnings-based valuaion models in he seing described, (M.2) has a number of addiional ineresing feaures. Firs, i expresses he cenral roles of he predicion of profiabiliy and of he predicion of growh in he ask of fundamenal analysis. Second, i suggess a focus for lieraure concerned wih he finie-horizon properies of accouning numbers. Examples of such lieraure include Bernard (1993) and Ou and Penman (1993). Under he condiions described in his paper, where persisen sreams of posiive NPV projecs are generaed, i is plausible o expec ha unscaled residual income will no approximae o zero wihin a finie horizon. However, where he normal characerisics of he company's projecs (denoed here by R, B, F, H) do no change, i is plausible o expec ha he abnormal ARR and he abnormal book value growh rae will approximae o zero over such a horizon. Therefore, he developmen of models based on finie horizon properies of accouning migh usefully focus on abnormal ARR and on he abnormal book value growh rae. Furhermore, he underlying analysis provides an indicaion of he impac of he acquisiion and uilisaion of compeiive advanage on normal profiabiliy levels. This is of poenial relevance boh for hose concerned wih he impac of real opions on financial saemen iems and for hose concerned wih he use of residual income, and is varians, as measures of managerial performance. 4. Conclusion This paper represens he join evoluion of economic value, accouning book value and accouning earnings as he produc of a process in which invesmens by companies include invesmen in compeiive advanage which gives rise o fuure posiive NPV projecs. The depreciaion is correc in 8 See Ohlson (1995) for an example of he form of such 17an oher informaion erm.
he sense ha he rae maches he rae of decline in projec cash flows bu is wrong in he sense ha i ignores he value of he compeiive advanage ha is embedded wihin projecs. This process may give rise o perpeual exponenial growh in he generaion of posiive NPV projecs, in unrecorded goodwill and in residual income, even in he absence of abnormal economic reurns for he company as a whole. Since such growh would make i difficul o exploi he ime-series properies of unscaled residual income (or of unscaled earnings) in earnings-based valuaion models, i is argued ha earnings-based valuaion models should employ he ime-series properies of residual income scaled by book value (or of oal earnings scaled by book value). The paper hen derives such a valuaion model. The model incorporaes normal profiabiliy, ransiory abnormal profiabiliy, he normal book value growh rae and he ransiory abnormal book value growh rae. The muliplier on abnormal profiabiliy is driven by persisence in abnormal profiabiliy; he muliplier on he abnormal book value growh rae is driven by he normal marke-o-book raio. The model expresses he cenral roles of he predicion of profiabiliy and of he predicion of growh in he ask of fundamenal analysis and suggess a focus for lieraure ha is concerned wih he finie-horizon properies of accouning numbers. Furhermore, he underlying analysis provides an indicaion of he impac of he acquisiion and uilisaion of compeiive advanage on normal profiabiliy levels and on normal marke-o-book levels. The analysis in his paper conains a number of simplifying feaures which indicae direcions in which his ype of analysis migh be developed boh empirically and heoreically. Firs, i is assumed ha he required reurn and payoff characerisics (R, F, B and H) of all projecs are consan boh across projecs and hrough ime: allowance for cross-secional and ime-series variaion in hese parameers migh prove o be imporan in an empirical seing. Second, i is assumed ha he payoffs from projecs ake he form of a declining perpeuiy. Alhough here is some empirical jusificaion for his simplifying assumpion, i may no hold in all seings: differen payoff paerns would give rise o differen mulipliers on he erms in he model. Third, i could be argued ha he model presened in his paper should be augmened by an oher informaion erm, such as ha included in he Ohlson (1995) analysis. In an empirical seing, his consideraion may be imporan bu no aemp is made here o 18
include such a erm. Fourh, alhough his paper affords some insighs as o he impac of real opions on iems such as profiabiliy and he marke-o-book raio, i does no employ he echnology of opions heory o represen he process: here is much scope for he exploraion of he impac of real opions on he properies of financial saemen iems which are used for valuaion purposes. 19
Appendix 1: Derivaion of (M.1) If accouning obeys he clean surplus relaionship, P y E x a τ = + ( + τ ) R, τ= 1 (20) where E (.) denoes expecaions a ime and he remaining erms are as defined earlier. In a cerainy seing where here have been no shocks o he economic rae of reurn series and where x a and y will grow a he consan rae of (R-D-1) = g, (20) can be re-wrien as a P = y + x τ= 1 R 1+ g τ. (A1.1) a The growh deflaed discoun facor, γ, is now defined as γ = R /( 1 + g). From (17), x a = χ y 1. Subsiuion of hese wo expressions ino (A1.1) gives P = y + χ a y τ= 1 1 γ τ. (A1.2) From (18), he asympoic rae of residual income is defined as χ a = A ( R 1 ). A he asympoe, in a cerainy seing, y x a 1 a = χ = χ a for all. In such a seing, (A1.2) can be re-wrien as a a τ χ P = y + χ y 1 γ = y + y γ 1 τ= 1 1. (A1.3) Subsiuion ino (A1.3) of y = y ( 1+ g) = y 1 1 R 1 g γ 1 and of χ a = A ( R 1 ) gives: P = y 1 A g. (M.1) γ 1 20
Appendix 2: Derivaion of (M.2) (M.1) is a no-shock accouning-based valuaion model, conaining an asympoic ARR erm and an asympoic book value growh rae erm: P = y 1 A g. (M.1) γ 1 The furher developmen of (M.1) is effeced hrough he analysis of he impac of a single shock o he economic reurn series a period s, where he shock generaes an abnormal economic reurn of Z in period s. The dollar value of he shock is ZP s-1. The impac on (unscaled) earnings in period s of he shock can be wrien as follows: 1 R 1+ B ( As A) ys 1 = ZPs 1 F= ZPs 1 F, 1 B R + 1 R 1+ B (A2.1) where A s is he ARR for period s and A, y, Z, P, B, R and F are as defined earlier. The erm in brackes is due o he declining perpeuiy naure of he expeced payoffs which are capialised ino he shock. This erm needs o be muliplied by F because only he proporion F of he period s payoffs accrues as cash flows in period s. The impac of he shock on he (unscaled) change in book value in period s is ( g g) y = ZP s s 1 s 1 R 1+ B ( 1 FH ), R 1 H (A2.2) where g s is he book value growh rae for period s and g is now defined o be he normal book value growh rae. In (A2.2), (1-F) is he proporion of he ime s payoff which arises in he form of posiive NPV projecs. H/(1-H) is he raio of cos o NPV of hese posiive NPV projecs. Therefore, H/(1-H) represens he effec on period s book value of each uni of posiive NPV arising in period s. Since accouning is assumed o obey he clean surplus relaionship, he impac of he shock on he (unscaled) dividend in period s is as follows, being he difference beween (A2.1) and (A2.2): R 1 + B F H (( A A) ( gs g)) ys 1 = ZPs 1. R 1 H (A2.3) 21
The quesion now arises as o wha valuaion muliples should be applied in he earnings-based valuaion model o hese disurbances o he various series. Since each of (i) earnings, (ii) change in book value and (iii) dividend can be deduced from he oher wo iems, he valuaion impac can be capured by focusing on wo iems only. For he purpose of his analysis, he wo iems ha are chosen are he impac of he shock on he change in book value, given by (A2.2), and he impac of he shock on he dividend, given by (A2.3). In addiion o wha would have been expeced o occur in he absence of he shock, he following is now expeced o occur: i. a declining perpeuiy of changes o he expeced sream of invesmen in projecs, where he firs change occurs a ime s and where he rae of decline is B. Given ha all new projecs have a raio of cos o presen value of H, he presen value a ime s of his declining perpeuiy of changes o he expeced invesmen sream is: 1 B ( g g) y + ( g g) y R ( B) 1 1 = 1 H s s 1 s s 1 which by subsiuion of (A2.2) is R R + B) 1 1 H, (A2.4) ZP R 1+ B ( 1 FH ) R F ZPs R H R + B 1 1 =. (A2.4a) 1 1 H 1 H s 1 1 ii. a declining perpeuiy of changes o he expeced dividend, where he firs change occurs a ime s and where he rae of decline is B. Since he economic value a ime s is saed ex-div, he capialisaion muliple applied o abnormal dividends in he earnings-based valuaion model reflecs he abnormal dividends for period s+1 and subsequen periods only: 1 B (( As A) ( gs g)) ys 1, R 1+ B (A2.5) which by subsiuion of (A2.3) is ZP R 1+ B F H R 1 H 1 B = ZP R 1+ B s 1 s 1 1 B F H. (A2.5.a) R 1 H As a check on he correcness of he above decomposiion of he shock o he economic reurn series, i can be verified ha he aggregae of he capialised abnormal changes in book value for ime s+1 22
onwards (equaion (A2.4a)), he capialised abnormal dividends for ime s+1 onwards (equaion (A2.5a)) and he ime s abnormal dividend (equaion (A2.3)), is equal o he ime s shock: ZP 1 F + ZP 1 H 1 B F H + ZP R 1 H R 1+ B F H = ZP R 1 H s 1 s 1 s 1 s 1 The capialisaion facors ha are applied o he abnormal change in book value and he abnormal dividend are now re-cas in erms of a parameer which measures persisence in he abnormal book value growh rae, in abnormal ARR and in he abnormal dividend scaled by opening book value. (Hereinafer, dividend scaled by opening book value is ermed he dividend rae.) Since he parameers R, B, F and H remain unchanged, each of he period s+k abnormal invesmens which resul from he posiive NPV projec componen of he period s shock is expeced o generae normal changes in book value, normal earnings and normal dividends afer i has been made. Therefore, he abnormal change in book value for period s+k will resul from he oal payoffs (C plus N) arising from he period s shock which accrue in period s+k. Successive abnormal changes in book value are relaed o each oher as follows:. ( g g) y = ( g g) y ( 1 B) s+ k s+ k 1 s s 1 ( g g) y = ( g g) y ( 1 B). s+ k 1 s+ k 2 s s 1 k k 1 (A2.6) Since y y s+ k 1 s+ k 2 = 1 + g, s+ k 1 successive deviaions from he normal book value growh rae are relaed o each oher as follows: ( gs+ k g) 1 B = ( g g) 1+ g s+ k 1 s+ k 1. Because of heir declining perpeuiy form, he abnormal changes in book value are expeced o become small relaive o he normal changes as k grows large. Therefore as k, ( gs+ k g) 1 B = ω, ( g g) 1+ g s+ k 1 (A2.7) 23
where ω is he asympoic persisence parameer for he abnormal book value growh rae. Successive abnormal earnings are relaed o each oher in a similar fashion o he abnormal changes in book value: ( A A) y = ( A A) y ( 1 B) s+ k s+ k 1 s s 1 ( A A) y = ( A A) y ( 1 B). s+ k 1 s+ k 2 s s 1 k k 1 (A2.8) Therefore, ω is also he asympoic persisence parameer for he abnormal ARR and for he abnormal dividend rae. Since he rae of residual income differs from ARR by a consan, i is also he persisence parameer for he rae of residual income. This persisence parameer, ω, is a measure of he decline horough ime in deviaions from he norm for ARR, for he rae of residual income, for he book value growh rae and for he dividend rae. I herefore akes he form of he auoregressive coefficien ha would be esimaed in an auoregressive model of order 1 (AR(1) model) for each of hese iems. The definiion of he persisence parameer in erms of an AR(1) coefficien resuls from he underlying assumpion ha payoffs ake he form of a declining perpeuiy. Now, he mulipliers on he abnormal book value growh rae and on he abnormal dividend rae can be re-expressed in erms of ω and γ ( = R/( 1 + g)) and, in he case of he abnormal book value growh rae, in erms of he normal marke-o-book raio ( M = 1/H). The muliplier ha is applied o he abnormal book value growh in (A2.4) can now be re-expressed as follows: R 1 γ M = R 1 + B H γ ω, allowing (A2.4) o be re-wrien as R 1 γ M ( gs g) ys 1 = ( gs g) ys 1. R 1 + B H γ ω (A2.9) Similarly, he muliplier ha is applied o he abnormal dividend in (A2.5) can be re-expressed as follows: 1 B R 1+ B ω = γ ω, allowing (A2.4) o be re-wrien as 24
1 B (( As A) ( gs g)) ys 1 R 1+ B ω = (( As A) ( gs g)) ys 1. γ ω (A2.10) Adding (A2.9) and (A2.10) o he no-shock valuaion model (M.1) gives P = y A g M + A A g g + g g γ 1 (( ) ( )) ω γ γ ω ( ) γ ω. s s 1 s s s Collecing he growh rae erms ogeher gives an expression in erms of abnormal profiabiliy and he abnormal book value growh rae: P = y A g M + A A + g g γ 1 ( ) ω γ ω γ ω ( ) γ ω. (A2.11) s s 1 s s The impac of he shock on abnormal changes in book value, abnormal dividends and abnormal earnings is, in each case, a consanly declining perpeuiy. Therefore, he mulipliers ha need o be applied o he deviaion from normal ARR and o he deviaion from he normal book value growh rae in adjusing (M.1) are he same regardless of wheher he shock giving rise o he deviaions occurred in he curren period or in a previous period. Therefore, he mulipliers can be applied o abnormal ARR in aggregae and o he abnormal book value growh rae in aggregae. This allows (A2.10) o be generalised o an expression for P : P = y A g M + A A + g g γ 1 ( ) ω γ ω γ ω ( ) γ ω. (M.2) 1 25
References Bernard, V. (1993). Accouning-based valuaion mehods, deerminans of marke-o-book raios, and implicaions for financial saemens analysis, Working paper, Universiy of Michigan. Copeland, T., T. Koller and J. Murrin (1995). Valuaion: Measuring and Managing he Value of Companies, Wiley. Dixi, A and R. Pindyck. (1994). Invesmen under Uncerainy, Princeon. Edey, H. (1962). Business valuaion, goodwill and he super-profi mehod, in Baxer, W. and S. Davidson (eds.), Sudies in Accouning Theory, Swee and Maxwell. Edwards, E. and P. Bell (1961). The Theory and Measuremen of Business Income, Universiy of California Press. Felham, G. and J. Ohlson (1995). Valuaion and clean surplus accouning for operaing and financial aciviies, Conemporary Accouning Research 11: 689-731. Felham, G. and J. Ohlson (1996). Uncerainy resoluion and he heory of depreciaion measuremen, Journal of Accouning Research 34: 209-234. McTaggar, J., P. Kones and M. Mankins (1994). The Value Imperaive, Free Press. O Hanlon, J. (1996). The ime-series properies of he componens of clean surplus earnings: UK evidence, Journal of Business Finance and Accouning 23: 159-183. Ohlson, J. (1995). Earnings, book values and dividends in securiy valuaion, Conemporary Accouning Research 11: 661-687. Ou, J. and S. Penman (1993). Financial saemen analysis and he evaluaion of marke-o-book raios, Working paper, Sana Clara Universiy and Universiy of California a Berkeley. Peasnell, K. (1982). Some formal connecions beween economic values and yields and accouning numbers Journal of Business Finance and Accouning 9: 361-381. Rappapor, A. (1986). Creaing Shareholder Value: The New Sandard for Business Performance, Free Press. 26
Sern, J, G. Sewar and D. Chew (1995). The EVA financial managemen sysem, Journal of Applied Corporae Finance 8: 32-46. Trigeorgis, L. (1996). Real Opions, MIT Press. 27