Accounting Based Valuation Formulae
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1 Accouning Based Valuaion Formulae James A. Ohlson *. Inroducion Equiy valuaion is a opic of grea ineres in pracice and academia. The broad issue concerns he forecasing of fuure expeced payoffs which are hen convered o some inrinsic equiy value via use of some discoun-facor. In his conex he word forecasing refers o a complex se of skills which are difficul o describe and even harder o each, when implemened in a superior fashion. Academics have much more o say abou how one idenifies he appropriae payoffs and how hese are fed ino valuaion formulae. Sudens ypically encouner 3 approaches o valuaion: The discouning of, (i) dividends, (ii) cash flows and, (iii) residual earnings. raciioners of equiy valuaion, ofen o he chagrin of academics, end o rely on none of he above class-room echniques. As a core organizing principle hey end o focus insead on forward earnings and he growh in he subsequen expeced earnings, i.e., he greaer he growh, he grea he price o forward earnings raio. Exacly how such a relaion acually reflecs a valuaion formula is more of a mysery, bu i can be developed. This paper will show, using a relaively lile known bu simple echnique, how one unifies various equiy valuaion models. The framework will reconcile he cash flows and residual income approaches o he more fundamenal dividends approach. Moreover, we will develop a formula ha deermines value on he basis of, (i) nex-year expeced /or forward, (ii) shor-erm growh - year 2 vs. nex-year - in, (iii) long-erm growh in and finally, (iv) he discoun facor which relaes direcly o cos-of-capial. We will argue ha he las formula is useful as i connecs wih analyss conc of how o value equiies. 2. The Valuaion Aribue - A Quick Review The heoreical saring poin in equiy valuaion is he so-called VED formula, i.e., VED sands for he presen value of expeced dividends: = R d = * W.. Carey rofessor a he W.. Carey School of Business, Arizona Sae Universiy, Tempe, AZ This paper summarizes some poins found in my paper On Accouning Based Valuaion Formulae, forhcoming, Review of Accouning Sudies, 24. 3
2 4 Ohlson = he value of equiy R = + r > is he discoun facor or plus he cos-of-equiy capial d = he expeced dividend a dae. The formula raises quesions abou he dividend policy. Who wans o forecas dividends if he dividend policy is irrelevan? Or, saed somewha differenly, should we no focus on he value creaion raher han he value disribuion? Finance ex-books end o deal wih hese quesions by inroducing he presen value of free cash flows or FCF. Specifically, he formula is: = D + R c = D = he deb ousanding oday c = expeced FCF, dae. Tex-book ofen moivaes his scheme by he saying cash is king! As a pracical maer, however, cash is a more ambiguous concep han one migh hink iniially. And i is no so obvious ha FCF reflecs value-creaion, a poin ha accounans surely appreciae. To inroduce accouning daa as a valuaion aribue, Financial Saemen Analysis ex-books generally inroduce he so-called Residual Income Valuaion, or RIV, formula: = bv + R RI = RI = ear rbv. bv = expeced book value, dae ear = expeced earnings, dae. Experienced praciioners who happen o ge exposed o his formula do no generally reac favorably when i is suggesed o be a useful ool: Why he emphasis on book value? In oher words, i is well o noe ha praciioners do no sar wih he curren book value and hen ry o esimae he incremenal value via a forecasing of fuure residual earnings. In oher words, wha is missing is he core principle: he growh in earnings should explain he price o forward earnings raio. To parially address he issue of growh in earnings, ex-books generally develop he so-called consan growh formula:
3 Accouning Based Valuaion Formulae 5 ear r g = K ear+ = ( + g). ear,, and he dividend payou is fixed according o d = K. ear. Bu his approach is so obviously unsaisfacory ha mus be given shor shrif. The dividend-policy is far oo sringen. In addiion, he same can be said for he requiremen ha here is one and only one growh-raio. The near erm is in his regard no differen from he long erm. The sae-of-he-ar as described is no encouraging. Wha one would like o see is a unifying framework of equiy-valuaion, including he possibiliy of providing a model ha shows how he growh in expeced earnings explains he / Ear raio, wihou placing unreasonable resricions on he dividend policy. We will do so in he final par of he paper. 3. A General Framework for Equiy Valuaion As always, we rely on VED as a foundaion. Thus he quesion becomes one of finding a scheme ha gives equivalen represenaions, including V of FCF and RIV. The following scheme will prove o be exceedingly useful. Le y, y, y 2,... be any sequence of numbers, subjec only o y / R as he laer is merely a mild regulariy condiion. I follows immediaely ha = y + R ( y Ry ) + R ( y Ry ) + R ( y Ry ) Adding his expression o VED, one obains = y + R z = z = y + d R. y In wha follows, we have o keep in mind ha he z - sequence depends direcly on he y - sequence. In applying he above mechanics, we pu wo cenral ideas ino place. Firs, y provides he saring-poin in valuaion. Second, we wan o pick some accouning/economics consrain such ha he z - sequence does no depend on he dividend policy. The las poin is suble: I allows us o shif he analysis away from he disribuion of wealh o he creaion wealh.
4 6 Ohlson Nex, we show how one applies he framework o he FCF and RIV approaches: A. FCF u y = D =he negaive of he expeced deb a dae. Assume furher ha he deb incurs an ineres expense according o he equaion in = rd. We pariion aciviies ino operaing and financial aciviies. Thus, he balance shee and he income saemens can be summarized by bv = oa D ear = opear in oa = operaing asses ne of operaing liabiliies, dae opear = earnings due o operaions, dae Le c d + in Δ D Or, equivalenly, per ex-books, c = opear Δ oa Assume ha he clean surplus relaion holds, i.e., Δ b = ear d. Wih respec o z, one obains z D + d RD. = in + d ΔD = c Thus, we have idenified he assumpions ha equae he VED approach o he FCF approach. Imporanly, if one furher assumes, reasonably, ha he operaing aciviies do no depend on he dividend policy - i.e., ne borrowings can always finance a change in he dividend-policy, hen z does no depend on he dividend policy. B. RIV In his case pu y = bv so ha
5 Accouning Based Valuaion Formulae 7 z bv + d Rbv. Given clean surplus, i follows immediaely ha z = ear rbv., i.e., he VED and RIV are idenical represenaions of value. And, again, under he same assumpion as in he previous case (FCF), z will no depend on he dividend policy. We nex provide he scheme ha focuses on forward earnings and heir subsequen growh. I will refer o his approach as he Abnormal Earnings Growh (AEG) model. C. AEG In his case pu y = ear r / + so ha z = ear + r d R ear r = Δ r (.. ) + ( ear r.( ear d )) + One inerpres rz. as he expeced incremen in earnings, adjused for expeced earnings forgone due o he disribuion of dividends. And, jus like residual earnings, for a savings accoun z =, regardless of he dividends. More generally, one sees ha under wo reasonable assumpions, ear / + d = r and ear / d =, does no depend on he dividend policy. This framework would seem o be much more aracive ha he RIV formula in ha i focuses on nex-period expeced earnings, and heir subsequen growh (adjused for dividends) consisen wih analyss view of he world. We believe ha RIV will never achieve he saus of a premier valuaion framework because i focuses, in essence, on he curren book value and is subsequen growh as expressed by z = bv + d Rbv.. Earnings and heir growh is he name of he game, no book values and heir growh. I is really ha simple! 4. A arameerized Version of he Abnormal Earnings Growh Model The formula relaed o earnings becomes more powerful if one adds an assumpion. Specifically, consider: z = + γ z,
6 8 Ohlson γ is some presumed growh parameer. The dynamic mus also presume some iniializaion z >. The case z = is of modes ineres since i follows ha /. = ear + r Wih hese assumpions in place one obains a formula ha expresses value in erms of: : Nex-year expeced or forward. Year 2 vs. Year growh (STG) in expeced. A measure of long-erm growh (LTG) in expeced. Discoun facor which reflecs risk (Cos of Equiy Capial). Thus he invesors vision of he fuure is given by: 2 LTG Some reasonably sraighforward algebra resuls in he valuaion formula g g s L = r r gl r = cos of capial r dps gs = + and g 2 L = as (assuming full payou) Noe ha he correcion o he shor-erm growh in, namely he erm r dps/ is ypically small compared o Δ 2 /. This erm reflecs he foregone year 2 earnings due o he disribuion of wealh a he end of year. In he very long run one can expec all firms o be idenical. Hence, one can reasonably sugges ha g L is he same for all firms and he quaniy will approximae he seady sae growh of GN such as 3-4%. Every valuaion formula leads o he familiar problem ha he discoun facor is no a known quaniy. Because of his somewha grim realiy, pracical analysis engages in reverse engineering. Tha is, one can ake he curren equiy value,, as a given and
7 Accouning Based Valuaion Formulae 9 solve for r. In he presen case one obains he following square roo formula: r A A Δ ( γ ) 2 2 = + + and dps A γ + 2 γ < R I believe his formula will be useful in pracice and research. Specifically, serves as an indicaor of he following possibiliies: (i) A firm s risk (ii) An indicaion ha is no wha he marke really believes in pricing he securiy. Tha is if r is high - which makes he sock look cheap - hen, will be revised downward in he near fuure (iii) A firm s equiy is mispriced and hus i poenially leads o an aracive invesmen opporuniy. More generally, I noe ha he valuaion approach ha focuses on earnings and heir subsequen expeced growh has a number of aracive feaures. Simple assumpions resul in a formula expressing value as a funcion of four variables: (i) nex year esimaed (ii) shor erm growh (iii) long erm growh and (iv) cos of capial. The valuaion formula is easy o implemen using forecass. The valuaion implies ha / increases if (i) shor-erm growh increases (ii) long-erm growh increase and (iii) he cos-of-capial decreases. The valuaion formula allows shor-erm growh o exceed cos-of-capial. The valuaion formula is consisen wih he fac ha he / raio generally exceeds he inverse of he cos-of-capial. The square-roo formula derives a firm s expeced marke reurn; i depends only on (i) /, (ii) he dps/ raio, (iii) shor-erm growh and, (iv) long-erm growh.
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