CAPITAL GAINS AN THE CAPITAL ASSET PRING MOEL WORKING PAPER SERIES Workng Paper No. 1 Martn Lally School of Econocs and nance aculty of Coerce and Adnstraton Vctora Unversty of Wellngton Tony van Zl School of Accountng and Coercal Law aculty of Coerce and Adnstraton Vctora Unversty of Wellngton Ths paper s work n progress. Please do not quote wthout the persson of the author. Please address all correspondence to: Professor Tony van Zl School of Accountng and Coercal Law Vctora Unversty of Wellngton PO Box 600, Wellngton, New Zealand Phone: +64-4-463-5329 ax: +64-4-463-5076 Eal: tony.vanzl@vuw.ac.nz
CAPITAL GAINS AN THE CAPITAL ASSET PRING MOEL Abstract Ths paper shows that, n the presence of dfferental taxaton of ordnary ncoe and captal gans, use of the Offcer (1994 verson of the Captal Asset Prcng Model can result n sgnfcant sestaton of the cost of equty captal. In partcular, wth a hgh dvdend yeld, the cost of equty ay be underestated by four percentage ponts. Underestaton s of partcular sgnfcance n the context of settng output prces for regulated utlty frs. JEL: G12, G31. Key Words: Captal Asset Prcng Model; Personal Taxes. Acknowledgeents We acknowledge the helpful coents of John Redayne, avd McCallu, and partcpants at the 13 th Australasan nance and Bankng Conference. 2
CAPITAL GAINS AN THE CAPITAL ASSET PRING MOEL 1. INTROUCTION The Offcer (1994 approach to estaton of the expected cost of equty captal under a syste of dvdend tax putaton, 1 has been wdely accepted n Australa aong both the acadec and practtoner countes n fnance. 2 Offcer vews the tax effect of putaton as a copany tax phenoenon and easured rates of return thus ncorporate the effect of tax credts. 3 He states the CAPM as : where [ E( R ] β E( = R + R = rsk free rate for the perod = rate of return on the equty of copany, ncludng putaton credts = rate of return on the arket portfolo, ncludng putaton credts β = Cov Var (, ( 1 A dvdend putaton tax syste was adopted n the UK n 1973, n Australa n 1987, and New Zealand followed n 1988. The basc syste now exsts n a wde range of countres; Sth (1993 provdes a coprehensve revew of the range of odels across countres. 2 Exaples of textbooks that have adopted the Offcer approach are Bshop et. al. (1993, Ch. 16 and Person et al (1998, Ch. 15. The reports of the utlty regulatory authortes n Vctora and New South Wales show general acceptance of the Offcer approach for utlty rate settng not only by the authortes but also by the enttes affected and by ther fnancal advsors. Anecdotal evdence the authors are aware of and ther own casual observaton both support there beng a slar degree of acceptance of the approach for applcatons n the prvate sector. 3 Offcer s vew of putaton tax stands n contrast to the vew of putaton tax beng an nvestor tax phenoenon. Under the latter vew, putaton s seen as provdng a reduced tax rate for nvestors on ncoe fro dvdends. The vews dffer only by a transfor and therefore the dfference s not substantve. The nvestor tax vew of putaton tax s the vew that has been taken alost unforly n the lterature on the CAPM and putaton tax systes. The lterature effectvely starts wth Brennan (1970 and ncludes Stapleton and Burke (1977, Ashton (1989, 1991, Clffe and Marsden (1992, Lally (1992, Okunev and Tahr (1992, Monkhouse (1993, van Zl (1993, Bralsford and avs (1995, epsey (1996, and Bralsford and Heaney (1998. The general body of ths lterature s revewed n Lally (2000. 3
The apparently sple for of Offcer s CAPM s due to the plct assupton that the tax rates on captal gans and ordnary ncoe are equal (or, ore generally, that the weghted average of the tax rato [ ] n equaton (5 below s zero. In Australa, the effectve captal gans tax rate has been and wll rean less than the tax rate on ordnary ncoe because ( n the past captal gans tax has appled only to the real eleent of a gan, and n future ndvduals and superannuaton funds wll pay the tax on only 50% and 67% respectvely of a gan, and ( the tax s payable only on realsaton of a gan and can therefore be deferred. The assupton of equalty of the rates on captal gans and ordnary ncoe s thus a sgnfcant abstracton fro the realty of the Australan tax syste and use of the Offcer CAPM for estaton of the cost of captal therefore nevtably nvolves a degree of approxaton. 4 Gven the recent revew of the Australan tax syste, ths paper exanes the agntude of the approxaton lkely to result fro contnued use of the Offcer approach under the new structure. In Secton 2 we derve a for of the CAPM that also treats putaton as a copany tax phenoenon but whch does not assue equalty of the tax rates on captal gans and ordnary ncoe. Coparson of that odel wth Offcer s for of the CAPM thus provdes an analytcal expresson for the approxaton ade n applcatons usng Offcer s CAPM. In Secton 3 we explore the agntude of the approxaton under a varety of assuptons about the values of the relevant paraeters deternng the cost of captal. Our concluson s that the degree of approxaton s n ost cases sall but, n the case of hgh dvdend yeld copanes, underestaton of around four percentage ponts could result. Approxatons of ths 4 The authors' experence of cost of captal estaton s that practtoners n New Zealand have not followed the Offcer approach. Instead, putaton s vewed as an nvestor tax phenoenon and easured rates of return therefore do not reflect tax credts. The for of the CAPM ost coonly used has been : E( R = R (1 T + [ E( R R (1 T ] β where R x s the return on x excludng tax credts, and T s the statutory axu personal tax rate whch untl recently was equal to the corporate tax rate, 0.33. The odel s often referred to as the after tax for of the CAPM. It assues that the tax on captal gans s zero across all nvestors, and that there s full attachent of putaton credts. There s evdence that, n recent tes, soe practtoners have swtched to versons of the CAPM whch gve recognton to the fact that the captal gans tax, whle low on average, s not zero. Exaples of such odels are Lally (1992 and van Zl (1993. It s not apparent why practce n New Zealand has developed dfferently fro that n Australa. The two countres have extensve coercal lnks and the swtch fro the classcal to the putaton tax systes occurred at about the sae te. The assupton of a zero captal gans tax underlyng the New Zealand approach s unrealstc but probably less so than the assupton ade n Australa of equalty of the tax rates across captal gans and ordnary ncoe. On the other hand, the New Zealand approach of assung full attachent of putaton credts s unrealstc, whereas the Australan approach has ade allowance for ths. 4
degree have potentally sgnfcant plcatons for proect adopton and for the settng of output prces for regulated utltes. Accordngly the adopton of a CAPM that recognses both dvdend putaton and dfferental taxaton of ordnary ncoe and captal gans would see to be ustfed. 5 2. THE CAPM WITH IERENTIAL TAXATION Under the Offcer approach, the rate of return on a stock coprses the captal gan, the cash dvdend, and the putaton credts (so far as they can be used. Thus the rate of return on the shares of copany, denoted by, s 6 where P P 1 0 = + 1 + U P 0 P0 = copany 's cash dvdend per share over the next perod P t = prce of shares n copany at te t = putaton credts attached to the cash dvdend of copany U = arket wde utlsaton rate for putaton credts, whch ranges fro 0 to 1 Wth returns defned n ths way, Offcer s for of the CAPM s E( = R + [ E( R ] β (1 However, as noted above, ths for s based on the assupton of equal tax rates across captal gans and ordnary ncoe. The odel developed n ths paper does not assue equalty of the tax rates; the dervaton s set out below and follows Elton and Gruber (1984. 5 The for of the CAPM adopted could be the odel derved n ths paper (and thus contnue wth the copany tax vew or alternatvely one of the odels referred to n footnote 3, based on the nvestor tax vew. 5
Investor chooses an effcent portfolo by cobnng the rskless asset wth the tangency portfolo K. Then fro Roll (1977 t follows that wth unrestrcted short sellng, the after tax expected return on asset to nvestor, denoted by E rˆ, s related to the beta of aganst portfolo K, as: ( Cov(ˆ r ˆ, rk E(ˆ r = r + [ E(ˆ rk r ] (2 Var(ˆ r K where rˆ K s nvestor 's after tax return on portfolo K and r s the nvestor s after-tax return on the rskfree asset. efnng T g as nvestor s tax rate on captal gans and T p as the nvestor s tax rate on ordnary ncoe, t follows that : rˆ = P 1 P P 0 0 (1 T g + P 0 1 + U (1 T P P P 1 0 = + 1 + U (1 T g 1 + U P P P 0 0 0 ( T T p g = ˆ R (1 Tg 1 + U ( Tp Tg P 0 and, slarly : rˆ K = K (1 T g P K K 0 1 + U k k ( T p T g Also r = R 1 T ( p 6 In ths forulaton the ter U( /P 0 s equvalent to Offcer s ter τ, defned as the value of the tax credts expressed as a proporton of the current value of the share (Offcer, 1994, p. 7. 6
Then, assung that the end of perod dvdend s non-stochastc, substtutng these results nto (2 and dvdng by 1 T gves : 7 ( g 1 Tp E(ˆ r K r Tp Tg E( = + R (1 Tg Cov(, K 1 + U 1 Tg Var(ˆ rk P0 1 Tg efnng w as the fracton of aggregate arket nvestents held by nvestor, and λ as λ E(ˆ rk r = Var(ˆ r K (1 T g then, ultplyng (3 through by w, dvdng by λ, sung across all nvestors, and notng that w K =, gves : (3 w 1 TP w E R R λ ( ˆ = 1 Tg λ Cov(, + P + T p 1 U 0 1 _ T T g g. w λ that s, where E( R (1 T = Cov(, w λ + d 1 + U T (4 d = P 0 T = x = Tp Tg x (5 1 Tg w λ w λ w = E(ˆ rk r Var(ˆ rk ( 1 T g E (ˆ rk r Var ( rˆ K w ( 1 T g (6 Snce (4 holds for all securtes, t ust also hold for the arket, that s : 7 In respect of the assupton of non-stochastc dvdends, Lally (1999 shows that, f dvdends are nstead assued to be stochastc, the only ateral effect s to replace dvdends by ther expectatons n the resultng odel. 7
E( R Var( (1 T = w λ + d 1 + U T Solvng for w / λ, and substtutng nto (4, gves the CAPM wth dfferental taxaton : ( E( = R (1 T + d 1 + U T + E( R (1 T d U 1+ that s : T β [ E( R ] + E( = R + β (7 where = + + + T d 1 U R β R d 1 U (8 Coparson of the CAPM derved above, wth the Offcer CAPM (equatons (7 and (1 respectvely, shows that the approxaton ade n usng the Offcer CAPM s gven by. ro (8 t s readly seen that (n general = 0 f (1 T = 0, that s, that captal gans and ordnary ncoe are taxed equally, on average. A suffcent condton s that T g = T p for all, or (2 β = 1, d = d and / = /, that s, the stock atches the arket n respect of each of beta, dvdend yeld, and putaton credts relatve to dvdends. As already noted earler, captal gans and ordnary ncoe are not taxed equally under the Australan tax syste and therefore condton (1 does not hold. Condton (2 ust hold (n a loose way on average and therefore the Offcer CAPM wll on average provde a very good approxaton to the result of applyng the CAPM wth dfferental taxaton. However, for any gven securty, the degree of approxaton could be sgnfcant. 8
3. EGREE O THE APPROXIMATION We exane the degree of approxaton by substtutng nto the forula for a plausble value or range of values for each of the paraeters deternng. 3.1 Paraeter Values The relevant paraeters are the rskfree rate, beta, dvdend yeld, the rato of putaton credts to cash dvdends, the utlsaton rate for putaton credts, and the tax paraeter T. Consstent wth recent experence, we assue that the rsk free rate s 0.065. In respect of beta, a plausble cross-sectonal range s 0.5 to 1.5. The arket dvdend yeld s about 0.03 (data courtesy of Ord Mnnett and a plausble cross-sectonal range s 0 to 0.1. The arket rato of putaton credts to cash dvdends s 0.33 (data courtesy of Ord Mnnett. At the fr level ths can range fro 0 to a axu of 0.56 (based on the current corporate tax rate of 36%. The axu wll fall to 0.49 durng the transton (whle the corporate tax rate s 33%, and to 0.43 when the corporate tax rate reduces to 30%. We therefore consder a cross-sectonal range fro 0 to 0.50. The utlsaton rate, U, s coonly estated at 0.6, whch s consstent wth the fact that foregn nvestors are sgnfcant n the arket but cannot use the credts (the supportng studes are Brown and Clarke, 1993; Bruckner et al, 1994; Offcer and Hathaway, 1995. However, the CAPMs consdered n ths paper assue that natonal sharearkets are fully segented. Consequently the utlsaton rate should be 1 other than for the arket weght of Australan nvestors unable to use the credts. The only nvestors of ths type are tax-exept, and Wood (1997, footnote 10 estates that ther arket weght s ust 3-4%. Thus 1.0 s a reasonable estate for U. However we also consder the pact of usng nstead the ore coon estate of 0.6. The fnal paraeter requrng estaton s T. As shown n equaton (5, ths s a weghted average over nvestors of the tax rato [ ], wth weghts x. Estaton of T thus requres specfcaton of the relevant nvestor set, estaton of ther tax rates on both 9
ordnary ncoe and captal gans, and estaton of the weghts, x. The holders of Australan equtes can be classfed as foregners, copanes, superannuaton funds and ndvduals. Snce the CAPM n queston, along wth the Offcer verson, assues that natonal captal arkets are segregated, then t would be nconsstent to recognse foregn nvestors. Accordngly we ot the fro consderaton. In respect of corporate holdngs of shares n other copanes, ncluson of the would lead to double-countng. Consequently we ot the. If copanes were subect to taxaton on the dvdends receved fro other copanes the personal tax rates faced by the ultate recpents (ndvduals and superannuaton funds would need to be ncreased to reflect ths. However, copanes are not taxed on dvdend ncoe, and therefore ths potental coplcaton s absent. Thus, havng excluded both foregn nvestors and corporate shareholders, only ndvduals and superannuaton funds need to be consdered. Under the new tax syste, the hghest argnal tax on ordnary ncoe for ndvduals wll rean at 0.47 but any ndvduals wll actually pay lower rates because of the progressve scale or because of ncoe splttng. We assue that ndvduals are, on average, subect to a 0.35 tax rate on ordnary ncoe. In contrast, we assue that superannuaton funds wll face the statutory tax rate of 0.15 on ordnary ncoe. Turnng to captal gans, n Australa there are two reasons for taxes on captal gans beng lower than on ordnary ncoe. rstly, only part of the assessable gan s taxable under the new tax syste. Indvduals wll be subect to tax on only 50% of assessable captal gans, and superannuaton funds on 67% of assessable captal gans. Under the old tax syste, only the real gan was subect to tax. Secondly, captal gans are taxed only on realsaton and the resultng opportunty to defer the tax effectvely reduces the rate of the tax. Protopapadaks (1983 estates that the opportunty to defer reduces the tax rate on captal gans by about 50%. 8 These two features of the taxaton rege for captal gans suggest that on average ndvdual nvestors and superannuaton funds wll pay captal gans tax at only 25% and 33% respectvely of the rates applcable to ordnary ncoe. Appled to the above estates for tax rates on ordnary ncoe ths 8 The opportunty to defer lowers the effectve tax rate not only because of the te value of oney but also, as Hason and Zegler (1990, p. 49 note, because gans can be realsed when the nvestor s tax rate s lower, such as n retreent. 10
ples effectve captal gans tax rates of 0.0875 and 0.05 respectvely. That captal gans are taxed less onerously than ordnary ncoe, because of exeptons and/or the deferral opton, s well recognsed, not only for Australa (see Howard and Brown, 1992 but other countres such as the US (see Constantndes, 1984 and the UK (see Ashton, 1991. In respect of the weghts appled to the rato n equaton (5, the weght for nvestor s x = w E(ˆ rk r Var( rˆ K ( 1 T g E (ˆ rk r Var ( rˆ K w ( 1 T g The ter [ ] reflects the rsk averson of nvestor, and s unknown. Gven the absence of nforaton about cross-sectonal varaton n rsk averson, we assue that t s unfor across nvestor tax categores. The weght for nvestor thus reduces to x = w ( 1 T ( 1 T g w g or ndvduals and superannuaton funds the arket nvestent weghts, w, are 23% and 11% respectvely. 9 Substtutng for these values and the captal gans tax rates estated above yelds values for x of 0.68 for ndvduals and 0.32 for superannuaton funds. Substtuton nto equaton (5 produces an estate for the tax paraeter T of 0.23. The results of research on the behavour of ex-day returns provdes broad support for the estate for T. 10 Based on Australan data for the perod 1986-1995, Hathaway and Offcer (1995, Table 2 report an ntercept of 0.70 to 0.84 n regressons of P/ (share prce change over the ex-dvdend day dvded by the cash dvdend on the putaton credts attached to the dvdend. The results are consstent wth the earler work by Brown and Walter (1986, coverng the perod 1974-1985. The ntercept n such 9 These weghts are taken fro the ASX act Book, 1999. We are grateful to avd McCallu of ABN AMRO for advce on estaton of the average tax rates. 10 We are grateful to John Redayne of PrcewaterhouseCoopers for suggestng ths approach to estatng T. 11
regressons can be nterpreted as beng the ean value of P/ n the absence of putaton credts. In such crcustances, arbtrage suggests that ( 1 T = ( P 1 ga T pa where T ga s the average tax rate on captal gans and T pa s the average rate on ordnary ncoe. Thus P = ( 1 Tpa ( 1 T ga = 1 ( Tpa Tga 1 Ta ( 1 T ga The ntercept values of.70 to.84 thus suggest an estate for T a n the range 0.16 to 0.30. In general T a s not equal to T, because of varaton n the captal gans tax rates across nvestors. However, n ths case, there s lttle such varaton and therefore T a should be close to T. The research nto ex-day returns thus ndcates that T les n the range of 0.16 to 0.30. Ths approach to estatng T a does gve rse to a nuber of concerns, ncludng statstcal uncertanty n the estate of the ntercept and varous alternatve explanatons for ntercept values dfferng fro 1. The latter nclude crostructure explanatons (rank and Jagannathan, 1998, evdence of anoalous behavour n the broader perod around the ex-day (Brown and Walter, 1986 and the possblty that the value reflects the actons of arbtrageurs n a partcular tax bracket buyng ust before and sellng ust after the ex-day. In vew of these concerns, n the senstvty analyss we adopt the estate for T of 0.23 derved above but, n recognton of the uncertanty surroundng that estate, we consder a range of possble values fro 0.13 to 0.33. 3.2 Senstvty Analyss Table 1 below shows the values of for selected cobnatons of the values of the paraeters. Adoptng the estates T = 0.23, R = 0.065, U = 1.0, d = 0.03, and / = 0.33, the senstvty of to varatons n d, /, and β s exaned by varyng one of the latter three paraeters over ts relevant range and holdng the other two at ther boundary values. Thus varyng d over the nterval [0, 0.10] results n varyng as follows: 12
over [-0.012, 0.011] for / = 0 and β = 0.5 over [-0.006, 0.017] for / = 0 and β = 1.5 over [-0.012, 0.022] for / = 0.5 and β = 0.5, and over [-0.005, 0.028] for / = 0.5 and β = 1.5 Slarly, varyng / over the nterval [0, 0.5] results n varyng as follows: over [-0.012, -0.012] for d = 0 and β = 0.5 over [-0.006, -0.005] for d = 0 and β = 1.5 over [0.011, 0.022] for d = 0.1 and β = 0.5, and over [0.017, 0.028] for d = 0.1 and β = 1.5 nally, varyng β over the nterval [0.5, 1.5] results n varyng as follows: over [-0.012, -0.006] for d = 0 and / = 0 over [-0.012, -0.005] for d = 0 and / = 0.5 over [0.011, 0.017] for d = 0.1 and / = 0, and over [0.022, 0.028] for d = 0.1 and / = 0.5 The senstvty of to varaton n U s exaned by repeatng the above calculatons wth U = 0.6 nstead of 1.0. The results are shown n the sxth colun of Table 1. nally, we consder T. Snce T s proportonal to then, f T ncreases by 43% fro 0.23 to 0.33, the absolute value of also ncreases by 43%. Slarly, f T s reduced to.13, the absolute value of declnes by 43%. Ths s evdent fro coparson of the fourth and seventh coluns of Table 1. The conclusons fro ths senstvty analyss are as follows. rst, across the range of values consdered for the paraeters, vares draatcally: wth T =.23, the varaton s fro 0.012 to 0.028; wth T = 0.33, the varaton ncreases proportonately fro 0.017 to 0.041. Second, varatons n each of β, / and U does not, n general, result n a sgnfcant effect on the value of (defned as ore than 0.01. Thrd, varatons n d are sgnfcant for any cobnaton of values of the other paraeters. 13
The key nfluences on are thus d and T. or copanes wth a hgh dvdend yeld, use of the Offcer CAPM results n underestaton of the cost of equty captal. Conversely, for low dvdend yelds, the cost of equty captal wll be overestated. As T ncreases ths effect s agnfed. The ost sgnfcant underestaton result occurs wth large values for both d and T, where the Offcer CAPM would underestate the cost of equty captal by as uch as 0.041. 3.3 Consequences The consequences of the approxaton dentfed n the precedng secton are twofold. rst, snce the cost of equty s a coponent of the weghted average cost of captal, whch s used to calculate the present value of the cash flows fro prospectve proects, use of the Offcer CAPM could lead to the ncorrect reecton and/or acceptance of soe proects. 12 Undoubtedly the adopton decson for any proects wll not be senstve to varatons n the cost of equty to the degree shown here. Nevertheless the decson for at least soe proects wll be affected. or proects wth very long lves, varatons of even two percentage ponts to the dscount rate can have a substantal effect upon present value, and therefore on the adopton decson. The second consequence s for utlty copanes whose output prces are set on the bass of estated cost of captal, such as those nvolved n electrcty, gas or arports. The recent prce deternaton for electrcty copanes ssued by the regulator for Vctora (Offce of the Regulator-General, Vctora, 2000 provdes a relevant exaple. The paraeter values adopted were R = 0.062, U = 0.60, and β was set equal to 1.00 for all copanes. Aong the copanes subect to the regulatons s Envestra, whch has a dvdend yeld of 0.097, and a rato of putaton credts to cash dvdends of zero (data fro Blooberg. Thus, usng the addtonal arket paraeter estates dscussed above, of T = 0.23, d = 0.03 and / = 0.33, the resultng value of for the copany s 0.014. That s, n ths case, the Offcer CAPM underestates the cost of equty captal by 1.4 percentage ponts. If T = 0.33, ths rses to two percentage ponts. The revenue plcatons of ths underestaton would be very substantal for the 12 Wth an average leverage level for Australan copanes of 19% (Ernst and Young, 2000, the cost of equty s the donant coponent n the weghted average cost of captal for the average Australan copany. 14
copany. urtherore, ths s not a pathologcal case as hgh dvdend yelds are coon aongst utlty copanes. One response to the analyss presented above ght be to argue that the true value of T s hghly uncertan and that the bounds on the value of are odest. Consequently a departure fro the Offcer odel n favour of the odel presented here s not ustfed. However, the Offcer CAPM essentally represents a frst step odfcaton to the standard verson of the CAPM (Sharpe, 1964; Lntner, 1965; Mossn, 1966, n that t ncorporates dvdend putaton but not dfferental taxaton of captal gans and ordnary ncoe. efnng asset s return n the standard way as 13 P 1 P 0 R = + P P 0 0 then the standard verson of the CAPM states that [ E( R R ] β E( R = R + (9 The Offcer CAPM n equaton (1 can be expressed as that s E R + d U = R + E R [ E( R R ] β + θ + d U R β E( R = R + (10 where θ = U β d d (11 13 Because returns are defned n ths way the beta n the standard CAPM wll be defned aganst such returns, and therefore ght see to dffer fro the beta n the Offcer CAPM. However the Offcer odel (as wth the odel presented n ths paper arses by assung, nter ala, that dvdends are non-stochastc. Consequently the betas wll be the sae. 15
Coparson of (10 wth (9 shows that the Offcer CAPM specfcaton of E(R dffers fro that of the standard verson of the CAPM by the addton of θ. Slarly, the CAPM derved n ths paper, at (7 above, can be restated as E( R [ E( R R ] β + + = R + θ Thus, the standard verson of the CAPM s-estates E(R by the aount (θ +, and the Offcer odel s a frst step n correctng ths through the addton of θ. Table 1 shows the values of θ and (θ +. Two sgnfcant conclusons are apparent fro a coparson of, θ, and (θ +, usng the values for U and T of 1 and 0.23 respectvely. rst, across the eght cases consdered n the rows of Table 1, the average absolute values for θ and are coparable, at 1.7% and 1.4% respectvely. 14 Thus, looked at n solaton, the Offcer adustent to the standard CAPM (θ and the adustent to the Offcer odel proposed n ths paper ( are of coparable portance. Second, across the eght cases consdered n Table 1, the average absolute error n the Offcer odel ( s uch the sae as that n the standard CAPM (θ +. Ths s because s typcally opposte n sgn to θ. 15 Consequently, as often as not, applcaton of the Offcer CAPM ether adusts the standard CAPM n the wrong drecton (relatve to the approprate adustent of θ + or adusts n the approprate drecton by over twce the approprate level. Thus, as often as not, the Offcer CAPM produces a cost of equty further fro the approprate value than that produced by the standard CAPM. A draatc exaple appears n the last row of Table 1: the standard odel overstates the cost of equty by only 0.7 percentage ponts (θ + whereas the Offcer odel understates t by 2.8 percentage ponts (. These ponts ply that, f dvdend putaton s to be recognsed, t s at least as portant to addtonally recognse dfferental personal taxaton of captal gans and ordnary ncoe. Such a CAPM could take the for derved n ths paper (reflectng the 14 If U = 0.6, the fgures becoe 1% and 1.3% respectvely. 15 Exanaton of the forulas for and θ n equatons (8 and (11 respectvely provdes the explanaton. The ter s a postve functon of d and /, and a negatve functon of d and /. or θ the reverse holds. 16
copany tax vew of putaton or, alternatvely, a odel reflectng the nvestor tax vew of putaton. 4. CONCLUSION In ths paper we have shown that, wth dfferental taxaton of captal gans and ordnary ncoe, the Offcer CAPM ay sgnfcantly sestate the cost of equty captal. Relatve to a odel that addtonally allows for ths dfferental taxaton, the degree of the approxaton fro use of the Offcer CAPM s on average zero and senstvty analyss shows that n any crcustances the degree of approxaton s qute sall. However, where the dvdend yeld s very hgh, the cost of equty could be underestated by around four percentage ponts. The prncpal consequences of ths are twofold. rst, soe proects wll be properly accepted or reected. Second, for copanes whose output prces are set on the bass of cost of captal, such as utlty copanes, underestaton of the cost of equty captal could have sgnfcant revenue plcatons. Accordngly t would see to be approprate to swtch to the use of a CAPM verson that recognses both dvdend putaton and dfferental taxaton of captal gans and ordnary ncoe. Such a CAPM could take the for derved n ths paper (reflectng the copany tax vew of putaton or, alternatvely, a odel reflectng the nvestor tax vew of putaton. 17
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TABLE 1 The egree of Approxaton n the Offcer Model d / β θ + θ T =.13 T =.23 T =.23 T =.33 T =.23 T =.23 T =.23 U = 1 U = 1 U =.6 U = 1 U = 1 U =.6 U = 1 0 0 0.5 -.007 -.012 -.012 -.017.005.003 -.007 0 0 1.5 -.004 -.006 -.005 -.009.015.009.009 0 0.5 0.5 -.007 -.012 -.012 -.017.005.003 -.007 0 0.5 0.5 -.003 -.005 -.005 -.007.015.009.010 0.1 0 0.5.006.011.011.016.005.003.016 0.1 0 1.5.009.017.018.024.015.009.032 0.1 0.5 0.5.013.022.018.032 -.045 -.027 -.023 0.1 0.5 1.5.016.028.025.041 -.035 -.021 -.007 Ths table show values for, θ and ther su for varous cobnatons of the fr specfc paraeters d, / and β, and the arket-wde paraeters T and U. All calculatons assue R =.065, d =.03 and / =.33. 21