1 Working Paper 2009:7 Deparmen of Economic Dividend axaion, hare repurchae and he equiy rap Tobia Lindhe and Jan Söderen
2 Deparmen of Economic Working paper 2009:7 Uppala Univeriy May 2009 P.O. Box 53 ISSN SE Uppala Sweden Fax: DIVIDEND TAXATION, SHAE EPUCHASES AND THE EQUITY TAP TOBIAS LINDHE AND JAN SÖDESTEN Paper in he Working Paper Serie are publihed on inerne in PDF forma. Download from hp:// or from S-WoPEC hp://wopec.hh.e/uunewp/
3 DIVIDEND TAXATION, SHAE EPUCHASES AND THE EQUITY TAP Abrac Thi paper reconider he effec of dividend axaion. Paricular aenion i paid o he form of he equiy rap, ha i, he exen o which cah paid o he hareholder mu be axed a dividend. Our analyi how ha Sinn (99) criicim of he well-known ing and Fulleron (984) mehodology for undereimaing he co of new hare iue amoun o a mileading comparion acro wo differen regime for he equiy rap. Conrary o Sinn, we find ha when dividend are paid following a new iue, a aumed by ing-fulleron, he co of capial i higher han i he cae when no dividend are paid. eyword: dividend axaion, hare repurchae, equiy rap, co of capial, nucleu heory, growh pah JEL Code: H24, H25, H32 Tobia Lindhe Uppala Cener for Fical Sudie (UCFS) Deparmen of Economic Uppala Univeriy Jan Söderen* Deparmen of Economic Uppala Univeriy Box 53, Uppala, Sweden May We are graeful o Michael ii Jacoben and Guorm Schjelderup a well a o oher paricipan of The eearch Forum on Taxaion a Holmbu, Norway, June 2-4, 2006 for valuable commen on an earlier verion of hi paper (Lindhe and Söderen, (2006)), and o Vea anniainen and Chuan-Zhong Li for helpful uggeion. *Correponding auhor.
4 2. Inroducion The economic conequence of dividend axaion have been he ubjec of a coninuing debae among public finance reearcher for more han a quarer of a cenury. Much of hi dicuion ha been concerned wih wheher he new or old view of dividend axaion be decribe i effec. A crucial difference beween he wo view i in he ource of equiy finance ued a he margin by he corporae firm. Under he new view, or rapped equiy" model, he marginal ource of equiy i reained earning. A he dividend ax reduce he opporuniy co o he hareholder of an addiional uni of profi reained for invemen in he ame proporion a i reduce fuure dividend, he dividend ax ha no impac on invemen incenive. Under he old view, he dividend ax fall alo on marginal invemen projec. Though he exac inerpreaion of he old view varie beween differen reearcher, a common aumpion i ha he firm i unable o cu dividend o finance new invemen projec or find i coly o do o. 2 Wih new iue of hare raher han reained profi a he marginal ource of equiy, he hareholder opporuniy co of invemen i no miigaed by he dividend ax, and a a reul, he ax reduce he rae of reurn o invemen. Tha he dividend ax fall on marginal invemen financed by new iue of equiy i, however, acceped alo by holder of he new view. New view- model ypically ae ha he co of new hare iue equal he hareholder afer-ax rae of reurn requiremen adjued for he oal ax a he corporae and peronal level levied on diribued profi. A ueful reference here i he udy by ing and Fulleron (984) whoe formulae for he co of capial ha been pu o a widepread ue in inernaional comparion and for policy oriened reearch. 3 Some ime ago, however, Sinn (99a) claimed ha he diorion from dividend axaion i larger han he convenional formulae uch a hoe derived in ing and Fulleron (ibid.) ugge. Sinn poin, alo argued in Sinn (99c), i ha care mu be aken o diinguih no only beween alernaive ource of finance bu alo, and equally imporan, beween alernaive ue for profi. The new view of equiy wa developed by Auerbach (979), Bradford (98) and ing (977). For a urvey of he debae, ee Auerbach (2002) and Auerbach and Hae (2002, 2005). 2 See Auerbach (2002). 3 See for example OECD (99) and EU (200).
5 3 To derive he co of equiy, Sinn (99a) e up a model of an all-equiy firm, wih a peronal ax on dividend a he only ax parameer. Share repurchae are ruled ou, leaving dividend and inernal invemen a he only poible ue of profi. The oucome of hi model i a nucleu heory of he corporaion. A firm faced by an iniial horage of reainable profi following a diurbance o he marginal produciviy of capial, will le he hareholder injec le han he oal amoun of fund needed o reach a new long-run equilibrium. Once he nucleu of new equiy ha been obained, he firm embark upon a growh pah uing le expenive reained earning. The firm hen coninue o grow by inernal fund, iuing no more hare, and paying no dividend unil he marginal produciviy of capial i equaed o he rae of inere. Though no parameric expreion for he co of new equiy i obained from hi analyi, Sinn find, for mild aumpion abou he form of he firm producion funcion, ha he marginal produciviy of capial ubequen o he iue of new equiy i higher han uggeed by ing and Fulleron (984) and oher 4. Sinn explanaion o hi reul i ha he ing-fulleron mehodology invariably aumed ha profi from marginal invemen projec were diribued a dividend 5, raher han ued for inernal invemen. Sinn nucleu heory, or life-cycle model of he firm, i widely cied, and hi claim ha convenional formulae underae he co of equiy fund eem no o be queioned. Sill, he ing-fulleron equaion have remained he generally acceped bai for meauring incenive effec of axe on income from capial, and over he pa decade a va lieraure ha emerged which ha developed he original model in variou direcion. 6 There are hence wo compeing view in he lieraure regarding he impac of axaion on he co of equiy fund. Thi paper reconider he effec of dividend axaion on he co of new hare iue. We conclude ha Sinn criicim of convenional formulae for undereimaing he co of new equiy i mileading and i in fac a comparion beween apple and orange. The reaon for hi i ha Sinn and ing-fulleron make ue of differen aumpion no only abou 4 Sinn (99a), p Ibid., p See for example, Chennell and Griffih (987), Jorgenon and Landau (993), Devereux and Griffih (2003), Sørenen (2004).
6 4 dividend behavior following a new iue of equiy (a Sinn poin ou) bu alo, and more imporanly, abou he equiy rap, ha i, he exen o which cah paid by he firm o he hareholder mu be axed a dividend. In Sinn model, new hare iue are conrained o be non-negaive, and hare repurchae (and oher form of a ax-free recovery of equiy) are ruled ou. The co-of-capial expreion of he ing-fulleron ype inead implicily rely on he oppoie aumpion, namely ha hareholder are allowed a ax-free recovery of original capial conribued hrough new hare iue. Thi mean ha new hare iue never fall ino he equiy rap. Thi fundamenal difference in aumpion abou he equiy rap, ha i, he deign of he ax code, explain Sinn finding ha he co of new hare iue i higher han he convenional ing-fulleron formulae ugge. In fac, he ing-fulleron aumpion ha dividend are paid ubequen o a new iue, doe no caue a downward bia in eimaing he co of capial, a Sinn argue. Wih dividend being paid in he year following he new iue, he co of capial raher urn ou o be higher han i he cae when he firm behave opimally (wha i opimal behavior depend on he equiy rap). The remainder of hi paper i organized a follow. In ecion 2 we e up a dynamic model of an all equiy firm, where, a in Sinn (ibid.), a peronal ax on dividend i he only ax parameer. To ome exen, he firm may avoid he equiy rap, hrough a ax-free recovery of original capial. In he preen model, hi i equivalen o repurchaing own hare, and we model a conrain on hare repurchae which reflec rule in force wihin he European Union. We derive a general expreion for he co of capial, where he reul of Sinn and ing-fulleron appear a pecial cae. For comparion wih our general model, ecion 3 preen a brief review of Sinn (99b) analyi of hare repurchae, where Sinn aume a fixed proporion beween hare repurchae and dividend. The opimal behavior of he firm following a new iue of equiy i deermined in ecion 4, which alo repor on numerical imulaion o compare he firm behavior under differen aumpion abou he equiy rap. Secion 5 conclude. 2. The model
7 5 We derive he firm co of capial by eing up a dynamic model in dicree ime wih a peronal ax on dividend τ a he only ax parameer. The owner i aumed o maximize he afer-ax dividend ream, ne of new hare iue and hare repurchae, given by θ D N +, () = ( + r) where D denoe dividend a defined in he firm accoun, N i he amoun of new hare iue, i he curren flow of hare repurchae, r i he dicoun rae and θ i he afer-ax value of a uni of dividend, θ τ. The firm budge conrain in period i a cah flow ideniy, where capial inflow equal capial ouflow ( ) F + N = D + I +. (2) The producion funcion F ( ) depend only on he ock of capial, where he ock in period become fully efficien in producion in period. To keep he model imple, capial depreciaion i ignored, which implie ha he ock of capial evolve over ime a + I =. (3) A uual, dividend mu be non-negaive D 0, (4) and we alo require iue of new equiy o be non-negaive N 0. (5) A Council Direcive fir adoped in 976, and laer amended in November 992, regulae he ue of hare repurchae for companie wihin he European Union 7. Preen rule ae 7 The Second Council Direcive on Company Law, Direcive 77/9/EEC on he formaion of public limiedliabiliy companie and he mainenance and aleraion of heir capial ( ). Amendmen: Direcive 92/0/EEC ( ).
8 6 ha own hare acquired by a company may no exceed 0 percen of he ubcribed capial. To capure hi rule and examine i impac on he co of capial, we inroduce a variable A which i he ock of pa equiy injecion (he firm hare capial), and a variable G defined a he ock of curren and pa hare repurchae. Variable A evolve a A + N = A, (6) and and G are relaed hrough he moion G + = G, (7) where 8 0, (8) and G α A. (9) Thi mean ha he firm may own a mo a fracion α of i own hare capial (EU law require α 0.). The model define a dicree-ime conrol problem wih conrol variable N, D, and I, and ae variable, A and G. By impoing hadow value for he conrain and moion for (2), for (3), A for (6), G for (7), D λ for (4), N λ for (5), λ for (8), D G λ for (9) and maximizing he owner afer-ax dividend ream he opimizaion problem ake he form max = Λ() ( + r). The Λ -funcion read a 8 Alernaively, we could allow he firm o revere pa re-purchae, ha i, o ell previouly acquired hare, <0. However, o preven he firm from circumvening rericion (9), by ubiuing negaive re-purchae for regular new hare iue, hi would require ha we alo impoe he rericion G 0.
9 7 D ( ( ) ) ( ) ( ) Λ= θd N + + F + N I D + + I + A + N A + ( G + G ) A G D N G + λ D + λ N + λ + λ ( αa G ). (0) The fir order condiion wih repec o he ae and conrol variable are D D D θ + λ = 0, () D I + = 0, (2) D F = 0. (3) + r + r N + D + A + λ N = 0, (4) A A + G A + + αλ = 0. (5) + r D + G + λ = 0 (6) G G + G G + λ = 0 + r (7) Equaion (2) and (3) yield he general expreion for he co of capial F ( + r) + =, (8) + ha i, he co of capial i deermined by he rae of inere and he marginal valuaion of capial,, for wo conecuive period.
10 8 2. The long-run co of capial For a firm ha relie on reained earning a he marginal ource of finance and alo pay D dividend, he hadow value of he dividend conrain appearing in (4) i zero, λ = 0. Since D = (eq. 2), he fir order condiion for D (eq. ) hen implie ha in long-run equilibrium, = + = θ. The general expreion for he long-run co of capial in (8) i herefore F = r. (9) Wih = θ, he owner i indifferen beween reaining earning and receiving dividend, and a a reul of hi, he dividend ax doe no dior he eady ae value of he firm capial ock. Thi i he well-known reul from he new view of equiy. 2.2 New equiy a he marginal ource of fund New hare are iued by he firm only occaionally a a repone o exogenou diurbance o he produciviy of capial when reained earning are inufficien o finance he required addiion o he capial ock. A firm hi by a produciviy hock in period will iue new N hare (wih λ = 0 ) ufficienly o depre he marginal value of equiy o uniy. In hi model, a een from equaion (4), hi marginal value come from wo concepually differen A ource, + =. The fir i he direc increae in he producive capaciy of he firm, D which i valued a he hadow price of capial, ( =, ee eq. 3). The econd derive from he fac ha he new equiy o ome exen (depending on α ) enable he owner a ax- A free reurn of capial, valued a he hadow price. A G Solving equaion (5) and (7), we find ha = α. Wih when N > 0, equaion (4) may hen be wrien a D = and wih λ N = 0 A G = = + α. (20) G G Since ( ) = + when conrain (9) doe no bind, equaion (6) and (7) give ha + r
11 9 + λ + r G + + =. (2) Combining (20) and (2) furher yield ( ) α λ = + r. (22) Finally, by inering (22) ino (8), we derive F ( ) + r α + + λ+ + =, (23) + which i he co of capial when he firm iue new hare a ime. I i clear from equaion (22) and (23) ha for a given hadow price of capial, +, allowing for harerepurchae ( α > 0 ), or oher form of ax-free diribuion of cah, reduce he co of capial. However, ince he marginal value of capial in he period ubequen o he new iue, +, canno be deermined wihou furher aumpion, no parameric expreion for he co of capial i available. 2.3 Sinn (99a) reul reconidered When he firm i no allowed o own i own hare (or i oherwie no allowed o underake ax-free diribuion of cah), α = 0, he model above i a dicree-ime verion of Sinn (99a) coninuou-ime model. Equaion (23) hen implifie o F + r + =, (24) + which correpond o Sinn expreion for he co of new equiy. One of he imporan concluion from Sinn analyi i ha, for mild aumpion abou he form of he firm producion funcion, he co of capial ubequen o an iue of new
12 0 equiy i higher han obained from he expreion for new equiy derived by ing- Fulleron and oher, ha i F ( + r) + r = >. (25) τ + Sinn furher claim ha earlier reearch undereimaed he rue co of equiy becaue of he aumpion ha profi from marginal invemen projec invariably were diribued a dividend. A fir queion here concern he validiy of Sinn explanaion o inequaliy (25). In he preen dicree-ime verion of Sinn model, i i raigh-forward o deermine he co of capial in cae he firm pay dividend in he year following he new iue. Wih when dividend are paid, and wihθ τ, expreion (24) implifie o 9 = + θ F r + τ =. (26) τ The aumpion ha he firm pay dividend in he year following he new iue hence doe no urn he general expreion for he co of new hare iue a derived by Sinn (99a), i.e. equaion (24), ino ing-fulleron expreion for co of new equiy, r /( τ ). Moreover, ince he hadow value + > θ, when no dividend are paid in he year following he new iue, he co of capial in (24) i acually lower han in he cae where he firm doe + r r + τ <. τ pay dividend, ha i ( ) + + Sinn explanaion o inequaliy (25) i herefore wrong, or a be, incomplee. Alhough he aumed dividend behavior doe affec he co of capial, here i acually a more fundamenal difference in aumpion beween Sinn (99a) and ing and Fulleron (984) ha drive he analyi of how he dividend ax affec he co of capial. Thi difference in aumpion will be explained below. 9 Expreion (26) correpond o a reul derived by Auerbach (983, p. 925).
13 Wih α =, i.e. where he firm i allowed o repurchae ouanding hare (or i oherwie allowed o underake ax-free diribuion of cah) o he exen of i conribued capial, i i raighforward o how ha he hadow price λ + in (23) i zero 0. The co of capial hen urn ou o be F r =. (27) + Thi equaion furher implifie when he firm pay dividend following he new iue. Wih = + θ and θ τ, we ge F r =. (28) τ Equaion (28) i immediaely recognized a ing-fulleron expreion for he co of capial wih new hare iue! I i alo clear ha wih + > θ, he co of capial in (27) i lower han in (28). The obviou concluion from he above analyi i ha Sinn criicim of he ing-fulleron model for undereimaing he co of new hare iue i mileading. The wo expreion for he co of capial which Sinn compare in hi analyi urn ou o differ no only in erm of he aumed dividend behavior, bu alo, and more fundamenally, by repreening differen ax regime. Sinn model explicily aume ha α = 0, while ing-fulleron approach may be viewed a a pecial cae of a regime wih α =. The aumpion ha profi from marginal invemen projec are paid a dividend (a in ing-fulleron) doe affec he co of capial, bu he direcion of hi effec i oppoie o ha uggeed by Sinn: Wih no dividend being paid in he year following he new iue, he co of capial i lower han i he cae when he firm pay dividend. Thi concluion hold irrepecive of he exen o which he firm may ecape he equiy rap hrough hare repurchae or oher form of axfree recovery of iniial equiy. 0 Adding he fir order condiion (4) and (6) and uing ha A G N α A = α give λ + λ =. Since α N λ 0 and λ 0, i i clear ha wih α = i mu hold ha λ = 0 and λ = 0,. N
14 2 3. Dividend and hare repurchae in fixed proporion (Sinn 99b) The model preened in ecion 2 allow he firm o freely chooe boh he iming and amoun of hare repurchae, ubjec o an upper limi of he ype implied by curren EU regulaion. In hi earlier conribuion Share repurchae, he new view and he co of capial, Sinn (99b) chooe a differen approach by impoing a fixed relaionhip beween cah dividend and hare repurchae. Thi ecion briefly explain Sinn approach and relae i o he model in ecion 2. A in ecion 2, we ignore boh corporae axaion, and hareholder axaion of capial gain. Wih hare repurchae (), he firm budge conrain (previouly given by eq. 2 above) i ( ) X D + = F + N I, (39) and Sinn aumpion ha cah diribuion o he hareholder are pli in fixed proporion beween dividend (γ ) and hare repurchae, ( γ ), implie ha D = γ X and ( γ ) = X. The firm objecive funcion wih hare re-purchae become (cf. eq. ) θγ X + ( γ ) X N, (40) = ( + r) where X i he oal cah flow paid o he hareholder (given in 39) and θ τ i he aferax value of a uni of dividend. Uing (39), hi i ( γτ )( ) ( + r) F ( + N I) N. (4) = Sinn aumpion ha he oal cah paid o he hareholder i pli in fixed proporion beween cah dividend and hare repurchae (axed a a preferenial rae, unaxed in hi cae), i herefore equivalen o diregarding hare repurchae and inroducing an overall Sinn model include boh corporae axaion (wih a pli rae yem) and peronal axaion of capial gain. Simplifying he analyi by ignoring hee axe doe no affec he characer of he reul, however.
15 3 reducion in he ax burden on dividend, from τ o γτ. The adjued ax rae γτ i imply a weighed average of he ax on dividend, τ, and he zero ax on hare repurchae, uing he proporion γ and γ a weigh. Given hi inigh (alo expreed in Sinn (99b)), i i obviou ha he new view reul for he long-run marginal produciviy of capial remain valid, bu alo ha he long-run marginal valuaion of equiy will equal uniy minu he adjued ax rae γτ. Tha he new view concluion regarding he marginal valuaion of equiy mu be revied in he preence of hare repurchae i no due o hare repurchae per e, however, bu raher o Sinn pecial aumpion ha dividend paymen and hare repurchae occur in fixed proporion. When he firm, a in ecion 2 above, i allowed o opimize he iming of boh hare repurchae and dividend, hare repurchae will precede he paymen of dividend, a we demonrae in ecion 4 below. A a reul, he long-run marginal valuaion of equiy i τ, ha i, he new view valuaion reul i fully preerved. 4. Opimal behavior and he firm growh pah We nex urn o analyzing he firm opimal behavior following a new iue of equiy. We fir decribe how he incenive faced by he firm depend on he hare-repurchae parameer α, and we hen proceed o illurae he behavior of he firm making ue of a few numerical imulaion. In Sinn (99a) cae, where all cah diribuion o hareholder mu be axed a dividend ( α = 0 ), he firm will iue new hare ufficien o depre he marginal valuaion of capial,, o uniy 2. A wa briefly decribed in ecion above, opimal behavior i hen o embark upon a growh pah uing le expenive reained earning. A long a > θ he firm coninue o grow by inernal fund, iuing no more hare, and paying no dividend. Thi proce end when he marginal produciviy of capial i equaed o he rae of inere and he marginal valuaion of capial equal uniy minu he dividend ax rae, = τ θ. eader looking for a more deailed and formal reamen of hi cae are referred o Sinn paper. 2 A A The aring condiion i + =, where = 0 when α = 0. For furher explanaion, ee ecion 2.
16 4 In hoe cae where hare repurchae or oher form of a ax-free reurn of original equiy are allowed ( α > 0 ), he aring condiion i, likewie, ha he marginal valuaion of he injecion of new equiy fund equal uniy. However, a explained in ecion 2, hi marginal valuaion come from wo concepually differen ource. The fir i he direc increae in he producive capaciy of he firm, which i valued a he hadow price of capial,. The econd derive from he fac ha he new equiy o a lea ome exen enable he owner a A ax-free reurn of capial, valued a he hadow price. N In he pecial cae wih α =, we find ha λ = 0 and λ = 0,, a hown in foonoe (). A From equaion (2) and (4) i i hen clear ha he condiion + = will hold all along he firm opimal pah, wih falling from i iniial value in period in he range θ < <, o i long-run value of uniy minu he dividend ax rae. A in Sinn cae (wih α = 0 ) no dividend will be paid a long a > θ. Thi leave in urn wo poible ue of profi, ubequen o he new iue: for invemen and for hare repurchae. Wih α = i i raigh-forward o demonrae ha addiion o he capial ock are no compaible wih he fir-order condiion, a long a he ock conrain on hare repurchae i no binding, G < A. A een from he general expreion for he firm co of capial (eq. 8), he marginal value of capial will decreae from he curren period o he nex, < +, when he marginal produciviy of capial i higher han i long-run value, i.e. he rae of inere. Since he co of capial wih α = and a non-binding ock conrain on hare repurchae i F = r + (ee eq. 27), hi decreae in he marginal valuaion of capial beween period and + alo implie a rie in he marginal produciviy of capial and, hence, a decreae in he capial ock, + <. Wih a new iue in period, he fir order condiion herefore rule ou he poibiliy ha he firm would ue curren profi in he following period + for invemen, which would add o he capial ock. The only feaible ue of profi for period + i herefore for repurchaing of hare, and by he reaoning above hee repurchae will be financed boh by curren profi and ome diinvemen. Thi proce of repurchaing will coninue during he following period unil he ock conrain on hare repurchae (eq. 9) bind. The firm will hen wich o reaining
17 5 profi earned in ubequen period and add o i capial ock. Thi econd phae correpond o he growh pah analyzed by Sinn, where he firm coninue o grow by inernal fund, paying no dividend unil he new long-run equilibrium i reached. When he conrain parameer α i in he inerval 0< α < opimal behavior i differen. Wih G A = (eq. 5 and 7) and α D =, equaion (6) may be re-wrien a A + λ = 0. (6 ) α A Since he firm aring condiion i + =, equaion (6 ) implie ha λ > 0 for 0< α <, ha i, he non-negaiviy conrain on hare repurchae bind. The firm wan o engage in negaive hare repurchae (i.e. elling previouly acquired hare) o finance he required addiion o he capial ock, bu of coure i canno. Auming 3 ha hi incenive remain for he following period +, we alo rule ou (poiive) hare repurchae a a ue of profi for +. Wih no dividend and no hare repurchae, he firm will ar on a growh pah, financed by inernal fund, ju a in Sinn cae (wih α = 0 ). Thi inernally financed growh will caue he marginal valuaion of capial o fall over ime and evenually he A incenive for negaive hare repurchae will vanih, ha i + =. Thi mean ha he α firm i indifferen beween reaining earning and repurchaing hare, and a a reul, he firm ener a phae where curren profi will be ued for hare repurchae. Thi econd phae coninue unil he ock conrain on hare repurchae will bind, G = α A. Wih > θ, he firm hen ener a hird phae, where profi again are ued for invemen. Thi final growh phae end when he marginal valuaion of capial equal i long-run value, = θ, and he marginal produciviy of capial equal he inere rae. 3 On heoreical ground we canno rule ou he poibiliy ha =. In hi cae he firm would ar α by repurchaing hare a ime +, ju a in he cae wih α =. However, in he numerical imulaion repored below for 0< α <, we have no been able o deec any pah, which boh begin wih hare repurchae and i compaible wih he fir-order condiion. Thi ugge ha i i reaonable o aume ha A + + > α +, i.e. he firm will ar growing following a new hare iue. A
18 6 4. Numerical imulaion The difference in behavior beween firm facing differen poibiliie o repurchae hare or uing oher form of ax-free reurn of new equiy may be furher clarified by way of numerical imulaion. We will aume ha here occur an exogenou diurbance o he firm ha raie he marginal produciviy of capial, and ha he reuling invemen need canno be financed from reained earning. We refer o Appendix for a ep-by-ep accoun of he imulaion. In general erm, we make ue of he fir order condiion o deermine he developmen over ime of he marginal valuaion of capial,, he pre-ax marginal rae of reurn, F, he capial ock,, and in he cae where α > 0 he ock of new equiy, A, and he ock of hare repurchae, G. We pecify he firm producion funcion in Appendix and we aume ha he marke rae of inere i 5 percen. For he e of parameer choen, he long run capial ock i 00. The reul of he imulaion are illuraed in figure -2 for a dividend ax rae of 30 per cen ( τ = 0.3 ). We how how he parameer α affec he co of capial and he firm capial ock. Following a capial injecion in period, he co of capial evolve over ime back o i long run value of 5 percen in period +3. For α =, he co of capial i iniially 6.22 percen, or.24 ime i long run value, compared o 2,75 percen, or 2.55 ime he long run value, when α = 0. Figure. The co of capial following a new hare iue for differen value of α and τ = 0.3.
20 8 Figure 2. The ock of capial following a new hare iue for differen value of α and τ = α=0 5,4 9,3 23,7 28,6 33,9 39,7 46,0 52,8 60, 67,9 76, 84,8 94,0 00,0 α=0, 6,7 20,8 25,4 30,4 35,9 4,9 48,4 53,7 6,0 68,8 77, 85,9 95, 00,0 α=0,5 24,2 29, 34,5 40,3 46,7 53,5 54,9 56,2 63,6 7,6 80, 89,0 98,5 00,0 α=0,9 42,9 49,4 56,5 59,4 57,7 55,8 54,0 55,5 63,0 70,9 79,3 88,2 97,6 00,0 α= 64,5 63,0 6,3 59,7 57,9 56, 54,2 54,5 6,9 69,7 78, 86,9 96,3 00,0 A a reul of hee difference, here i a riking difference in he amoun of new equiy injeced by he hareholder. The iniial new iue i more han 4 ime a large when α = a i i when α = 0 (64.5 v. 5.4). Following he new iue, he firm ue all profi for inernal invemen when α = 0, and complee i growh pah in 3 year. The adjumen phae when α = i of approximaely he ame lengh, bu during he fir half of hi phae, he firm ue boh curren profi and diinvemen o reurn he original new equiy by way of hare repurchae. The inermediae cae where 0< α < are illuraed for α = 0,, α = 0, 5 and α = 0, 9. On heoreical ground we are no able o rule ou he poibiliy ha he firm will ar by repurchaing hare (a when α = ). The numerical imulaion rongly indicae, however, ha he firm, following he injecion of capial, will inead embark upon an invemen pah (a when α = 0 ), ee foonoe 4. Thi iniial growh phae i hen followed by a phae of hare repurchae (a when α = ). When he firm ha repurchaed he amoun of hare allowed by he ax code (a deermined by α ), a econd phae of invemen follow on he firm way oward long-run equilibrium. We alo find, a i clearly een in figure 2, ha he lower he parameerα, he longer i he fir invemen phae and he horer i he phae of hare repurchae.
21 9 Figure 3 and 4 give he correponding reul when he dividend ax rae i 5 percen ( τ = 0.5 ). A ax cu reduce he co of new equiy and increae he ize of he iniial equiy injecion. In general, a cu in he ax rae alo make he adjumen period horer, and hi effec i ronger he lower i α. The dioring effec of dividend axaion remain larger, however, he lower i α. Figure 3. The co of capial following a new hare iue for differen value of α, τ =. 5. 3% 2% % 0% 9% 8% 7% 6% 5% 4% α=0 9,07% 8,34% 7,72% 7,9% 6,72% 6,3% 5,95% 5,62% 5,33% 5,07% 5,00% 5,00% 5,00% 5,00% α=0, 8,87% 8,7% 7,58% 7,06% 6,6% 6,37% 6,00% 5,67% 5,37% 5,% 5,00% 5,00% 5,00% 5,00% α=0,5 7,98% 7,4% 6,92% 6,48% 6,48% 5,82% 5,58% 5,29% 5,03% 5,00% 5,00% 5,00% 5,00% 5,00% α=0,9 6,28% 5,92% 5,6% 5,64% 5,68% 5,7% 5,76% 5,80% 5,76% 5,45% 5,8% 5,00% 5,00% 5,00% α= 5,52% 5,55% 5,58% 5,62% 5,65% 5,69% 5,73% 5,77% 5,8% 5,6% 5,33% 5,06% 5,00% 5,00% Figure 4. The ock of capial following a new hare iue for differen value of α, τ = α=0 30,4 35,9 4,9 48,4 55,3 62,8 70,7 79, 88,0 97,4 00,0 00,0 00,0 00,0 α=0, 3,8 37,4 43,5 50, 57,2 6,6 69,4 77,8 86,6 95,9 00,0 00,0 00,0 00,0 α=0,5 39,3 45,5 52,3 59,5 59,5 73,9 80,4 89,4 98,8 00,0 00,0 00,0 00,0 00,0 α=0,9 63,3 7,3 79,6 78,6 77,6 76,6 75,5 74,3 75,4 84, 93,2 00,0 00,0 00,0 α= 82,0 8, 80,2 79,3 78,3 77,3 76,2 75, 74,0 79,6 88, 97,5 00,0 00,0
22 20 A we have explained in ecion 3, a raher differen approach o hare repurchae i aken in Sinn (99b). A fixed relaionhip i impoed beween hare repurchae and dividend. I i eaily een ha hi aumpion i anamoun o a reducion in he dividend ax rae, equal o he proporion of he firm cah flow which i diribued a ax-free hare repurchae. The impac on he co of capial and he firm capial ock when hare repurchae and dividend occur in equal proporion, may herefore be direcly inferred by comparing figure and 2, for τ = 0.3 and α = 0, o figure 3 and 4, for τ = 0.5 and α = 0. A he reul of hi ax cu hrough hare repurchae, he iniial injecion of equiy i doubled, and he adjumen period i hored by almo one hird. 5. Concluding commen In everal conribuion, Sinn (99a, c) ha argued ha he firm co of capial depend no only on he ource of fund, bu alo on he firm ue of profi. In our re-examinaion of he effec of dividend axaion on he co of new hare iue, we have emphaized a hird facor, namely he imporance of aking ino accoun alo he ax reamen of he reurn of he original capial injeced ino he firm by he hareholder. Earlier lieraure ha implicily or explicily inroduced varying aumpion on he ax conequence of a reurn of hareholder capial. In hi nucleu heory of he corporaion, Sinn (99a) conrain new iue o be non-negaive and rule ou hare repurchae. Thee aumpion, which are common in ax model of he firm, effecively urn he dividend ax ino a combinaion of a ax on (diribued) profi and a capial levy on iue of new equiy. In conra, model in he ing and Fulleron (984) radiion implicily aume ha hareholder are allowed a ax-free recovery of heir iniial equiy. Thi implie ha he dividend ax i confined o be a ax on (diribued) profi. Pu differenly, new hare iue never fall ino he equiy rap. Sinn (99a) criicim of he ing and Fulleron mehodology for undereimaing he co of new equiy hu amoun o a comparion acro wo differen ax regime. By emphaizing difference in he aumed ue of profi dividend v. reenion hi criicim i alo mileading. Though he firm dividend behaviour following a new hare iue doe affec he co of capial, our analyi how ha he direcion of hi effec i oppoie o ha uggeed by Sinn: Wih no dividend being paid, he co of capial i lower han i he cae when
23 2 dividend are paid. Thi reul hold irrepecive of he exen o which he firm may ecape he equiy rap hrough hare repurchae or oher form of ax-free recovery of iniial equiy. The firm behavior following a new hare iue crucially depend on he equiy rap. When no ecape i available, a aumed in Sinn analyi, he firm will embark upon a growh pah following he new iue, uing reained earning a he ource of fund. The growh pah i inead preceded by a phae of hare repurchae when he ax code allow he full amoun conribued by he hareholder o be reurned free of ax. Our numerical imulaion indicae a ubanial difference beween hee cae in he amoun of iniial equiy injecion, and a reuling difference in he oupu loe over he adjumen period. When he ax code i le generou, allowing ome ax-free reurn of equiy, our analyi indicae ha he firm will inead embark upon an invemen pah, following he injecion of capial. Thi iniial growh phae i hen followed by a phae of hare repurchae, ucceeded in urn by a econd phae of invemen on he firm way oward long-run equilibrium. We find moreover ha he le generou he cope for hare repurchae, he longer i he fir invemen phae and he horer i he phae of hare repurchae. The model preened in ecion 2 allow he firm o opimize he iming and amoun of hare repurchae, and we find ha hare repurchae will alway precede he paymen of dividend. In Sinn approach o hare repurchae (99b), however, hare repurchae and dividend by aumpion occur in a fixed proporion. A demonraed in ecion 3, and alo poined ou by Sinn, hi i anamoun o reducing he dividend ax rae. Once hi equivalence i underood, no addiional inigh abou he effec of hare repurchae are offered from hi approach. In concluion, we emphaize ha he choice beween Sinn (99a) and ing and Fulleron aumpion abou he equiy rap, a well a beween he inermediae cae, i ulimaely an empirical queion. I i clearly he cae ha echnique uch a hare repurchae and combinaion of pli and hare redempion, have gained in imporance in mo counrie ince he 990. Though he ax code varie acro counrie, mo counrie would alo allow hareholder a ax-free recovery of heir iniial equiy following a winding-up deciion. Thee procedure may rigger capial gain axaion, bu he deducibiliy of he acquiiion co of
24 22 hare old or redeemed enure ha he original conribuion of equiy capial o a large exen do ecape he equiy rap. eference Auerbach, Alan J., 979, Wealh Maximizaion and he Co of Capial, Quarerly Journal of Economic, Vol.93(3), pp Auerbach, Alan J., 983, Taxaion, Corporae Financial Policy and he Co of Capial, Journal of Economic Lieraure, Vol. 2, No. 3. (Sep., 983), pp Auerbach, Alan J., 2002, Taxaion and Corporae Financial Policy, in Handbook of Public Economic, Vol. 3, Ch. 9, pp Auerbach, Alan J. and evin Hae, 2002, On he marginal ource of invemen fund, Journal of Public Economic, Vol. 89, pp Auerbach, Alan J. and evin Hae, 2005, The 2003 dividend ax cu and he value of he firm: An even udy, NBE WP 449. Bradford, David F., 98, The Incidence and Allocaion Effec of a Tax on Corporae Diribuion, Journal of Public Economic, Vol. 5, pp Direcive 77/9/EEC (The Council of he European Communiie) Direcive 92/0/EEC (The Council of he European Communiie) Devereux, M. P. and. Griffih, 2003, Evaluaing ax policy for locaion deciion, Inernaional Tax and Public Finance,0, pp Devereux, M. P.,. Griffih and A. lemm, 2002, Corporae income ax reform and inernaional ax compeiion Economic Policy, 35, pp
25 23 EU (200), Company axaion in he inernal marke, Commiion aff working paper, COM(200) 582 final. ing, M. A., 977, Public Policy and he Corporaion (Chapman and Hall, London). ing, M. A. and D. Fulleron, 984, The Taxaion of Income from Capial. A Comparaive Sudy of he Unied Sae, he Unied ingdom, Sweden and We-Germany (Univeriy of Chicago Pre, Chicago). Lindhe, Tobia and Söderen, Jan, 2006, The Equiy Trap, he Co of Capial and he Firm Growh Pah, CESifo Working Paper no. 80. OECD (99), Taxing Profi in a Global Economy: Domeic and Inernaional Iue (OECD Publicaion, Pari). Sinn, Han-Werner, 99a, The vanihing Harberger riangle, Journal of Public Economic, Vol. 45, pp Sinn, Han-Werner, 99b, Share epurchae, he New View and he Co of Capial, Economic Leer 36, 99, pp Sinn, Han-Werner, 99c, Taxaion and he Co of Capial: The Old View, he New View, and anoher View, in Bradford, D. (ed.), 99, Tax Policy and he Economy 5, (MIT Pre, Cambridge) Sørenen, Peer Birch (ed.), 2004, Meauring he Tax Burden on Capial and Labor, CESifo Seminar Serie, (MIT Pre, Cambridge. Maachue, London). Chennell, L. and. Griffih, 987, Taxing Profi in a Changing World, (IFS: London). Jorgenon, Dale and alph Landau (ed.), 993, Tax eform and he Co of Capial. An Inernaional Comparion, (The Brooking Iniuion, Wahingon, D.C.)
26 24 Appendix: Deail on he imulaion of he growh pah The numerical imulaion repored in ecion 4 make ue of he fir order condiion o deermine he developmen over ime of he marginal valuaion of capial,, he pre-ax marginal rae of reurn, F, and he capial ock,. The imulaion alo require a pecificaion of he firm producion funcion. We le F( ) = C ρ (A) repreen he firm oupu, where C deermine he level of echnology, and ρ i capial hare of oupu. Wih ρ = 0.5, C = and he marke inere rae r = 0.05, he long-run capial ock, a deermined by F = r (eq. 9), i =00. For α = 0, he model replicae Sinn analye. Since he firm aring condiion for period i ha he marginal valuaion of capial equal uniy, he imulaion ar by chooing, enaively, a value for he marginal valuaion of capial for he nex period, <. From he general co-of-capial expreion (8), and he producion funcion (A) he iniial capial ock,, i calculaed. By adding invemen equal o I F( ) + + =, we obain he capial ock + = + I + (eq. 3), he marginal produciviy F + = ρc ρ (eq. A) and he + marginal valuaion of capial = r + F + (eq. 8). Thi epwie procedure i coninued unil he marginal produciviy of capial equal he rae of inere. If he marginal valuaion of capial happen o exceed (fall below) θ, he imulaion procedure i repeaed, picking a lower (higher) aring value for +. N Wih α =,we find ha (foonoe 0) λ = 0 and λ = 0 for all ime period. Furher, a new hare iue a ime implie a poiive ock of new equiy, i.e. A > 0, and, becaue of G hi G < A and λ = 0. By he fir order condiion for N and A (eq. 4 and 5), we hen derive ( ) = + r r = r( ) <, (A2) +
27 25 A explained in ecion 4, he only feaible ue of profi for period + i for repaymen of he iniial iue of equiy, i.e. + > 0 and λ 0 + =. Auming fir ha repaymen ake place G gradually, i.e. 0 < G + < A + and λ 0, we may ue (A2) and an updaed verion of (27) o + = G olve for he firm capial ock, +, and alo he ock of repurchae G +. Since λ + = 0 implie ha + < (ee p. 4), hi parial repaymen of he original iue of equiy i financed boh by curren profi and diinvemen. Alernaively, he firm may chooe o repay he enire iue of new equiy a ime +, by a furher reducion in he ock of capial. G However, uch a reducion i no compaible wih he fir order condiion, ince λ 0 + > when G + = A +, yield a lower co of capial, implying a larger capial ock. epaying he enire iue of equiy a ime + i herefore ruled ou. In he imulaion we begin by chooing, enaively, a aring value for in he feaible G inerval θ < <. Wih λ = 0 we deermine + from (A2) and olve for he iniial ock of capial implicily given by he co-of-capial expreion F r + = (eq. 27). The capial ock in period will be fully efficien in producion in period + and generae profi F ( ) G in ha period. Since λ 0 when G + < A +, we ue an updaed verion of (A2) o compue + = + 2, and olve for he firm capial ock, (27). We alo accoun for profi ( ) +, implicily given by an updaed verion of F + and he ock of repurchaed equiy G +. epaymen ake place gradually, and if profi in, ay, ime period -, i inufficien o reurn he remaining ock of new equiy, i.e. ( ) F < G A, a poiive ock will be 2 kep for he following period, and he abovemenioned procedure i repeaed. If, on he oher hand, ( ) F G A, he reurn of he iniial equiy iue will be compleed in period, 2 poibly in conjuncion wih an addiion o he capial ock (if ( ) F > G A ), which 2 will erminae he phae of hare repurchae. In he econd phae (which follow he cae where α = 0 ), having repaid he new equiy, he firm ue all of he profi earned in ubequen period for invemen, which mean ha we add ( ) I = F, v= +, v v
28 26 o he capial ock of he previou year, v (cf. eq. 3). Thi growh phae i coninued unil he marginal produciviy of capial i equaed o he rae of inere. Again, if he marginal valuaion of capial in he fir round of imulaion hen happen o exceed (fall below) θ, he whole procedure i repeaed, uing a lower (higher) aring value for. In he inermediae cae where 0 < α <, opimal behavior i differen. When he firm iue new hare in period, he non-negaiviy conrain on hare repurchae will bind, λ > 0, ju a i he cae where α =, ee p. 5 above. However, for he following period, our numerical imulaion rongly ugge ha profi will be ued for invemen raher repurchae, ha i λ + > 0. On heoreical ground, we canno rule ou he poibiliy ha he firm will repurchae hare in period +, bu uch behavior would violae he firm budge conrain: The fir-order condiion wih λ + = 0 imply an increae in he capial ock beween period and + ha clearly exceed curren profi. Compared o he cae where α equal zero or uniy we now exogenouly chooe aring value for boh and + order condiion, we find ha in he long-run. The range of hi choice i narrowed in wo way. From he fir A = ατ. Since hi marginal valuaion of he ock of pa equiy injecion fall over ime from period and onward, i mu hen hold ha A N < ατ. Hence, by (2) and (4) and wih λ = 0, we require ha > ατ. Moreover, he marginal valuaion and + mu be choen uch ha he hadow price of he non-negaiviy conrain on hare repurchae (derived from (22) above) + r λ = α ( ) ( ) + + decline over ime. Thi implie ha a ome period of ime λ = 0, ha i, he firm will ar repurchaing hare (oherwie he firm would grow indefiniely and would never diribue any profi). From he general co-of-capial expreion (8), he iniial marginal valuaion and + deermine boh he iniial new hare iue and he capial ock,. During hi fir
29 27 phae profi i reained and inveed, I F( ) = + I. =, adding o he capial ock Uing (eq. A) we alo derive he marginal produciviy of capial F + = ρc ρ and he + marginal valuaion of capial unil λ = 0. = r + F +. Thi epwie procedure i repeaed In he nex phae, he firm ue i profi and ome diinvemen for repurchaing equiy. Wih λ = 0 for wo conecuive period, and a non-binding ock conrain on hare G repurchae, λ = 0, i i raighforward o demonrae ha he marginal valuaion of capial fall over ime according o (A2). The co of capial i hen, F = r +, independen of α, which implie a hrinking capial ock. The firm will coninue o repurchae equiy unil (in ay period v) he ock conrain, defined a α i reached. If ( ) Av F > G α A he v v v repaymen of equiy i finihed ( Gv = α Av) in conjuncion wih an addiion o he capial ock. The firm will hen ue profi earned in ubequen period for invemen, i.e. a econd invemen phae i enered, which mean ha we add curren profi o he capial ock of he previou year. Again, he growh proce i coninued unil he marginal produciviy of capial i equaed o he rae of inere. If he marginal valuaion of capial in he fir round of imulaion hen happen o exceed or fall below θ, he whole procedure i repeaed, uing new aring value for and. +
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31 2008: anjula Bali Swain and Fan Yang Wallenin, Economic or Non-Economic Facor Wha Empower Women?. 34pp. 2008:2 Maz Dahlberg, Heléne Lundqvi and Eva Mörk, Inergovernmenal Gran and Bureaucraic Power. 34pp. 2008:3 Maz Dahlberg, aja Johanon and Eva Mörk, On mandaory acivaion of welfare receiver. 39pp. 2008:4 Magnu Guavon, A Longiudinal Analyi of Wihin-Educaion-Group Earning Inequaliy. 26pp. 2008:5 Henrique S. Bao, Delegaion, Time Inconiency and Suainable Equilibrium. 24pp. 2008:6 Sören Blomqui and Håkan Selin, Hourly Wage ae and Taxable Labor Income eponivene o Change in Marginal Tax ae. 3 pp. 2008:7 Jie Chen and Aiyong Zhu, The relaionhip beween houing invemen and economic growh in China:A panel analyi uing quarerly provincial daa. 26pp. 2009: Per Engröm, Parik Heeliu and Beril Holmlund, Vacancy eferral, Job Search, and he Duraion of Unemploymen: A andomized Experimen. 25 pp. 2009:2 Chuan-Zhong Li and Gunnar Iacon, Valuing urban acceibiliy and air qualiy in Sweden: A regional welfare analyi. 24pp. 2009:3 Luca Micheleo, Opimal nonlinear rediribuive axaion and public good proviion in an economy wih Veblen effec. 26 pp. 2009:4 Håkan Selin, The ie in Female Employmen and he ole of Tax Incenive. An Empirical Analyi of he Swedih Individual Tax eform of pp. 2009:5 Lar M. Johanon and Jan Peeron, Tied Aid, Trade-Faciliaing Aid or Trade-Divering Aid? 47pp. 2009:6 Håkan Selin, Marginal ax rae and ax-favoured penion aving of he elfemployed Evidence from Sweden. 32pp. 2009:7 Tobia Lindhe and Jan Söderen, Dividend axaion, hare repurchae and he equiy rap. 27pp. See alo working paper publihed by he Office of Labour Marke Policy Evaluaion hp:// ISSN
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