Beakeve Holdig Peiods fo Tax Advataged Savigs Accouts with Ealy Withdawal Pealties Stephe M. Hoa Depatmet of Fiace St. Boavetue Uivesity St. Boavetue, New Yok 4778 Phoe: 76-375-209 Fax: 76-375-29 e-mail: shoa@sbu.edu Octobe 2003 This vesio: Jue 6, 2004 JEL Classificatio Codes: D9 Itetempoal Cosume Choice; Life Cycle Models ad Savig G Potfolio Choice G2 Fiacial Istitutios ad Sevices, Geeal G23 Pesio Fuds; Othe Pivate Fiacial Istitutios Keywods: IRA 40(k Retiemet plaig Savig Tax Plaig * I am gateful fo the helpful commets of a aoymous efeee. All emaiig eos ae my ow.
Abstact At what poit does a IRA with a ealy withdawal pealty accumulate moe wealth tha a fully taxable ivestmet? This pape models beakeve holdig peiods, allowig tax ates to chage ad the aual etu to be patitioed ito odiay icome, ealized capital gais, ad uealized capital gais each beig taxed diffeetly. Beakeve holdig peiods decease at a deceasig ate with the etu ad ca be quite shot fo ivestos facig decliig tax ates. I additio, beakeve poits ae vey sesitive to how the etu o the o-ira ivestmet is taxed, doublig o tiplig whe the etu is taxed as a typical mutual fud athe tha taxed as odiay icome.
. Itoductio The Uited States fedeal govemet ecouages etiemet savig though may diffeet tax-advataged savigs pogams, such as taditioal IRA, Roth IRA, 40(k, ad 403(b accouts. These pogams offe tax-defeed accumulatio of savigs ad allow the taxpaye to eithe cotibute to o withdawal fom the accout o a tax-exempt basis. They also ecouage savig fo etiemet athe tha savig fo some othe pupose by imposig a pealty (typically 0% fo fuds that ae withdaw pio to eachig age 59½. Although the ealy withdawal pealty ecouages a ivesto to keep fuds i a etiemet accout oce they have bee ivested, it may also discouage a ivesto fom savig i the fist place. A impotat questio the fo taxpayes cosideig a tax-advataged accout is how log must fuds be ivested i a etiemet accout fo the tax advatages to outweigh the 0% pealty should fuds eed to be withdaw ealy. The aswe is called the beakeve time hoizo, o beakeve holdig peiod. All else equal, saves facig shot beakeve time hoizos should be moe iclied to commit moey to a tax-advataged savigs accout, ad those with loge beakeve time hoizos should be moe cicumspect about savig via a potetially estictive ivestmet accout. I fact, ivestos with shot beakeve holdig peiods may eve choose to use a IRA puposefully fo oetiemet ivestmet goals, kowig they would face a ealy withdawal pealty. This pape models the beakeve holdig peiod fo tax-advataged savigs accouts with both fot-ed tax beefits, like the taditioal IRA ad 40(k plas, ad with back-ed tax beefits, like the moe ecetly itoduced but ubiquitous Roth IRA. It epesets a advace fom the existig liteatue o the topic of beakeve time hoizos because the model allows fo The citeia fo the ealy withdawal pealty ae ot the same fo all tax-advataged accouts. Fo example, the Roth IRA has moe libeal withdawal policies tha the taditioal IRA that exempt a ivesto fom the pealty, such as withdawals fo a fist time home puchase o payig fo a educatio.
tax ates to chage ove the tem of the ivestmet fom the time fuds ae ivested, though the accumulatio phase, ad at the time they ae withdaw. This featue is paticulaly impotat sice evidece idicates that ivestos ae likely to fall ito lowe tax backets upo etiemet (e.g., Beheim, Skie, ad Wiebeg (997. The model also accommodates a taxig scheme i which potios of the aual etu ae teated as eithe tax-defeed uealized capital gai, taxable ealized capital gai, o taxable odiay icome. Fially, it cosides the elevace of the size of the iitial pe-tax cotibutio. This issue deseves attetio sice Hoa (2003 shows that the elative afte-tax accumulatios of taditioal ad Roth IRAs ae affected by whethe the pe-tax cotibutio is above o below the afte-tax cotibutio limit. Seveal authos have compaed the advatages of the taditioal IRA ad the Roth IRA. 2 Bugess ad Madeo (980, Boge ad Boge (982, ad O Neil, Safte, ad Dillway (983 ae amog the fist to addess the beakeve time hoizo i the pesece of a ealy withdawal pealty. Boge ad Boge (982 model it by calculatig the temial values of a taxable ivestmet ad a tax-deductible IRA ivestmet ad solvig fo the time hoizo that makes them equal. They coclude that, eve i the pesece of the pealty, ivestos may be bette off usig a IRA with a ealy withdawal pealty tha a taxable ivestmet fo peetiemet savigs goals, especially fo high ivestmet etus. Doyle (984 exteds thei esults by developig a model that allows a potio of the etu fom the ivestmet to be teated as uealized capital gai ad ot taxed util the ed of the holdig peiod. He cocludes that the ability to defe tax liabilities i taxable accouts though uealized capital gais sigificatly iceases the beakeve holdig peiod compaed to Boge ad Boge s (982 model. His model, howeve, has oe tax ate fo all taxable evets 2 See Cai ad Austi (997, Hoa, Peteso, ad McLeod (997, Kisha ad Lawece (200, Hoa ad Peteso (200, ad Hoa (2003 fo examples of how the ecet liteatue has developed. 2
ad does ot distiguish betwee potios of the etus that ae taxed as ealized capital gais vesus odiay icome. Mao ad Bu (984 compae the afte-tax accumulatios of taditioal IRAs ad oshelteed assets usig the simplified tax stuctue ad fid evidece suppotig the claim that the IRA is ofte a supeio vehicle fo accumulatig fuds fo peetiemet spedig goals despite a 0% ealy withdawal pealty. Moe ecetly, Pakash ad Smyse (2003 follow a appoach idetical to Boge ad Boge (982. As Bevi (2003 ad Kitces (2003 poit out, howeve, the ivestmet etu i the Pakash ad Smyse (2003 model is taxed etiely as odiay icome, which may be the appoximate case fo fixed icome ivestmets but is cetaily ot so with equity o mutual fud ivestmets. I eality, the tax o a potio of ivestmet etu may defeed i the fom of uealized capital gai o may be paid as ealized capital gai tax. I additio, although Pakash ad Smyse (2003 model the beakeve poit fo a tax-deductible ivestmet (i.e., oe with a fot-ed tax beefit, thei model caot be applied to a Roth IRA, despite thei claim to the cotay. This pape exteds the liteatue o beakeve time hoizos by accommodatig a moe ealistic tax stuctue with sepaate tax ates fo odiay icome ad capital gais ad allowig tax ates to chage ove time. The balace of the pape is stuctued as follows. Sectio 2 models the beakeve ivestmet hoizo fo diffeet types of tax-advataged savigs accouts usig ealistic tax stuctues fo calculatig temial values of taxable ad tax-defeed ivestmets. Sectio 3 pesets sceaio ad sesitivity aalyses to povide ivestos ad fiacial plaes with a sese of how log o shot beakeve hoizos ca be ad what affects thei legth. The effect of chagig the size of the ealy withdawal pealty, which may be elevat to lawmakes, is examied i sectio 4. Sectio 5 cocludes ad offes aveues fo futue eseach. 3
2. A Model fo the Beakeve Time Hoizo 2.. Taditioal IRA with Geealized Tax Stuctue The basic appoach to detemiig the beakeve poit is to calculate the poit at which the afte-tax accumulatios of a taxable ivestmet ad a tax-advataged ivestmet ae equal takig ito accout a ealy withdawal pealty. Hoa (2002 daws o the wok of Cai ad Austi (997 ad shows that the afte-tax accumulatio of a pe-tax ivestmet (I BT ca be expessed as FV = I ( T [( * ( T* T*] ( TX BT o whee T o = the ivesto s iitial magial tax ate upo makig the ivestmet; * = p oi t oi p cg t cg, o the aual afte-tax etu; T* = t cg ( p oi p cg /( p oi t oi p cg t cg ; = the umbe of yeas util the ivestmet is sold fo withdawal; = the expected pe-tax ate of etu o the ivestmet; t oi = the magial tax ate o odiay icome ove the tem of the ivestmet; t cg = the magial tax ate o capital gais ove the tem of the ivestmet; p oi = the pecet of aual etu cosideed odiay icome; ad p cg = the pecet of aual etu cosideed capital gais. I BT ( T o is the afte-tax ivestmet. The tem i backets is a futue value iteest facto that teats a potio of the ivestmet etu as odiay icome (p oi ad taxes it accodigly at t oi. Aothe potio is taxed as capital gai (p cg ad taxed at a diffeet capital gais tax ate, t cg. The emaide of the aual etu is uealized capital gai, the tax o which 4
is defeed util the ed of the ivestmet hoizo,, at which time the ivestmet is assumed to be liquidated, ad the capital gai ealized. The amout of the fial ealized capital gai is equal to the temial value less the adjusted basis, which is iceased by the amout of taxes that have bee paid up to that poit i time. It is impotat to ecogize that diffeet pats of the etu ae teated diffeetly fo tax puposes. The etus o may mutual fuds, fo example, typically have sigificat compoets of ealized ad uealized capital gais. Sice the tax o uealized capital gais ae defeed ad ealized gais ae typically taxed at a low 5% accodig to the Jobs ad Gowth Tax Relief Recociliatio Act (JGTRRA of 2003, mutual fuds have iheet tax advatages ot extat i, say, fixed icome secuities, which have etus that ae etiely taxed as odiay icome. Hoa (2003 itoduces a elated model to calculate the afte-tax accumulatio of a taditioal IRA. 3 It distiguishes betwee sceaios i which the pe-tax cotibutio is less tha o geate tha the afte-tax cotibutio limit ad ca be expessed as FV = mi[ I, L]( ( T max[0,( I L( T ][( * ( T* T*] ( 2 Tad BT BT o whee T is the tax ate upo withdawal at time, ad L is the afte-tax cotibutio limit. A ivesto ca make a pe-tax cotibutio up to L/( T o i a taditioal IRA. Ay cotibutio i excess of L, howeve, is taxable ad is assumed to be placed i a taxable ivestmet simila to that descibed i equatio (. The fist tem of equatio (2 epesets the futue accumulatio of the IRA ivestmet. It is subject to a pealty if fuds ae withdaw ealy. The secod tem epesets the futue accumulatio of the taxable ivestmet, if ay, that is equied if the pe-tax ivestmet exceeds the afte-tax cotibutio limit. 3 Fo bevity ad claity, this pape uses the tems taditioal IRA ad Roth IRA. The model is actually moe geeal i that it applies to ay tax-advataged accout with fot-ed o back-ed tax beefits, espectively. 5
A ivesto is idiffeet betwee a taxable ivestmet ad a tax-advataged ivestmet with a ealy withdawal pealty whe the accumulatio i the taxable ivestmet equals that fo the taditioal IRA less a ealy withdawal pealty of, say, ø. Applyig the ealy withdawal pealty, ø, to the fist tem of equatio (2 ad settig equatio ( equal to equatio (2 poduces I BT ( T o [( * ( T* T*] = mi[ I BT, L]( ( T φ. ( 3 max[0,( I L( T ][( * ( T* T*] BT o Expessig the beakeve coditio i this way allows tax ates to chage ove time, accommodates a ealistic tax stuctue, ad allows fo a aalysis based o whethe the pe-tax cotibutio, I BT, is geate tha o less tha the afte-tax cotibutio limit, L. We begi by examiig the sceaio i which the pe-tax cotibutio is less tha o equal to that the cotibutio limit (i.e., I BT L. I this case, the secod tem o the RHS is equal to zeo, ad I BT ca be divided fom both sides, leavig ( T [( * ( T* T*] = ( ( T φ. ( 4 o Dividig both sides by ( ad ( T o, distibutig tems, ad dividig though by ( T* yields a coditio fo the beakeve time hoizo whe I BT L of * ( T φ T * =. ( 5 ( T ( T* ( ( T* o Sice is a expoet o both sides of equatio (5, o closed fom solutio exists ad solvig fo equies a iteative pocess of tial-ad-eo. Iteestigly, the sceaio i which the pe-tax cotibutio is maximized, amely I BT = L/( T o, yields the same coditio as equatio (5 fo pe-tax cotibutios less tha the 6
cotibutio limit. Fo example, substitutig I BT ( T o fo L i equatio (3 ad dividig both sides by I BT ( T o yields [( * ( T* T*] = ( ( T φ T [( * ( T* T*]. ( 6 o Subtactig the secod tem o the RHS ad collectig tems poduces equatio (5, idicatig that the beakeve time hoizo does ot deped o the size of the pe-tax cotibutio. The ituitio fo this equivalece is that ay ivestmet i excess of the cotibutio limit is assumed to be ivested i a taxable istumet, which is teated i the same way as the taxable ivestmet optio. Teatig them diffeetly would ot poduce a meaigful compaiso. Theefoe, ou aalysis is simplified i that thee is o eed to coside the size of the ivestmet whe detemiig the beakeve time hoizo. 2.2. Taditioal IRA with Simplified Odiay Icome Tax Stuctue Although the size of the ivestmet does ot affect the beakeve holdig peiod, tax stuctue does. Equatio (5 is the geealized beakeve coditio fo a sophisticated taxig scheme that distiguishes betwee odiay icome, ealized capital gais, ad uealized capital gais. Sometimes the ivestmet etu is fully taxed as odiay icome, esultig i a simplified tax stuctue i which p oi = ad p cg = 0. I this case, T* = 0 ad * = ( t oi, which simplifies the beakeve coditio to ( toi ( T φ = ( T o ( 7 ad pemits a diect solutio fo, 7
( T φ = l ( To ( t l oi. ( 8 A withdawal afte this peiod of time esults i a highe afte-tax accumulatio fo a taditioal IRA with the ealy withdawal pealty tha the taxable ivestmet. Equatio (8 offes some isights. Whe the tem i backets o the umeato is equal to oe, the the beakeve time hoizo is zeo. I othe wods, whe ( T ø = ( T o, a ivesto should take use a tax-advataged accout eve if fuds ae withdaw immediately icuig a pealty. The same is tue whe ( T ø > ( T o. I this case, the beakeve time hoizo is egative. (Note that fo ay positive tax ate, t oi, the factio i backets i the deomiato is less tha oe makig its atual log egative. The umeato is positive whe the factio i its backet is geate tha oe. Whe the umeato is positive ad the deomiato is egative, the beakeve time hoizo is egative, ad a ivesto should use a tax-advataged accout eve if fuds ae withdaw immediately theeby icuig a pealty. The beakeve time hoizo is positive whe ( T ø < ( T o. Aothe way to itepet this elatio is that the beakeve poit depeds o the elative size of the cotibutio ad withdawal tax ates. As the withdawal tax ate deceases, the beakeve poit deceases, makig the taditioal IRA moe attactive to ivestos despite a ealy withdawal pealty. This esult is easoable sice the taditioal IRA allows a taxpaye to avoid taxes ow i exchage fo payig them late. A decliig tax ate woks to the taxpaye s advatage i this case. Aothe iteestig elatioship is that as t oi appoaches zeo, the absolute value of the deomiato becomes ifiitesimally small ad the beakeve holdig peiod becomes ifiitely lage. This elatioship suggests two thigs. Fist, the taditioal IRA becomes less attactive at 8
low tax ates because it tax advatages would be elatively less valuable. Secod, fo low tax ates, a small chage i the tax ate will poduce lage chages i the beakeve time hoizo. This effect ca be see i the sceaio aalyses i Sectio 3. 2.3. Taditioal IRA with Simplified Capital Gai Tax Stuctue Aothe simplified tax stuctue to coside is oe i which the etie ivestmet etu is i the fom capital gai that is ealized ad taxed at the ed of the peiod. I this case, p oi = p cg = 0, which makes * = ad T* = t cg. Substitutig these values ito equatio (5 ad solvig fo yields a beakeve time hoizo of tcg ( To = l l ( T φ ( To ( tcg (. ( 9 A withdawal afte this peiod of time esults i a highe afte-tax accumulatio fo a taditioal IRA with the ealy withdawal pealty tha the taxable ivestmet. Equatio (9 yields loge beakeve poits tha equatio (8 because defeig capital gais tax util the ed of the ivestmet peiod achieves some of the same tax shelte beefits of the taditioal IRA. This elatio will become appaet i the sceaio aalysis that follows. 2.4. Roth IRA with Geealized Tax Stuctue The ealy withdawal pealty fo the Roth IRA applies oly to eaigs, ot the iitial cotibutio. Theefoe, if the ealy withdawal is less the iitial cotibutio, the beakeve time hoizo is effectively zeo. Howeve, withdawals i excess of the iitial cotibutio ae subject ot oly to the 0% ealy withdawal pealty but odiay icome tax, as well. This oqualified distibutio tax ceates a double pealty whe eaigs ae withdaw ealy ad ca 9
ceate log beakeve poits whe withdawals exceed the iitial cotibutio. Whe cosideig the taxes ad pealties associated with a complete ealy withdawal fom a Roth IRA, we fid that the cotibutio is taxed as odiay icome ad eaigs that ae withdaw ealy ae taxed as odiay icome ad pealized. The followig aalysis is simila i spiit to Tey ad Goolsby (2003 who aalyze the usefuless of Sectio 529 plas, which ae desiged fo educatio savigs, fo etiemet savigs. The tax stuctues of Sectio 529 plas ad Roth IRAs ae ealy equivalet, ad withdawals fo puposes othe tha educatio ae subject to a simila pealty ad icome tax as ealy withdawals fom a Roth IRA. This aalysis exteds Tey ad Goolsby s (2003 wok by icopoatig a moe geealized tax stuctue. Fo a Roth IRA, the afte-tax accumulatio afte payig odiay icome tax ad a pealty fo ealy withdawal o eaigs is FV RothP = I = I BT BT ( T o ( T o {[( ]( T φ }. ( 0 [( ( T φ T φ] A ivesto is idiffeet betwee a taxable ivestmet ad a Roth IRA with a ealy withdawal pealty whe equatio ( equals equatio (0. Establishig that equality, dividig both sides by I BT ( T o ad (, ad eaagig yields * T φ φ T T * =. ( T * ( ( T* Equatio ( equies a iteative pocess of tial-ad-eo to solve fo the beakeve time hoizo. Sice T o is ot peset eithe diectly o idiectly i equatio (, the beakeve poit fo the Roth IRA does ot deped o the iitial tax ate. 0
2.5. Roth IRA with Simplified Capital Gai Tax Stuctue Assumig a simplified tax stuctue fo the Roth IRA i which ivestmets etus ae taxed each yea as odiay icome does ot yield a closed fom solutio fo. Howeve, assumig the etus ae taxed as capital gais at the ed of the peiod does. I this cicumstace, p oi = p cg = 0, which makes * = ad T* = t cg. Substitutig these values ito equatio ( ad solvig fo yields a beakeve time hoizo of zeo i all cases. I othe wods, a ivesto is always bette off with a taxable ivestmet athe tha a Roth IRA with a withdawal pealty assumig all fuds i the Roth IRA ae withdaw ealy. Recall, withdawals of iitial cotibutios ae eithe pealized o taxed as a o-qualified distibutio, makig the beakeve time hoizo fo ealy withdawals of oly iitial cotibutios effectively zeo. But whe compaig a complete ealy withdawal fom a Roth IRA with a taxable ivestmet taxed as capital gai both alteatives ae iitially taxed; both offe tax defeal duig the accumulatio phase; ad both ae taxed as capital gais at the ed of the ivestmet peiod. The oly diffeece is the ealy withdawal pealty o eaigs associated with the Roth IRA, makig it less desiable tha the taxable ivestmet. 3. Results To povide additioal guidace to ivestos ad fiacial plaes, this sectio calculates beakeve time hoizos usig aveage distibutio ates of mutual fuds fo odiay icome ad capital gais epoted by Cai ad Austi (997 ad magial tax ates established by the Jobs ad Gowth Tax Relief Recociliatio Act (JGTRRA of 2003 ecetly passed by Cogess i May of 2003. Accodig to Cai ad Austi (997 the aveage distibutio ates fo odiay icome ad capital gais fo thei sample of gowth fuds ae 6.99% ad 44.23%,
espectively. That is, p oi = 0.0699 ad p cg = 0.4423. 4 The JGTRRA establishes magial tax ates of 0%, 5%, 25%, 28%, 33%, ad 35%, depedig o icome. It also sets a 5% tax ate o capital gais ad divided icome fo taxpayes i all but the two lowest tax backets. 5 So we assume t cg ad t oi ae equal to 5%. 3.. Taditioal IRAs Table displays the beakeve time hoizos usig these iputs fo a taditioal IRA ivestmet with a ealy withdawal pealty fo vaious tax ates ad aual etus assumig a ealy withdawal pealty of 0%. Seveal teds ae appaet. Accodig to Pael A, which assumes the withdawal tax ate is 25%, the beakeve time hoizo is quite sesitive to the aual etu ad deceases at a deceasig ate as the ivestmet etu iceases. This elatioship is explaied i a compaative statics aalysis i Appedix A.. The ituitio fo this esult ests i the fact the value of the tax defeal associated with a IRA is geate as the pe-tax etu iceases. Aothe ted evidet i Pael A is that the beakeve time hoizo is deceases apidly as the ivesto s iitial tax ate iceases because the iitial tax deductio of the taditioal IRA is moe valuable fo high tax backet ivestos. I fact, the zeo beakeve poits fo taxpayes i the 35% tax backet idicate that a ivesto is always bette off usig a taditioal IRA ad payig a ealy withdawal pealty as log as the fuds ca be withdaw at a 25% tax ate (although this sceaio is ot vey likely. Simila teds ae see i Pael B, which assumes that withdaw fuds ae taxed at 28%. The beakeve time hoizos ae quite shot fo ivestos i high tax backets. 4 The esults ae qualitative simila usig the aveage distibutio ates fo gowth ad icome fuds (p oi = 0.2046 ad p cg = 0.4536. 5 Fo taxpayes i the 0% ad 5% tax backets, the JGTRRA of 2003 educes the tax ate o divideds ad capital gais to 5%. 2
Futhemoe, the beakeve poits i Pael B ad substatially highe tha those i Pael A, suggestig that the beakeve poit is quite sesitive to the withdawal tax ate. It should be oted that if a ivesto stays i the 0% o 5% tax backets, divideds ad capital gais ae taxed at oly 5%. Sice the withdawal tax ates i this aalysis ae 25% ad 28%, howeve, it is easoable to assume that divideds ad capital gais ae taxed at the usual 5%. It is also impotat to ote that IRA withdawals afte the age of 59½ ae pealty fee. Cosequetly, vey high beakeve holdig peiods i Table have o pactical sigificace because the ealy withdawal pealty disappeas at age 59½. I such cases, the IRA accout without the pealty domiates the taxable ivestmet, but the taxable ivestmet domiates if IRA fuds ae withdaw ealy. Table 2 pesets beakeve holdig peiods fo diffeet taxig schemes assumig that a ivesto emais i the same tax backet fom the iitial cotibutio, though the accumulatio phase, ad at the time of withdawal. As show i Pael A, beakeve poits ae shotest if etus ae taxed each yea as odiay icome because the IRA tax shelte becomes elatively moe valuable. If a potio of the etu is taxed as ealized capital gai ad uealized capital gai, as i Pael B, beakeve poits legthe substatially, doublig ad tiplig i some cases. The beakeve poits i this pael ae loge tha those i Pael A because the elative advatage of the IRA tax shelte is geate whe the ivestmet is fully taxed as odiay icome as compaed to a mutual fud ivestmet that has some iheet tax advatages. Whe etus ae taxed oly as capital gai at the ed of the ivestmet peiod, as i Pael C, the beakeve poits become eve loge ad, i some cases, appoach ifiity because the tax defeal chaacteistics of the taditioal IRA ae eplicated somewhat by the tax defeal of the 3
uealized capital gai i the taxable ivestmet. I ay case, the beakeve poits ae sesitive to the assumed tax stuctue. To examie the effect of decliig tax ates, Table 3 displays beakeve time hoizos fo ivestos doppig to the ext lowe tax backet whe fuds ae withdaw. Doppig ito a lowe tax backet upo withdawal is impotat. Accodig to Pael A of Table 3, the beakeve holdig peiods ca be shot whe the taxable ivestmet is fully taxed as odiay icome at the ivesto s iitial tax ate, T o, which is the case fo iteest icome o fixed icome ivestmets. Fo ivestos i high tax backets facig a 0% expected etu, the tax shelte of the IRA is elatively valuable ad the beakeve time hoizos decease substatially to fou yeas o less. Fo ivestos i the 25% tax backet doppig to the 5% tax backet, a taditioal IRA with a ealy withdawal pealty is a supeio ivestmet vehicle fo ay time hoizo as idicated by the zeo beakeve time hoizo. 6 Pael B cotais esults assumig the ivestmet is a mutual fud with aveage distibutio ates fo odiay icome ad capital gais. Agai, beakeve poits i this pael ae loge tha those i Pael A, suggestig that the tax stuctue of the o-ira ivestmet is impotat i detemiig the beakeve poit. The last ow of Pael B, displays beakeve time hoizos whe divideds ad capital gais ae taxed at 5% as is the case fo taxpayes emaiig i the 5% ad 0% tax backets. These ivestmet hoizos ae much loge sice the dimiutive tax ate fo the taxable ivestmet appoximates the tax defeal associated with the taditioal IRA. Beakeve time hoizos whe the ivestmet etu is fully taxed as a capital gai at the ed of the ivestmet peiod ae displayed i Pael C. The beakeve poits ae slightly loge 6 The algebaic easo fo these zeo beakeve poits is that the fist coefficiet i equatio (8 becomes zeo i this istace. 4
tha those i Pael B because the taxable ivestmet i this case offes sigificat tax defeal chaacteistics. The diffeeces ae ot lage, howeve. Pael A ad Pael C epeset diffeet extemes fo the taxable ivestmet. Fo most ivestos, the actual taxig scheme would fall somewhee betwee these two extemes. The beakeve time hoizos i Table 3 do ot follow a pedictable patte with espect to the iitial tax ate. Rathe, the beakeve poits ae ifluece moe by the diffeece betwee the iitial ad withdawal tax ates. Whe the icemet to the ext lowe tax backet is lage, beakeve time hoizos ae shot ad vice vesa, idicatig oce agai that chagig tax ates ae impotat. 3.2. Roth IRAs Table 4 displays beakeve holdig peiods fo a Roth IRA assumig a total withdawal of cotibutio ad eaigs. Recall that withdawals less tha the iitial cotibutio ae ot pealized o taxed but that eaigs ae subject to the 0% ealy withdawal pealty as well as icome tax as a o-qualified distibutio. I Pael A, etus ae assumed to be fully taxed as odiay icome at a ate of T duig the accumulatio phase. The beakeve time hoizos ae sigificatly loge tha those associated with taditioal IRAs because eaigs associated with ealy withdawals fom Roth IRAs ae taxed as odiay icome i additio to beig pealized wheeas qualified withdawals ae eithe taxed o pealized. Pael B pesets some vey log beakeve ivestmet hoizos fo etus taxed as a typical gowth mutual fud, especially fo ivestos i high tax backets. Recall that IRA withdawals afte the age of 59½ ae pealty fee. Cosequetly, vey high beakeve holdig peiods i Table 4 have o pactical sigificace. The beakeve poits ae sigificatly loge 5
tha Pael A because the beefits of tax defeal associated with the Roth IRA ae elatively less valuable whe compaed to a mutual fud ivestmet. Futhemoe, beakeve poits icease with the accumulatio phase tax ate athe tha decease as i Pael A. The easo fo this iteestig cotast is that the tax defeal beefits outweigh the added withdawal pealty fo ivestos who ae taxed heavily o thei ivestmet icome. Although ot displayed i this table, oe could use diffeet tax ates fo the accumulatio ad withdawal phases. Take at face value, these esults suggest that, i most istaces, usig Roth IRAs exclusively fo oetiemet ivestmet goals i ot advatageous. Two factos mitigate this coclusio. Fist, the Roth IRA has moe libeal exclusios fom payig ealy withdawal pealties. Avoidig the ealy withdawal pealty makes the beakeve poit zeo. Secod, the ealy withdawal pealty ad the o-qualified distibutio icome tax oly apply to withdawals geate tha the iitial ivestmet. The aalysis above assumes a total withdawal of fuds athe tha a patial withdawal. Fo a patial withdawal ot exceedig total cotibutios, the beakeve peiod fo a Roth IRA is essetially zeo. O the othe had, withdawals that exceed the iitial cotibutio have loge beakeve poits. If withdawals ae made ove time, howeve, the the ealy withdawal pealty may disappea fo late withdawals whe the eaigs ae take out of the accout. As metioed i the pevious sectio whe the ivestmet etu is taxed etiely as capital gais at the ed of the ivestmet peiod, the taxable ivestmet is always bette tha the Roth IRA. I this case, the beakeve time hoizo is zeo because the two alteatives have the same tax scheme save fo the ealy withdawal pealty. Theefoe, the taxable ivestmet would always be moe attactive whe cosideig a ealy withdawal all Roth IRA cotibutios ad eaigs. Patial withdawals of iitial cotibutios ae teated less hashly. 6
4. The Size of the Ealy Withdawal Pealty The esults peseted above idicate that, despite the 0% ealy withdawal pealty, idividual etiemet accouts ca be supeio to fully taxable ivestmets eve fo ivestos with peetiemet ivestmet goals. If the pupose of the ealy withdawal pealty is esue that these accouts ae used fo etiemet savigs, oe might coclude that a 0% ealy withdawal pealty is ot substatial eough to discouage ivestos fom usig IRAs fo oetiemet puposes. A iteestig questio the is what effect does the ealy withdawal pealty have o the beakeve ivestmet hoizo. Table 5 displays hypothetical beakeve poits assumig a 20% ealy withdawal pealty ad that etus ae fully taxed at T o. Pael A examies the case whe a ivesto stays i the same tax backet. To examie the effect of a icease i the ealy withdawal pealty o the beakeve time hoizo, Pael A of Table 5 should be compaed to the Pael A of Table 2. The beakeve holdig peiods fo a 20% ealy withdawal pealty ae about twice as log as those with a 0% ealy withdawal pealty. Pael B pesets beakeve poits fo a ivesto who dops oe tax backet whe withdawig fuds. Fo a pope compaiso, Pael B of Table 5 should be compaed to Pael A of Table 3. The beakeve holdig peiods ae about thee times loge tha those associated with a 0% ealy withdawal pealty. We ca sumise the that a icease i the ealy withdawal pealty would effectively discouage taxpayes fom usig a IRA fo peetiemet savigs puposes, especially fo ivestos that pefe low isk ivestmets that cay low expected etus ad fo ivestos ot expectig a sigificat declie i thei magial tax ate. I fact, it ca be show that, holdig all else equal, the beakeve time hoizo iceases at a deceasig ate with espect to the size of 7
the ealy withdawal pealty. See the Appedix A.2 fo a poof. A icease i the pealty, howeve, may also discouage ivestos fom savig fo etiemet, as well. 5. Coclusio Seveal authos have aalyzed the beakeve holdig peiod fo a tax-advataged savigs accout havig a ealy withdawal pealty. Noe, howeve, has fully cosideed that a ivestmet s etu may have thee diffeet compoets fo tax puposes, each teated diffeetly fo tax puposes odiay icome, ealized capital gai, uealized capital gai. This pape develops a model that icopoates this eality ad allows tax ates to chages fom the time a cotibutio is made though the time of withdawal. Though sesitivity aalysis ad compaative statics, we show that the beakeve holdig peiod is sesitive to the aual etu ad deceases at a deceasig ate as the etu iceases. Moeove, the taxatio scheme fo the o-ira ivestmet geatly iflueces the attactiveess of usig a IRA fo oetiemet puposes. Beakeve poits ae substatially loge whe a sigificat popotio of the etu o the taxable ivestmet is i the fom of eithe ealized o uealized capital gais as is the case with may equity mutual fuds. Fo the taditioal IRA, the beakeve poit is also sesitive to whethe tax ates icease o decease fom the time of cotibutio to withdawal. Beakeve poits ca be shot (a few yeas whe ivestos dop ito the ext lowe tax backet ad etus ae high. I cotast, the beakeve ivestmet hoizos fo the Roth IRA ae substatially highe because eaigs associated with ealy withdawals ae taxed as o-qualified distibutios i additio to beig subject to a ealy withdawal pealty. 8
Sice the beakeve holdig peiod fo taditioal IRAs is sometimes quite shot, some ivestos may fid tax-advataged etiemet savigs accouts with a 0% ealy withdawal pealty useful ivestmet tools fo oetiemet puposes. We show that a hypothetical icease i the pealty to 20% damatically iceases beakeve time hoizos two to thee times, especially fo low-isk ivestos with costat tax ates. If lawmakes wee iteested i discouagig taxpayes fom usig a IRA fo peetiemet savigs puposes, they might coside iceasig the pealty. The applicatio of this eseach exteds beyod simply taditioal IRAs ad Roth IRAs. It applies to ay tax advataged savigs vehicle with eithe fot-ed o back-ed tax beefits. Howeve, the model does ot take ito accout diffeeces i ealy withdawal exemptios fom oe accout to the ext. Fo example, the Roth IRA ad othe back-ed loaded tax shelteed accouts typically have moe flexibility egadig ealy withdawals ad cotibutio limits, which iceases the attactiveess of the Roth IRA fo oetiemet savigs puposes. Also, although this model accommodates chages i tax ates ove time, tax ates duig the accumulatio phase ae assumed costat. If tax ates chage duig the accumulatio phase, the model may ot povide good guidace. Fially, this pape calculates beakeve holdig peiods assumig fuds ae withdaw fom a IRA accout as a lump sum. Pevious eseach idicates that the afte-tax peset value of a IRA depeds o the aticipated withdawal patte fom the accout. Fo example, a auitized withdawal patte damatically iceases the peset value of a tax-advataged accout (see Hoa (2002 ad would damatically affect the beakeve aalysis. These issues ae fuitful aeas fo futue eseach. I ay case, it ca be used i a divese set of cicumstaces ad ca povide valuable isights fo ivestos, fiacial plaes, ad lawmakes. 9
20 APPENDIX A.. The Effect of Retu o the Beakeve Holdig Peiod fo the Taditioal IRA Takig a patial deivative of with espect to will help us aalyze the effect of etu o the beakeve holdig peiod. Assumig a simplified tax stuctue, the beakeve holdig peiod is give by equatio (8. Takig the deivative with espect to gives = 2 2 ( } ( { ( ( ( ( l ( ( ( l t t t t T T oi oi oi oi o φ, ( A which ca be educed to = 2 2 ( ( ( l ( ( l t t t T T oi oi oi o φ. ( A2 The last thee coefficiets ae all positive. The fist coefficiet is positive whe the umeato iside the atual log opeato is geate tha the deomiato, o whe ( T ø > ( T o. This is the same coditio that makes the beakeve poit egative. Theefoe, whe the beakeve holdig peiod is egative, is a iceasig fuctio of. Similaly, the fist coefficiet is egative whe ( T ø < ( T o, which also makes the beakeve poit positive. So whe the beakeve holdig peiod is positive, it is a deceasig fuctio of. A.2. The Effect of the Ealy Withdawal Pealty o the Beakeve Holdig Peiod Takig a patial deivative of equatio (8 with espect to ø, yields = o o oi T T T T t ( ( l φ φ, ( A3
2 which educes to = φ φ oi T T t ( l > 0. ( A4 Not supisigly, is a iceasig fuctio of ø. Takig the secod patial deivative shows the fuctio is cocave. = 2 2 2 ( ( l φ φ oi T T t < 0. ( A5 Theefoe, the beakeve holdig peiod iceases at a deceasig ate with espect to ø.
REFERENCES Bevi, A. B. (2003. O The beak-eve fotie fo ealy withdawal fom a tax defeed accout, Joual of Fiacial Plaig 6(, 20. Boge, E.C. & Boge, T.R. (982. Idividual etiemet accouts ad peetiemet savigs goals, Fiacial Aalysts Joual 38(6, 45-47. Bugess, R.D. & Maddeo, S.A. (980. A simulatio study of tax shelteed etiemet plas. Joual of the Ameica Taxatio Associatio, 34-4. Cai, T. L. & Austi, J.R (997. A aalysis of the tadeoff betwee tax defeed eaigs i IRAs ad Pefeetial Capital Gais, Fiacial Sevices Review 6 (4, 227-242. Doyle, R. J. (984. IRAs ad the capital-gais tax effect, Fiacial Aalysts Joual 40(3, 60-66. Hoa, S. M. (2003. Choosig betwee tax-advataged savigs accouts: A Recociliatio of Stadadized Pe-tax ad Afte-tax Famewoks, Fiacial Sevices Review 2(4, fothcomig. Hoa, S. M. (2002. Afte-tax valuatio of tax shelteed assets, Fiacial Sevices Review (3, 253-276. Hoa, S. M., Peteso, J. H. (200. A eexamiatio of tax-deductible IRAs, Roth IRAs, ad 40(k ivestmets. Fiacial Sevices Review 0(, 87-00. Hoa, S. M., Peteso, J. H., & McLeod, R. (997. A aalysis of o-deductible IRA cotibutios ad Roth IRA covesios. Fiacial Sevices Review 6 (4, 243-256. Kitces, M. E. (2003. Moe o ealy withdawals ad the beakeve fotie, Joual of Fiacial Plaig 6(, 20-2. Kisha, V. S. & Lawece, S. (200. Aalysis of ivestmet choices fo etiemet: A ew appoach ad pespective, Fiacial Sevices Review 0(, 75-86. Mao, R. M. & Bu, T. (984. IRAs vesus Noshelteed Alteatives fo Retiemet Savigs Goals, Fiacial Aalysts Joual 40(3, 67-65. O,Neil, C.J., Safte, D.V., & Dillaway, M. P. (983. Pematue withdawals fom etiemet accouts: A beak-eve aalysis. Joual of the Ameica Taxatio Associatio 4, 35-43. Pakash, R. J. ad Smyse, M. W. (2003. The beak-eve fotie fo ealy withdawal fom a tax defeed accout, Joual of Fiacial Plaig 6(8, 56-6. Tey A. ad Goolsby, W. C. (2003. Sectio 529 plas as etiemet accouts, Fiacial Sevices Review 2(4, 309-38. 22
Table Beakeve time hoizos i yeas fo a taditioal IRA with a 0% ealy withdawal pealty assumig a. divideds ad capital gais ae taxed at 5% though the accumulatio phase, ad b. p oi = 0.0699 ad p cg = 0.4423. Aual Retu ( T o 4% 6% 8% 0% 2% 4% 6% Pael A: 25% Withdawal Tax Rate (T = 25% 0% 83.5 56.6 43.2 35.2 29.8 26.0 23. 5% 65.4 44.4 33.9 27.6 23.4 20.3 8. 25% 30. 20.4 5.5 2.6 0.7 9.3 8.2 28% 20.3 3.7 0.5 8.5 7.2 6.2 5.5 33% 5.4 3.7 2.8 2.3.9.7.5 35% 0.0 0.0 0.0 0.0 0.0 0.0 0.0 Pael B: 28% Withdawal Tax Rate (T = 28% 0% 98.8 67. 5.2 4.7 35.3 30.8 27.4 5% 80.3 54.5 4.6 33.9 28.7 25.0 22.2 25% 42.6 28.9 22.0 7.9 5. 3.2.7 28% 3.7 2.5 6.4 3.3.3 9.8 8.7 33% 4.9 0. 7.7 6.2 5.2 4.6 4.0 35% 8.7 5.9 4.5 3.6 3. 2.7 2.4 23
Table 2 Beakeve time hoizos i yeas fo a taditioal IRA with a 0% ealy withdawal pealty assumig a. divideds ad capital gais ae taxed at 5% though the accumulatio phase, ad b. a ivesto s tax backet emais uchaged whe fuds ae withdaw. Aual Retu ( T o 4% 6% 8% 0% 2% 4% 6% Pael A: Retu Fully Taxed as Odiay Icome at t oi = T o 5% 2.6 4.7.2 9. 7.7 6.7 6.0 25% 4.8 0.0 7.7 6.2 5.3 4.6 4. 28% 3.8 9.4 7. 5.8 4.9 4.3 3.8 33% 2.7 8.6 6.5 5.3 4.5 3.9 3.5 35% 2.3 8.3 6.4 5.2 4.4 3.8 3.4 Pael B: Tax Stuctue fo a Typical Gowth Mutual Fud (p oi = 0.0699 ad p cg = 0.4423 5% 27.9 8.9 4.4.7 9.9 8.6 7.6 25% 32.9 22.3 7.0 3.8.7 0. 9.0 28% 34.7 23.5 7.9 4.5 2.3 0.7 9.5 33% 38.2 25.9 9.7 6.0 3.6.8 0.5 35% 36.3 24.6 8.7 5.2 2.9.2 0.0 Pael C: Retu Fully Taxed as Capital Gai at the Ed of the Peiod (p oi = p cg = 0 5% 39. 26.3 9.9 6. 3.5.7 0.3 25% 56.0 37.7 28.5 23. 9.4 6.8 4.8 28% 66.4 44.7 33.8 27.3 23.0 9.9 7.5 33% 35.2 9.0 68.9 55.6 46.8 40.5 35.7 35% a - - - - - - - a Beakeve time hoizos i this ow appoach ifiity ad ae isoluble. 24
Table 3 Beakeve time hoizos i yeas fo a taditioal IRA with a 0% ealy withdawal pealty assumig a. divideds ad capital gais ae taxed at 5% though the accumulatio phase, ad b. a ivesto dops to the ext lowe tax backet whe fuds ae withdaw. Aual Retu ( T o 4% 6% 8% 0% 2% 4% 6% Pael A: Retu Fully Taxed as Odiay Icome at t oi = T o 5% 0.5 7. 5.4 4.4 3.7 3.3 2.9 25% 0.0 0.0 0.0 0.0 0.0 0.0 0.0 28% 9.4 6.4 4.9 4.0 3.4 2.9 2.6 33% 6. 4. 3. 2.5 2.2.9.7 35% 9.7 6.6 5.0 4. 3.4 3.0 2.7 Pael B: Tax Stuctue fo a Typical Gowth Mutual Fud (p oi = 0.0699 ad p cg = 0.4423 5%.3 7.7 5.8 4.7 4.0 3.5 3. 25% 0.0 0.0 0.0 0.0 0.0 0.0 0.0 28% 20.3 3.7 0.5 8.5 7.2 6.2 5.5 33% 4.9 0. 7.7 6.2 5.2 4.6 4.0 35% 27.2 8.4 4.0.4 9.6 8.4 7.4 5% a 4.2 27.9 2.3 7.3 4.7 2.8.4 Pael C: Retu Fully Taxed as Capital Gai at the Ed of the Peiod (p oi = p cg = 0 5% 2.7 8.5 6.5 5.2 4.4 3.8 3.4 25% 0.0 0.0 0.0 0.0 0.0 0.0 0.0 28% 26.6 7.9 3.6.0 9.2 8.0 7.0 33% 7.5.8 8.9 7.2 6. 5.3 4.6 35% 43.8 29.5 22.3 8.0 5.2 3..6 a Beakeve time hoizos i this ow ae calculated assumig that divideds ad capital gais ae taxed at 5%. 25
Table 4 Beakeve time hoizos i yeas fo a Roth IRA with a 0% ealy withdawal pealty assumig divideds ad capital gais ae taxed at 5% though the accumulatio phase. Aual Retu ( T oi = T 4% 6% 8% 0% 2% 4% 6% Pael A: Retu Fully Taxed as Odiay Icome at t oi = T 0% 48.3 33.0 25.3 20.7 7.6 5.4 3.8 5% 36.5 24.9 9.2 5.7 3.4.8 0.5 25% 26.6 8.3 4..6 9.9 8.7 7.9 28% 25. 7.3 3.3.0 9.4 8.3 7.4 33% 23.4 6. 2.4 0.2 8.8 7.7 7.0 35% 22.9 5.7 2.2 0.0 8.6 7.6 6.8 Pael B: Tax Stuctue fo a Typical Gowth Mutual Fud (p oi = 0.0699 ad p cg = 0.4423 0% 34.6 23.7 8.3 5.0 2.8.2 0. 5% 62.8 42.8 32.8 26.7 22.7 9.9 7.7 25% 6.2 78.9 60.3 49. 4.7 36.4 32.4 28% 32.7 90.2 68.9 56. 47.6 4.5 36.9 33% 6.7 09.8 83.9 68.3 57.9 50.5 44.9 35% 73.9 8. 90.2 73.4 62.3 54.3 48.3 26
Table 5 Hypothetical beakeve time hoizos i yeas fo a taditioal IRA with a 20% ealy withdawal pealty assumig the aual etu fo the o-ira ivestmet is fully taxed at T o. Aual Retu ( T o 4% 6% 8% 0% 2% 4% 6% Pael A: Costat Tax Rate (T o = T 5% 46.4 3.5 24.0 9.5 6.6 4.4 2.8 25% 32. 2.8 6.6 3.5.4 9.9 8.8 28% 30. 20.4 5.5 2.6 0.7 9.3 8.3 33% 27.8 8.8 4.3.6 9.8 8.6 7.6 35% 27. 8.4 4.0.4 9.6 8.4 7.4 Pael B: Doppig Oe Tax Backet 5% 33.6 22.8 7.4 4. 2.0 0.4 9.3 25% 4.8 0.0 7.7 6.2 5.3 4.6 4. 28% 24.9 6.9 2.9 0.4 8.8 7.7 6.8 33% 9.8 3.4 0.2 8.3 7.0 6. 5.4 35% 23.9 6.2 2.3 0.0 8.5 7.4 6.6 27