Breakeven Holding Periods for Tax Advantaged Savings Accounts with Early Withdrawal Penalties

Size: px
Start display at page:

Download "Breakeven Holding Periods for Tax Advantaged Savings Accounts with Early Withdrawal Penalties"

Transcription

1 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: Fax: 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.

2 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.

3 . 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.

4 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

5 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

6 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

7 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

8 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

9 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 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

10 ( 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

11 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 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 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

12 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

13 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 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%,

14 espectively. That is, p oi = ad p cg = 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 = ad p cg = 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

15 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

16 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

17 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 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

18 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

19 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

20 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

21 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

22 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

23 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. = ( ( l φ φ oi T T t < 0. ( A5 Theefoe, the beakeve holdig peiod iceases at a deceasig ate with espect to ø.

24 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, Bugess, R.D. & Maddeo, S.A. (980. A simulatio study of tax shelteed etiemet plas. Joual of the Ameica Taxatio Associatio, 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, Doyle, R. J. (984. IRAs ad the capital-gais tax effect, Fiacial Aalysts Joual 40(3, 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, Hoa, S. M., Peteso, J. H. (200. A eexamiatio of tax-deductible IRAs, Roth IRAs, ad 40(k ivestmets. Fiacial Sevices Review 0(, 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, Kitces, M. E. (2003. Moe o ealy withdawals ad the beakeve fotie, Joual of Fiacial Plaig 6(, Kisha, V. S. & Lawece, S. (200. Aalysis of ivestmet choices fo etiemet: A ew appoach ad pespective, Fiacial Sevices Review 0(, Mao, R. M. & Bu, T. (984. IRAs vesus Noshelteed Alteatives fo Retiemet Savigs Goals, Fiacial Aalysts Joual 40(3, 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, 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, Tey A. ad Goolsby, W. C. (2003. Sectio 529 plas as etiemet accouts, Fiacial Sevices Review 2(4,

25 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 = ad p cg = Aual Retu ( T o 4% 6% 8% 0% 2% 4% 6% Pael A: 25% Withdawal Tax Rate (T = 25% 0% % % % % % Pael B: 28% Withdawal Tax Rate (T = 28% 0% % % % % %

26 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% % % % % Pael B: Tax Stuctue fo a Typical Gowth Mutual Fud (p oi = ad p cg = % % % % % Pael C: Retu Fully Taxed as Capital Gai at the Ed of the Peiod (p oi = p cg = 0 5% % % % % a a Beakeve time hoizos i this ow appoach ifiity ad ae isoluble. 24

27 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% % % % % Pael B: Tax Stuctue fo a Typical Gowth Mutual Fud (p oi = ad p cg = % % % % % % a Pael C: Retu Fully Taxed as Capital Gai at the Ed of the Peiod (p oi = p cg = 0 5% % % % % a Beakeve time hoizos i this ow ae calculated assumig that divideds ad capital gais ae taxed at 5%. 25

28 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% % % % % % Pael B: Tax Stuctue fo a Typical Gowth Mutual Fud (p oi = ad p cg = % % % % % %

29 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% % % % % Pael B: Doppig Oe Tax Backet 5% % % % %

Understanding Financial Management: A Practical Guide Guideline Answers to the Concept Check Questions

Understanding Financial Management: A Practical Guide Guideline Answers to the Concept Check Questions Udestadig Fiacial Maagemet: A Pactical Guide Guidelie Aswes to the Cocept Check Questios Chapte 4 The Time Value of Moey Cocept Check 4.. What is the meaig of the tems isk-etu tadeoff ad time value of

More information

Money Math for Teens. Introduction to Earning Interest: 11th and 12th Grades Version

Money Math for Teens. Introduction to Earning Interest: 11th and 12th Grades Version Moey Math fo Tees Itoductio to Eaig Iteest: 11th ad 12th Gades Vesio This Moey Math fo Tees lesso is pat of a seies ceated by Geeatio Moey, a multimedia fiacial liteacy iitiative of the FINRA Ivesto Educatio

More information

Finance Practice Problems

Finance Practice Problems Iteest Fiace Pactice Poblems Iteest is the cost of boowig moey. A iteest ate is the cost stated as a pecet of the amout boowed pe peiod of time, usually oe yea. The pevailig maket ate is composed of: 1.

More information

Learning Objectives. Chapter 2 Pricing of Bonds. Future Value (FV)

Learning Objectives. Chapter 2 Pricing of Bonds. Future Value (FV) Leaig Objectives Chapte 2 Picig of Bods time value of moey Calculate the pice of a bod estimate the expected cash flows detemie the yield to discout Bod pice chages evesely with the yield 2-1 2-2 Leaig

More information

Annuities and loan. repayments. Syllabus reference Financial mathematics 5 Annuities and loan. repayments

Annuities and loan. repayments. Syllabus reference Financial mathematics 5 Annuities and loan. repayments 8 8A Futue value of a auity 8B Peset value of a auity 8C Futue ad peset value tables 8D Loa epaymets Auities ad loa epaymets Syllabus efeece Fiacial mathematics 5 Auities ad loa epaymets Supeauatio (othewise

More information

Periodic Review Probabilistic Multi-Item Inventory System with Zero Lead Time under Constraints and Varying Order Cost

Periodic Review Probabilistic Multi-Item Inventory System with Zero Lead Time under Constraints and Varying Order Cost Ameica Joual of Applied Scieces (8: 3-7, 005 ISS 546-939 005 Sciece Publicatios Peiodic Review Pobabilistic Multi-Item Ivetoy System with Zeo Lead Time ude Costaits ad Vayig Ode Cost Hala A. Fegay Lectue

More information

Derivation of Annuity and Perpetuity Formulae. A. Present Value of an Annuity (Deferred Payment or Ordinary Annuity)

Derivation of Annuity and Perpetuity Formulae. A. Present Value of an Annuity (Deferred Payment or Ordinary Annuity) Aity Deivatios 4/4/ Deivatio of Aity ad Pepetity Fomlae A. Peset Vale of a Aity (Defeed Paymet o Odiay Aity 3 4 We have i the show i the lecte otes ad i ompodi ad Discoti that the peset vale of a set of

More information

FM4 CREDIT AND BORROWING

FM4 CREDIT AND BORROWING FM4 CREDIT AND BORROWING Whe you purchase big ticket items such as cars, boats, televisios ad the like, retailers ad fiacial istitutios have various terms ad coditios that are implemeted for the cosumer

More information

between Modern Degree Model Logistics Industry in Gansu Province 2. Measurement Model 1. Introduction 2.1 Synergetic Degree

between Modern Degree Model Logistics Industry in Gansu Province 2. Measurement Model 1. Introduction 2.1 Synergetic Degree www.ijcsi.og 385 Calculatio adaalysis alysis of the Syegetic Degee Model betwee Mode Logistics ad Taspotatio Idusty i Gasu Povice Ya Ya 1, Yogsheg Qia, Yogzhog Yag 3,Juwei Zeg 4 ad Mi Wag 5 1 School of

More information

5.4 Amortization. Question 1: How do you find the present value of an annuity? Question 2: How is a loan amortized?

5.4 Amortization. Question 1: How do you find the present value of an annuity? Question 2: How is a loan amortized? 5.4 Amortizatio Questio 1: How do you fid the preset value of a auity? Questio 2: How is a loa amortized? Questio 3: How do you make a amortizatio table? Oe of the most commo fiacial istrumets a perso

More information

Two degree of freedom systems. Equations of motion for forced vibration Free vibration analysis of an undamped system

Two degree of freedom systems. Equations of motion for forced vibration Free vibration analysis of an undamped system wo degee of feedom systems Equatios of motio fo foced vibatio Fee vibatio aalysis of a udamped system Itoductio Systems that equie two idepedet d coodiates to descibe thei motio ae called two degee of

More information

The dinner table problem: the rectangular case

The dinner table problem: the rectangular case The ie table poblem: the ectagula case axiv:math/009v [mathco] Jul 00 Itouctio Robeto Tauaso Dipatimeto i Matematica Uivesità i Roma To Vegata 00 Roma, Italy tauaso@matuiomait Decembe, 0 Assume that people

More information

Long-Term Trend Analysis of Online Trading --A Stochastic Order Switching Model

Long-Term Trend Analysis of Online Trading --A Stochastic Order Switching Model Asia Pacific Maagemet Review (24) 9(5), 893-924 Log-Tem Ted Aalysis of Olie Tadig --A Stochastic Ode Switchig Model Shalig Li * ad Zili Ouyag ** Abstact Olie bokeages ae eplacig bokes ad telephoes with

More information

CHAPTER 3 THE TIME VALUE OF MONEY

CHAPTER 3 THE TIME VALUE OF MONEY CHAPTER 3 THE TIME VALUE OF MONEY OVERVIEW A dollar i the had today is worth more tha a dollar to be received i the future because, if you had it ow, you could ivest that dollar ad ear iterest. Of all

More information

Soving Recurrence Relations

Soving Recurrence Relations Sovig Recurrece Relatios Part 1. Homogeeous liear 2d degree relatios with costat coefficiets. Cosider the recurrece relatio ( ) T () + at ( 1) + bt ( 2) = 0 This is called a homogeeous liear 2d degree

More information

INVESTMENT PERFORMANCE COUNCIL (IPC)

INVESTMENT PERFORMANCE COUNCIL (IPC) INVESTMENT PEFOMANCE COUNCIL (IPC) INVITATION TO COMMENT: Global Ivestmet Performace Stadards (GIPS ) Guidace Statemet o Calculatio Methodology The Associatio for Ivestmet Maagemet ad esearch (AIM) seeks

More information

Abstract. 1. Introduction

Abstract. 1. Introduction Optimal Tax Deferral Choices i the Presece of Chagig Tax Regimes Terrace Jalbert (E-mail: jalbert@hawaii.edu), Uiversity of Hawaii at Hilo Eric Rask (E-mail: rask@hawaii.edu) Uiversity of Hawaii at Hilo

More information

Present Value Tax Expenditure Estimate of Tax Assistance for Retirement Saving

Present Value Tax Expenditure Estimate of Tax Assistance for Retirement Saving Preset Value Tax Expediture Estimate of Tax Assistace for Retiremet Savig Tax Policy Brach Departmet of Fiace Jue 30, 1998 2 Preset Value Tax Expediture Estimate of Tax Assistace for Retiremet Savig This

More information

.04. This means $1000 is multiplied by 1.02 five times, once for each of the remaining sixmonth

.04. This means $1000 is multiplied by 1.02 five times, once for each of the remaining sixmonth Questio 1: What is a ordiary auity? Let s look at a ordiary auity that is certai ad simple. By this, we mea a auity over a fixed term whose paymet period matches the iterest coversio period. Additioally,

More information

ANNUITIES SOFTWARE ASSIGNMENT TABLE OF CONTENTS... 1 ANNUITIES SOFTWARE ASSIGNMENT... 2 WHAT IS AN ANNUITY?... 2 EXAMPLE 1... 2 QUESTIONS...

ANNUITIES SOFTWARE ASSIGNMENT TABLE OF CONTENTS... 1 ANNUITIES SOFTWARE ASSIGNMENT... 2 WHAT IS AN ANNUITY?... 2 EXAMPLE 1... 2 QUESTIONS... ANNUITIES SOFTWARE ASSIGNMENT TABLE OF CONTENTS ANNUITIES SOFTWARE ASSIGNMENT TABLE OF CONTENTS... 1 ANNUITIES SOFTWARE ASSIGNMENT... WHAT IS AN ANNUITY?... EXAMPLE 1... QUESTIONS... EXAMPLE BRANDON S

More information

Chapter 5 Unit 1. IET 350 Engineering Economics. Learning Objectives Chapter 5. Learning Objectives Unit 1. Annual Amount and Gradient Functions

Chapter 5 Unit 1. IET 350 Engineering Economics. Learning Objectives Chapter 5. Learning Objectives Unit 1. Annual Amount and Gradient Functions Chapter 5 Uit Aual Amout ad Gradiet Fuctios IET 350 Egieerig Ecoomics Learig Objectives Chapter 5 Upo completio of this chapter you should uderstad: Calculatig future values from aual amouts. Calculatig

More information

How to read A Mutual Fund shareholder report

How to read A Mutual Fund shareholder report Ivestor BulletI How to read A Mutual Fud shareholder report The SEC s Office of Ivestor Educatio ad Advocacy is issuig this Ivestor Bulleti to educate idividual ivestors about mutual fud shareholder reports.

More information

On the Optimality and Interconnection of Valiant Load-Balancing Networks

On the Optimality and Interconnection of Valiant Load-Balancing Networks O the Optimality ad Itecoectio of Valiat Load-Balacig Netwoks Moshe Babaioff ad Joh Chuag School of Ifomatio Uivesity of Califoia at Bekeley Bekeley, Califoia 94720 4600 {moshe,chuag}@sims.bekeley.edu

More information

CHAPTER 4: NET PRESENT VALUE

CHAPTER 4: NET PRESENT VALUE EMBA 807 Corporate Fiace Dr. Rodey Boehe CHAPTER 4: NET PRESENT VALUE (Assiged probles are, 2, 7, 8,, 6, 23, 25, 28, 29, 3, 33, 36, 4, 42, 46, 50, ad 52) The title of this chapter ay be Net Preset Value,

More information

Things to Remember. r Complete all of the sections on the Retirement Benefit Options form that apply to your request.

Things to Remember. r Complete all of the sections on the Retirement Benefit Options form that apply to your request. Retiement Benefit 1 Things to Remembe Complete all of the sections on the Retiement Benefit fom that apply to you equest. If this is an initial equest, and not a change in a cuent distibution, emembe to

More information

CDs Bought at a Bank verses CD s Bought from a Brokerage. Floyd Vest

CDs Bought at a Bank verses CD s Bought from a Brokerage. Floyd Vest CDs Bought at a Bak verses CD s Bought from a Brokerage Floyd Vest CDs bought at a bak. CD stads for Certificate of Deposit with the CD origiatig i a FDIC isured bak so that the CD is isured by the Uited

More information

PENSION ANNUITY. Policy Conditions Document reference: PPAS1(7) This is an important document. Please keep it in a safe place.

PENSION ANNUITY. Policy Conditions Document reference: PPAS1(7) This is an important document. Please keep it in a safe place. PENSION ANNUITY Policy Coditios Documet referece: PPAS1(7) This is a importat documet. Please keep it i a safe place. Pesio Auity Policy Coditios Welcome to LV=, ad thak you for choosig our Pesio Auity.

More information

Introducing Your New Wells Fargo Trust and Investment Statement. Your Account Information Simply Stated.

Introducing Your New Wells Fargo Trust and Investment Statement. Your Account Information Simply Stated. Itroducig Your New Wells Fargo Trust ad Ivestmet Statemet. Your Accout Iformatio Simply Stated. We are pleased to itroduce your ew easy-to-read statemet. It provides a overview of your accout ad a complete

More information

I. Why is there a time value to money (TVM)?

I. Why is there a time value to money (TVM)? Itroductio to the Time Value of Moey Lecture Outlie I. Why is there the cocept of time value? II. Sigle cash flows over multiple periods III. Groups of cash flows IV. Warigs o doig time value calculatios

More information

Trusteed IRAs. Integrate and simplify your retirement and estate plans

Trusteed IRAs. Integrate and simplify your retirement and estate plans Trusteed IRAs Itegrate ad simplify your retiremet ad estate plas Trusteed IRAs from Merrill Lych Trust Compay To create the legacy of your dreams, you may eed more tha a Idividual Retiremet Accout ad a

More information

FI A CIAL MATHEMATICS

FI A CIAL MATHEMATICS CHAPTER 7 FI A CIAL MATHEMATICS Page Cotets 7.1 Compoud Value 117 7.2 Compoud Value of a Auity 118 7.3 Sikig Fuds 119 7.4 Preset Value 122 7.5 Preset Value of a Auity 122 7.6 Term Loas ad Amortizatio 123

More information

How to use what you OWN to reduce what you OWE

How to use what you OWN to reduce what you OWE How to use what you OWN to reduce what you OWE Maulife Oe A Overview Most Caadias maage their fiaces by doig two thigs: 1. Depositig their icome ad other short-term assets ito chequig ad savigs accouts.

More information

ESSAYS IN THE ECONOMICS OF NETWORKS

ESSAYS IN THE ECONOMICS OF NETWORKS ESSYS IN THE ECONOMICS OF NETWORKS y MIRCE ION MRCU DISSERTTION PRESENTED TO THE GRDUTE SCHOOL OF THE UNIVERSITY OF FLORID IN PRTIL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY

More information

Savings and Retirement Benefits

Savings and Retirement Benefits 60 Baltimore Couty Public Schools offers you several ways to begi savig moey through payroll deductios. Defied Beefit Pesio Pla Tax Sheltered Auities ad Custodial Accouts Defied Beefit Pesio Pla Did you

More information

Solving Logarithms and Exponential Equations

Solving Logarithms and Exponential Equations Solvig Logarithms ad Epoetial Equatios Logarithmic Equatios There are two major ideas required whe solvig Logarithmic Equatios. The first is the Defiitio of a Logarithm. You may recall from a earlier topic:

More information

THE TIME VALUE OF MONEY

THE TIME VALUE OF MONEY QRMC04 9/17/01 4:43 PM Page 51 CHAPTER FOUR THE TIME VALUE OF MONEY 4.1 INTRODUCTION AND FUTURE VALUE The perspective ad the orgaizatio of this chapter differs from that of chapters 2 ad 3 i that topics

More information

580.439 Course Notes: Nonlinear Dynamics and Hodgkin-Huxley Equations

580.439 Course Notes: Nonlinear Dynamics and Hodgkin-Huxley Equations 58.439 Couse Notes: Noliea Dyamics ad Hodgki-Huxley Equatios Readig: Hille (3 d ed.), chapts 2,3; Koch ad Segev (2 d ed.), chapt 7 (by Rizel ad Emetout). Fo uthe eadig, S.H. Stogatz, Noliea Dyamics ad

More information

I apply to subscribe for a Stocks & Shares ISA for the tax year 20 /20 and each subsequent year until further notice.

I apply to subscribe for a Stocks & Shares ISA for the tax year 20 /20 and each subsequent year until further notice. IFSL Brooks Macdoald Fud Stocks & Shares ISA Trasfer Applicatio Form IFSL Brooks Macdoald Fud Stocks & Shares ISA Trasfer Applicatio Form Please complete usig BLOCK CAPITALS ad retur the completed form

More information

Time Value of Money. First some technical stuff. HP10B II users

Time Value of Money. First some technical stuff. HP10B II users Time Value of Moey Basis for the course Power of compoud iterest $3,600 each year ito a 401(k) pla yields $2,390,000 i 40 years First some techical stuff You will use your fiacial calculator i every sigle

More information

Learning objectives. Duc K. Nguyen - Corporate Finance 21/10/2014

Learning objectives. Duc K. Nguyen - Corporate Finance 21/10/2014 1 Lecture 3 Time Value of Moey ad Project Valuatio The timelie Three rules of time travels NPV of a stream of cash flows Perpetuities, auities ad other special cases Learig objectives 2 Uderstad the time-value

More information

The Predictive Power of Dividend Yields for Stock Returns: Risk Pricing or Mispricing?

The Predictive Power of Dividend Yields for Stock Returns: Risk Pricing or Mispricing? The Pedictive Powe of Dividend Yields fo Stock Retuns: Risk Picing o Mispicing? Glenn Boyle Depatment of Economics and Finance Univesity of Cantebuy Yanhui Li Depatment of Economics and Finance Univesity

More information

I. Chi-squared Distributions

I. Chi-squared Distributions 1 M 358K Supplemet to Chapter 23: CHI-SQUARED DISTRIBUTIONS, T-DISTRIBUTIONS, AND DEGREES OF FREEDOM To uderstad t-distributios, we first eed to look at aother family of distributios, the chi-squared distributios.

More information

SECTION 1.5 : SUMMATION NOTATION + WORK WITH SEQUENCES

SECTION 1.5 : SUMMATION NOTATION + WORK WITH SEQUENCES SECTION 1.5 : SUMMATION NOTATION + WORK WITH SEQUENCES Read Sectio 1.5 (pages 5 9) Overview I Sectio 1.5 we lear to work with summatio otatio ad formulas. We will also itroduce a brief overview of sequeces,

More information

Retirement By the Numbers

Retirement By the Numbers Retiremet By the Numbers Fiacial priorities may vary depedig o your age, but every perso wats a successful retiremet. This workbook ca help you estimate your retiremet eeds ad explai the optios available

More information

INVESTMENT PERFORMANCE COUNCIL (IPC) Guidance Statement on Calculation Methodology

INVESTMENT PERFORMANCE COUNCIL (IPC) Guidance Statement on Calculation Methodology Adoptio Date: 4 March 2004 Effective Date: 1 Jue 2004 Retroactive Applicatio: No Public Commet Period: Aug Nov 2002 INVESTMENT PERFORMANCE COUNCIL (IPC) Preface Guidace Statemet o Calculatio Methodology

More information

Analyzing Longitudinal Data from Complex Surveys Using SUDAAN

Analyzing Longitudinal Data from Complex Surveys Using SUDAAN Aalyzig Logitudial Data from Complex Surveys Usig SUDAAN Darryl Creel Statistics ad Epidemiology, RTI Iteratioal, 312 Trotter Farm Drive, Rockville, MD, 20850 Abstract SUDAAN: Software for the Statistical

More information

Enhance Your Financial Legacy Variable Annuity Death Benefits from Pacific Life

Enhance Your Financial Legacy Variable Annuity Death Benefits from Pacific Life Ehace Your Fiacial Legacy Variable Auity Death Beefits from Pacific Life 7/15 20172-15B As You Pla for Retiremet, Protect Your Loved Oes A Pacific Life variable auity ca offer three death beefits that

More information

Taking DCOP to the Real World: Efficient Complete Solutions for Distributed Multi-Event Scheduling

Taking DCOP to the Real World: Efficient Complete Solutions for Distributed Multi-Event Scheduling Taig DCOP to the Real World: Efficiet Complete Solutios for Distributed Multi-Evet Schedulig Rajiv T. Maheswara, Milid Tambe, Emma Bowrig, Joatha P. Pearce, ad Pradeep araatham Uiversity of Souther Califoria

More information

Subject CT5 Contingencies Core Technical Syllabus

Subject CT5 Contingencies Core Technical Syllabus Subject CT5 Cotigecies Core Techical Syllabus for the 2015 exams 1 Jue 2014 Aim The aim of the Cotigecies subject is to provide a groudig i the mathematical techiques which ca be used to model ad value

More information

CHAPTER 11 Financial mathematics

CHAPTER 11 Financial mathematics CHAPTER 11 Fiacial mathematics I this chapter you will: Calculate iterest usig the simple iterest formula ( ) Use the simple iterest formula to calculate the pricipal (P) Use the simple iterest formula

More information

Valuing Firms in Distress

Valuing Firms in Distress Valuig Firms i Distress Aswath Damodara http://www.damodara.com Aswath Damodara 1 The Goig Cocer Assumptio Traditioal valuatio techiques are built o the assumptio of a goig cocer, I.e., a firm that has

More information

Present Value Factor To bring one dollar in the future back to present, one uses the Present Value Factor (PVF): Concept 9: Present Value

Present Value Factor To bring one dollar in the future back to present, one uses the Present Value Factor (PVF): Concept 9: Present Value Cocept 9: Preset Value Is the value of a dollar received today the same as received a year from today? A dollar today is worth more tha a dollar tomorrow because of iflatio, opportuity cost, ad risk Brigig

More information

THE PRINCIPLE OF THE ACTIVE JMC SCATTERER. Seppo Uosukainen

THE PRINCIPLE OF THE ACTIVE JMC SCATTERER. Seppo Uosukainen THE PRINCIPLE OF THE ACTIVE JC SCATTERER Seppo Uoukaie VTT Buildig ad Tapot Ai Hadlig Techology ad Acoutic P. O. Bo 1803, FIN 02044 VTT, Filad Seppo.Uoukaie@vtt.fi ABSTRACT The piciple of fomulatig the

More information

TIAA-CREF Wealth Management. Personalized, objective financial advice for every stage of life

TIAA-CREF Wealth Management. Personalized, objective financial advice for every stage of life TIAA-CREF Wealth Maagemet Persoalized, objective fiacial advice for every stage of life A persoalized team approach for a trusted lifelog relatioship No matter who you are, you ca t be a expert i all aspects

More information

Asian Development Bank Institute. ADBI Working Paper Series

Asian Development Bank Institute. ADBI Working Paper Series DI Wokig Pape Seies Estimatig Dual Deposit Isuace Pemium Rates ad oecastig No-pefomig Loas: Two New Models Naoyuki Yoshio, ahad Taghizadeh-Hesay, ad ahad Nili No. 5 Jauay 5 sia Developmet ak Istitute Naoyuki

More information

1 Correlation and Regression Analysis

1 Correlation and Regression Analysis 1 Correlatio ad Regressio Aalysis I this sectio we will be ivestigatig the relatioship betwee two cotiuous variable, such as height ad weight, the cocetratio of a ijected drug ad heart rate, or the cosumptio

More information

Death Beefits from Pacific Life

Death Beefits from Pacific Life Ehace Your Fiacial Legacy Variable Auities with Death Beefits from Pacific Life 9/15 20188-15C FOR CALIFORNIA As You Pla for Retiremet, Protect Your Loved Oes A Pacific Life variable auity ca offer three

More information

This chapter considers the effect of managerial compensation on the desired

This chapter considers the effect of managerial compensation on the desired Chapter 4 THE EFFECT OF MANAGERIAL COMPENSATION ON OPTIMAL PRODUCTION AND HEDGING WITH FORWARDS AND PUTS 4.1 INTRODUCTION This chapter cosiders the effect of maagerial compesatio o the desired productio

More information

BENEFIT-COST ANALYSIS Financial and Economic Appraisal using Spreadsheets

BENEFIT-COST ANALYSIS Financial and Economic Appraisal using Spreadsheets BENEIT-CST ANALYSIS iacial ad Ecoomic Appraisal usig Spreadsheets Ch. 2: Ivestmet Appraisal - Priciples Harry Campbell & Richard Brow School of Ecoomics The Uiversity of Queeslad Review of basic cocepts

More information

Amendments to employer debt Regulations

Amendments to employer debt Regulations March 2008 Pesios Legal Alert Amedmets to employer debt Regulatios The Govermet has at last issued Regulatios which will amed the law as to employer debts uder s75 Pesios Act 1995. The amedig Regulatios

More information

Estimating Surface Normals in Noisy Point Cloud Data

Estimating Surface Normals in Noisy Point Cloud Data Estiatig Suface Noals i Noisy Poit Cloud Data Niloy J. Mita Stafod Gaphics Laboatoy Stafod Uivesity CA, 94305 iloy@stafod.edu A Nguye Stafod Gaphics Laboatoy Stafod Uivesity CA, 94305 aguye@cs.stafod.edu

More information

Hypothesis testing. Null and alternative hypotheses

Hypothesis testing. Null and alternative hypotheses Hypothesis testig Aother importat use of samplig distributios is to test hypotheses about populatio parameters, e.g. mea, proportio, regressio coefficiets, etc. For example, it is possible to stipulate

More information

est using the formula I = Prt, where I is the interest earned, P is the principal, r is the interest rate, and t is the time in years.

est using the formula I = Prt, where I is the interest earned, P is the principal, r is the interest rate, and t is the time in years. 9.2 Inteest Objectives 1. Undestand the simple inteest fomula. 2. Use the compound inteest fomula to find futue value. 3. Solve the compound inteest fomula fo diffeent unknowns, such as the pesent value,

More information

An Introduction to Omega

An Introduction to Omega An Intoduction to Omega Con Keating and William F. Shadwick These distibutions have the same mean and vaiance. Ae you indiffeent to thei isk-ewad chaacteistics? The Finance Development Cente 2002 1 Fom

More information

5: Introduction to Estimation

5: Introduction to Estimation 5: Itroductio to Estimatio Cotets Acroyms ad symbols... 1 Statistical iferece... Estimatig µ with cofidece... 3 Samplig distributio of the mea... 3 Cofidece Iterval for μ whe σ is kow before had... 4 Sample

More information

The Arithmetic of Investment Expenses

The Arithmetic of Investment Expenses Fiacial Aalysts Joural Volume 69 Number 2 2013 CFA Istitute The Arithmetic of Ivestmet Expeses William F. Sharpe Recet regulatory chages have brought a reewed focus o the impact of ivestmet expeses o ivestors

More information

How To Get A Kukandruk Studetfiace

How To Get A Kukandruk Studetfiace Curret Year Icome Assessmet Form Academic Year 2015/16 Persoal details Perso 1 Your Customer Referece Number Your Customer Referece Number Name Name Date of birth Address / / Date of birth / / Address

More information

In nite Sequences. Dr. Philippe B. Laval Kennesaw State University. October 9, 2008

In nite Sequences. Dr. Philippe B. Laval Kennesaw State University. October 9, 2008 I ite Sequeces Dr. Philippe B. Laval Keesaw State Uiversity October 9, 2008 Abstract This had out is a itroductio to i ite sequeces. mai de itios ad presets some elemetary results. It gives the I ite Sequeces

More information

TO: Users of the ACTEX Review Seminar on DVD for SOA Exam FM/CAS Exam 2

TO: Users of the ACTEX Review Seminar on DVD for SOA Exam FM/CAS Exam 2 TO: Users of the ACTEX Review Semiar o DVD for SOA Exam FM/CAS Exam FROM: Richard L. (Dick) Lodo, FSA Dear Studets, Thak you for purchasig the DVD recordig of the ACTEX Review Semiar for SOA Exam FM (CAS

More information

Grow your business with savings and debt management solutions

Grow your business with savings and debt management solutions Grow your busiess with savigs ad debt maagemet solutios A few great reasos to provide bak ad trust products to your cliets You have the expertise to help your cliets get the best rates ad most competitive

More information

Strategic Remanufacturing Decision in a Supply Chain with an External Local Remanufacturer

Strategic Remanufacturing Decision in a Supply Chain with an External Local Remanufacturer Assoiatio fo Ifomatio Systems AIS Eletoi Libay (AISeL) WHICEB 013 Poeedigs Wuha Iteatioal Cofeee o e-busiess 5-5-013 Stategi Remaufatuig Deisio i a Supply Chai with a Exteal Loal Remaufatue Xu Tiatia Shool

More information

An Analysis of Manufacturer Benefits under Vendor Managed Systems

An Analysis of Manufacturer Benefits under Vendor Managed Systems An Analysis of Manufactue Benefits unde Vendo Managed Systems Seçil Savaşaneil Depatment of Industial Engineeing, Middle East Technical Univesity, 06531, Ankaa, TURKEY secil@ie.metu.edu.t Nesim Ekip 1

More information

Lesson 17 Pearson s Correlation Coefficient

Lesson 17 Pearson s Correlation Coefficient Outlie Measures of Relatioships Pearso s Correlatio Coefficiet (r) -types of data -scatter plots -measure of directio -measure of stregth Computatio -covariatio of X ad Y -uique variatio i X ad Y -measurig

More information

CS103A Handout 23 Winter 2002 February 22, 2002 Solving Recurrence Relations

CS103A Handout 23 Winter 2002 February 22, 2002 Solving Recurrence Relations CS3A Hadout 3 Witer 00 February, 00 Solvig Recurrece Relatios Itroductio A wide variety of recurrece problems occur i models. Some of these recurrece relatios ca be solved usig iteratio or some other ad

More information

STUDENT RESPONSE TO ANNUITY FORMULA DERIVATION

STUDENT RESPONSE TO ANNUITY FORMULA DERIVATION Page 1 STUDENT RESPONSE TO ANNUITY FORMULA DERIVATION C. Alan Blaylock, Hendeson State Univesity ABSTRACT This pape pesents an intuitive appoach to deiving annuity fomulas fo classoom use and attempts

More information

Chapter 3 Savings, Present Value and Ricardian Equivalence

Chapter 3 Savings, Present Value and Ricardian Equivalence Chapte 3 Savings, Pesent Value and Ricadian Equivalence Chapte Oveview In the pevious chapte we studied the decision of households to supply hous to the labo maket. This decision was a static decision,

More information

How deductible plans work

How deductible plans work Idividual ad Family Plas DEDUCTIBLE PLANS How deductible plas work Deductible plas geerally offer lower mothly premiums i exchage for payig more out of your ow pocket for services covered by your health

More information

where: T = number of years of cash flow in investment's life n = the year in which the cash flow X n i = IRR = the internal rate of return

where: T = number of years of cash flow in investment's life n = the year in which the cash flow X n i = IRR = the internal rate of return EVALUATING ALTERNATIVE CAPITAL INVESTMENT PROGRAMS By Ke D. Duft, Extesio Ecoomist I the March 98 issue of this publicatio we reviewed the procedure by which a capital ivestmet project was assessed. The

More information

Here are a couple of warnings to my students who may be here to get a copy of what happened on a day that you missed.

Here are a couple of warnings to my students who may be here to get a copy of what happened on a day that you missed. This documet was writte ad copyrighted by Paul Dawkis. Use of this documet ad its olie versio is govered by the Terms ad Coditios of Use located at http://tutorial.math.lamar.edu/terms.asp. The olie versio

More information

How To Solve The Homewor Problem Beautifully

How To Solve The Homewor Problem Beautifully Egieerig 33 eautiful Homewor et 3 of 7 Kuszmar roblem.5.5 large departmet store sells sport shirts i three sizes small, medium, ad large, three patters plaid, prit, ad stripe, ad two sleeve legths log

More information

Get advice now. Are you worried about your mortgage? New edition

Get advice now. Are you worried about your mortgage? New edition New editio Jauary 2009 Are you worried about your mortgage? Get advice ow If you are strugglig to pay your mortgage, or you thik it will be difficult to pay more whe your fixed-rate deal eds, act ow to

More information

AMB111F Financial Maths Notes

AMB111F Financial Maths Notes AMB111F Financial Maths Notes Compound Inteest and Depeciation Compound Inteest: Inteest computed on the cuent amount that inceases at egula intevals. Simple inteest: Inteest computed on the oiginal fixed

More information

9:6.4 Sample Questions/Requests for Managing Underwriter Candidates

9:6.4 Sample Questions/Requests for Managing Underwriter Candidates 9:6.4 INITIAL PUBLIC OFFERINGS 9:6.4 Sample Questions/Requests fo Managing Undewite Candidates Recent IPO Expeience Please povide a list of all completed o withdawn IPOs in which you fim has paticipated

More information

Create Income for Your Retirement. What You Can Expect. What to Consider. Page 1 of 7

Create Income for Your Retirement. What You Can Expect. What to Consider. Page 1 of 7 Page 1 of 7 RBC Retiremet Icome Plaig Process Create Icome for Your Retiremet At RBC Wealth Maagemet, we believe maagig your wealth to produce a icome durig retiremet is fudametally differet from maagig

More information

Domain 1: Designing a SQL Server Instance and a Database Solution

Domain 1: Designing a SQL Server Instance and a Database Solution Maual SQL Server 2008 Desig, Optimize ad Maitai (70-450) 1-800-418-6789 Domai 1: Desigig a SQL Server Istace ad a Database Solutio Desigig for CPU, Memory ad Storage Capacity Requiremets Whe desigig a

More information

I apply to subscribe for a Stocks & Shares NISA for the tax year 2015/2016 and each subsequent year until further notice.

I apply to subscribe for a Stocks & Shares NISA for the tax year 2015/2016 and each subsequent year until further notice. IFSL Brooks Macdoald Fud Stocks & Shares NISA trasfer applicatio form IFSL Brooks Macdoald Fud Stocks & Shares NISA trasfer applicatio form Please complete usig BLOCK CAPITALS ad retur the completed form

More information

Discrete Mathematics and Probability Theory Spring 2014 Anant Sahai Note 13

Discrete Mathematics and Probability Theory Spring 2014 Anant Sahai Note 13 EECS 70 Discrete Mathematics ad Probability Theory Sprig 2014 Aat Sahai Note 13 Itroductio At this poit, we have see eough examples that it is worth just takig stock of our model of probability ad may

More information

VALUATION OF FINANCIAL ASSETS

VALUATION OF FINANCIAL ASSETS P A R T T W O As a parter for Erst & Youg, a atioal accoutig ad cosultig firm, Do Erickso is i charge of the busiess valuatio practice for the firm s Southwest regio. Erickso s sigle job for the firm is

More information

Comparing Credit Card Finance Charges

Comparing Credit Card Finance Charges Comparig Credit Card Fiace Charges Comparig Credit Card Fiace Charges Decidig if a particular credit card is right for you ivolves uderstadig what it costs ad what it offers you i retur. To determie how

More information

Bond Valuation I. What is a bond? Cash Flows of A Typical Bond. Bond Valuation. Coupon Rate and Current Yield. Cash Flows of A Typical Bond

Bond Valuation I. What is a bond? Cash Flows of A Typical Bond. Bond Valuation. Coupon Rate and Current Yield. Cash Flows of A Typical Bond What is a bod? Bod Valuatio I Bod is a I.O.U. Bod is a borrowig agreemet Bod issuers borrow moey from bod holders Bod is a fixed-icome security that typically pays periodic coupo paymets, ad a pricipal

More information

Valuing Bonds and Stocks

Valuing Bonds and Stocks Leaig Objecives 5- Valuig Bods ad Socks 5 Copoae Fiacial Maageme e Emey Fiey Sowe 5- Udesad ypical feaues of bods & socks. Lea how o obai ifomaio abou bods ad socks. Ideify he mai facos ha affec he value

More information

For customers Key features of the Guaranteed Pension Annuity

For customers Key features of the Guaranteed Pension Annuity For customers Key features of the Guarateed Pesio Auity The Fiacial Coduct Authority is a fiacial services regulator. It requires us, Aego, to give you this importat iformatio to help you to decide whether

More information

Logistic Regression, AdaBoost and Bregman Distances

Logistic Regression, AdaBoost and Bregman Distances A exteded abstact of this joual submissio appeaed ipoceedigs of the Thiteeth Aual Cofeece o ComputatioalLeaig Theoy, 2000 Logistic Regessio, Adaoost ad egma istaces Michael Collis AT&T Labs Reseach Shao

More information

Development of Customer Value Model for Healthcare Services

Development of Customer Value Model for Healthcare Services 96 Developmet of Custome Value Model fo Healthcae Sevices Developmet of Custome Value Model fo Healthcae Sevices Wa-I Lee ad Bih-Yaw Shih Depatmet of Maetig ad Distibutio Maagemet, Natioal Kaohsiug Fist,

More information

Incremental calculation of weighted mean and variance

Incremental calculation of weighted mean and variance Icremetal calculatio of weighted mea ad variace Toy Fich faf@cam.ac.uk dot@dotat.at Uiversity of Cambridge Computig Service February 009 Abstract I these otes I eplai how to derive formulae for umerically

More information

Information about Bankruptcy

Information about Bankruptcy Iformatio about Bakruptcy Isolvecy Service of Irelad Seirbhís Dócmhaieachta a héirea Isolvecy Service of Irelad Seirbhís Dócmhaieachta a héirea What is the? The Isolvecy Service of Irelad () is a idepedet

More information

Ignorance is not bliss when it comes to knowing credit score

Ignorance is not bliss when it comes to knowing credit score NET GAIN Scoing points fo you financial futue AS SEEN IN USA TODAY SEPTEMBER 28, 2004 Ignoance is not bliss when it comes to knowing cedit scoe By Sanda Block USA TODAY Fom Alabama comes eassuing news

More information

Statement of cash flows

Statement of cash flows 6 Statemet of cash flows this chapter covers... I this chapter we study the statemet of cash flows, which liks profit from the statemet of profit or loss ad other comprehesive icome with chages i assets

More information

Project Request & Project Plan

Project Request & Project Plan Poject Request & Poject Pla ITS Platfoms Cofiguatio Maagemet Pla Vesio: 0.3 Last Updated: 2009/01/07 Date Submitted: 2008/11/20 Submitted by: Stephe Smooge Executive Sposo: Gil Gozales/Moia Geety Expected

More information

PROCEEDINGS OF THE YEREVAN STATE UNIVERSITY AN ALTERNATIVE MODEL FOR BONUS-MALUS SYSTEM

PROCEEDINGS OF THE YEREVAN STATE UNIVERSITY AN ALTERNATIVE MODEL FOR BONUS-MALUS SYSTEM PROCEEDINGS OF THE YEREVAN STATE UNIVERSITY Physical ad Mathematical Scieces 2015, 1, p. 15 19 M a t h e m a t i c s AN ALTERNATIVE MODEL FOR BONUS-MALUS SYSTEM A. G. GULYAN Chair of Actuarial Mathematics

More information