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 Mercedes Jalbert (E-mail: mercedesjalbert@yahoo.com), The IBFR Abstract I this paper the attractiveess of tax-deferred ad o-deferred ivestmets i periods of chagig tax regimes are examied. Specifically the desirability of deferrig taxes give oe s curret tax rate, estimate of future tax rates, umber of years util retiremet, ad the expected rate of retur o ivestmet is explored. Uder some combiatios of tax rates ad ivestmet horizos, tax deferral is foud to be udesirable while i others it is foud to be desirable. Usig the formulas ad tables developed here, a idividual ca idetify the rate of retur o ivestmet at which he is idifferet betwee deferrig ad ot deferrig, rates at which tax deferral is preferred ad rates at which tax deferral is iferior. I additio, the sesitivity of the decisio to the timig of future tax rate chages is explored. This research provides ivestors a more comprehesive uderstadig of the factors that determie optimal tax deferral choices ad will permit ivestors to make better tax deferral decisios.. Itroductio Tax deferred ivestmet is a commo method for people to save moey for retiremet. The beefit of deferrig taxes is that oe has more moey to ivest util retiremet, thereby gaiig from the time value of moey. At retiremet, taxes are paid o ay balaces that have ot bee previously taxed. There are at least four risks associated with ivestig i tax deferred accouts. The first risk is that, i cotrast to other ivestmets, ay losses o ivestmet i a deferred accout are ot deductible agaist curret icome. The secod risk is that the idividual eeds access to the fuds prior to retiremet, requirig the idividual to pay a pealty for early withdrawal. The third risk is that tax rates will icrease betwee the time of deposit ad withdrawal, resultig i deferral to a higher tax rate. The fourth risk is that the idividual s icome will icrease sufficietly i retiremet to move the idividual to a higher tax bracket. The focus of this paper is o the third ad fourth risks, that tax rates or brackets will chage. There are a umber of tax deferral savigs vehicles available to ivestors. The Traditioal Idividual Retiremet Arragemet (IRA) was first itroduced by the Retiremet Icome Security Act (ERISA) of 974. Its goal was to ecourage icreased savigs by tax payers. Traditioal IRAs allow idividuals youger tha 70½ years of age to deduct a prescribed amout of icome from his/her taxable icome by placig the moey ito a accout targeted for use i their retiremet years. The ivestor must meet certai icome limitatios to qualify to take the deductio. If the idividual takes the moey out of the accout after age 59.5, the idividual pays ordiary icome taxes o the amout of moey received. I the evet that a idividual takes the moey out of the accout prior to age 59.5, a 0% pealty is assessed o the withdrawals ad the remaider is taxed as ordiary icome. Idividuals are required to begi takig moey out of a traditioal IRA by age 70½ years. More recetly, Roth IRA s were itroduced. Cotributios to Roth IRA s are ot tax-deductible, ad there are o age restrictios o cotributios. However, returs from a Roth IRA are tax free. Like traditioal IRA s, Roth IRA s are subject to icome ad filig status limitatios (U.S Iteral Reveue Service 2004). Other cotributory plas iclude o-deductible IRA s, 40K s 403B s, 457 s, Simplified Employee Pesios (SEP) ad The Savig Icetive Match Pla for Employees (SIMPLE). Each of these plas has its ow advatages, disadvatages, rules ad limitatios. Each year, millios of taxpayers are faced with the questio Should I defer taxes o my retiremet savigs? At first glace tax-deferral appears to be the best choice i all cases, but questios about the beefits of deferrig arise whe tax rates ad ivestmet returs are expected to follow certai patters i the future ad whe Electroic copy available at: http://ssr.com/abstract=46869
the time to retiremet is shorter. I certai istaces, it may ot be beeficial to defer taxes. This holds particularly true if the idividual expects low returs o ivestmet, has a short time to retiremet ad expects tax rates to icrease. I this paper we precisely idetify situatios whe tax deferral is advatageous ad disadvatageous. The importace of this issue ca be illustrated with some geeral statistics about the popularity of IRA s. I 2000, over $2.6 trillio were held i IRAs ($2.4 trillio i traditioal IRAs ad $77.6 billio i Roth IRA s). Durig the same tax year, over $36 billio were cotributed to IRAs ($0.04 billio to traditioal IRAs, $.56 billio to Roth IRAs). I 2000, over 29 millio taxpayers could techically make a IRA cotributio, but less tha 2 percet elected to cotribute to a IRA (Sailer ad Nutter, 2000). Further uderscorig the importace of the issue is a agig U.S. populatio ad icrease i baby boomers reachig retiremet age. The U.S. Cesus Bureau reported that 2 percet of the total populatio were age 65 or over i 2002, ad estimated that approximately 20 percet of the total populatio will be age 65 ad over by 2030 (U.S.C.B., 2003). I this paper, we explore how various issues iteract to determie if a idividual should defer taxes. The remaider of the paper is orgaized as follows. Sectio 2 provides a summary of the relevat literature. A discussio of the possible future courses of tax rates follows i Sectio 3. Next the methodology ad results of the paper are preseted ad discussed. Fially, Sectio 5 cotais cocludig commets. 2. Literature Review Hora, Peterso ad McLeod (997) aalyze the impact of decliig margial tax rates o ivestmet choices. Their study evaluates the after-tax future value of odeductible IRAs ad taxable ivestmets o comparable mutual fuds by decreasig margial tax rates from 3% to 28%. They coclude that, holdig margial capital gai rates costat, icreases i margial tax rates favor taxable ivestmets ad decreases i margial tax rates favor o-deductible ivestmets. Burgess ad Madeo (980) model a break-eve ivestmet horizo ad IRA withdrawals takig ito accout impact of withdraw pealties. Radolph (994) argues i favor of o-deductible IRAs over outright ivestmet. He determies that IRAs performed better if ivested i high turover, high distributio mutual fuds ad the iverse holds true for taxable ivestmets. Crai ad Austi (997) improve o Radolph s work by cotrollig for differeces i ordiary icome ad capital gai tax rates. They coclude that deductible IRAs are more favorable for idividuals who expect to be i a lower tax bracket upo retiremet, while Roth IRAs are more favorable for those expectig to be i a higher tax bracket upo retiremet. This fidig is particularly iterestig whe take together with the work of Berheim, Skier ad Wieberg (997) who fid that idividual icomes drop by approximately 36 percet after retiremet, ad thus move the idividual to lower margial tax rates. Krisha ad Lawrece (200) examie IRAs, Roth IRAs, o-deductible IRAs ad ope taxable ivestmets. They itroduce a break-eve tax rate which they defie as the tax rate at withdrawal where alterate ivestmets will produce the same future value for a give ivestmet horizo ad rate of retur. That is, the tax rate that would make the idividual idifferet betwee ivestig i a taxable or tax deferred accout. They coclude that ivestors will beefit from deductible IRAs if they are i a low tax bracket at the time of the first withdrawal ad that ivestors will beefit from Roth IRAs if they have loger ivestmet horizos. I their compariso of o-deductible IRAs ad ope taxable ivestmets, they coclude that ivestors with loger ivestmet horizos beefit from o-deductible IRA s. However, o-deductible IRAs may become less desirable if a ivestor selects a ivestmet istrumet of which returs largely come from log-term capital gais. Hora ad Peterso (200) improved o the Hora, Peterso ad McLeod (997) model. Similar to Krisha ad Lawrece (200), they assume that tax savigs are ivested i taxable ivestmets, ad allow for chages i tax brackets. They coclude that Roth IRAs ad tax-deductible IRAs perform better whe tax savigs are ivested i istrumets that are ot taxed at the ordiary icome levels. Hora (2002) exteds his prior work by itroducig valuatios based o auitized patters istead of sigle cash flow withdraws, ad developig after-tax preset value iterest factors. Kuter, Doey ad Trebby (200) used the same equal before-tax ivestmet as Crai ad Austi (997) to compare deductible IRAs ad Roth IRAs ad determied that the performace of both IRAs are affected by the idividual s margial tax rate at the begiig ad at the ed of the ivestmet period. Electroic copy available at: http://ssr.com/abstract=46869
Sibley (2002) uses capital ivestmet theory to develop a more complex model that accouts for differeces betwee deferred-tax ad o-deferred tax assets to assist idividuals i valuig their asset mix. Specifically, his model determies the curret o-deferred tax dollar equivalet of assets held i tax-deferred retiremet accouts. He otes that If a prospective retiree has specific expectatios of future chages i either rates of retur or tax rates, the geeral valuatio process ca be applied usig a Excel spreadsheet that permits separate estimates of retur ad tax rate for each future year (Sibley, 2002). The work i this paper is most closely related to the work of Krisha ad Lawrece (200), Sibley (2002), Burgess ad Madeo (980) ad Hora (2002). Kirsha ad Lawrece (200) ad Burgess ad Madeo (980) solved for the break eve tax rates ad ivestmet horizos respectively. The research i this paper exteds this lie of literature by idetifyig the break eve retur o ivestmet. That is the retur o ivestmet that makes a idividual idifferet betwee tax deferral ad foregoig tax deferral. While Krisha ad Lawrece (200) hold retur costat ad solve for the break-eve tax rate, i this paper, tax rates are held costat ad the break-eve retur o ivestmet is solved for. 3. The Future Course of Tax Rates The future course of tax rates is ukow. Nevertheless, expectatios about the future course of tax rates are critical i determiig if a idividual should defer taxes or ot. As such, each idividual must make a estimate about future tax rates i order to determie the optimal tax deferral strategy. To assist i this estimate, some iformatio about the likely future course of tax rates ca be gleaed from iformatio that is curretly available. Specifically, the curret fiacial positio of the federal govermet, ad the historical record of tax rates provide clues about the likely future course of tax rates. The federal govermet curretly owes approximately 7.7 trillio dollars (Samuel, 2005). Curret deficit spedig was just over $500 billio per year i fiscal year 2004 (Bureau of the Public Debt, 2005). This iformatio idicates quite clearly that the combiatio of curret tax rates ad taxable ecoomic activity are ot sufficiet to accommodate curret spedig patters of the U.S. Govermet. There are at least four ways that U.S. Govermet deficit spedig ca be rectified. The first cadidate is for tax rates to be icreased or deductios decreased, thereby brigig additioal fuds ito the system to offset the deficit. A secod possibility is for the U.S. Govermet to udertake massive cuts i spedig. If spedig were cut sufficietly, curret tax receipts may be sufficiet to balace the budget. However, it is ot likely that spedig cuts of this size are possible as it would ivolve chages o the magitude of elimiatig the U.S. Defese Departmet. A third possibility is that the U.S. ecoomy grows sufficietly so that associated icreases i tax reveues would offset the budget deficit, i which case o tax rate icreases would be ecessary. A fial, though remote, possibility is the U.S. Govermet defaultig o its debts. While U.S. Govermet bods have log bee cosidered a risk free ivestmet, a remote possibility of a future U.S. Govermet default exists. It ca be argued that this chace of default icreases with the level of debt. If the U.S. were to default, elimiatig the eed to pay iterest o the $7.7 trillio dollars of public debt, curret tax receipts may be sufficiet to meet or exceed expeditures. Each of these solutios has merit ad drawbacks. Which course the U.S. will follow is ukow. However, it is at least possible ad probably likely that the solutio will iclude some form of tax rate icreases. Others argue that the level of public debt has ot reached a critical level. They argue that higher tax rates are ot ecessary. As log as the fuds borrowed are for productive ivestmets, there is little eed to worry about the level of the deficit. Moreover, they may argue that a large amout of taxes have bee deferred through the use of IRA s ad other ivestmet vehicles. These deferred taxes imply large future tax iflows for the federal govermet whe the fuds are removed from the accouts ad taxed. I fact, some argue that lower tax rates are desirable eve give the curret federal debt level ad budget deficits of the U.S. While may speculative argumets, such as those preseted above ca be forwarded regardig the possible future course of tax rates, perhaps the most compellig evidece regardig the likely future course of tax rates ca be gleaed from a look at historical tax rates. Wilso ad Jorda (2002), provide just such a historical aalysis. They report the highest ad lowest positive margial tax rates from 93 through 2002. Figure, created from data provided i Wilso ad Jorda (2002), shows how the margial tax rates have chaged sice 93. The highest margial tax rate for idividuals started at seve percet i 93. The rate gradually icreased to 94 percet by the year 944. The rate the was the reduced to 28 percet by 988, ad subsequetly icreased to 38.6 percet by
2002. The highest margial tax rate remaied at or above 70 percet durig the etire period betwee 936 ad 980. The lowest positive margial tax rate has show similar shifts, startig at oe percet i 93, dippig to 0.375 percet i 929, the icreasig to 23 percet by 944. The rate subsequetly fell to 0 percet by 2002. This historical evidece clearly shows that tax rates have chaged dramatically throughout the history of the Uited States. Also oteworthy from Figure is that the highest margial tax rate has bee more volatile tha the lowest margial tax rate throughout our history. The history of chages clearly idicates that future tax rates are by o meas certai, ad could take o highly varyig values. Give the argumets oted above alog with the historical record of tax rates, the oly thigs that are clear are that tax rates are likely to chage i the future ad the future course of tax rate chages is ucertai. Despite this ucertaity, ivestors must make a estimate about future tax rates ad expected ivestmet returs i order to make a iformed decisio cocerig the extet to which tax deferral is a wise choice. This decisio must be reevaluated for each cotributio ad withdrawal date combiatio that the ivestor is cosiderig. As oted above, Berheim, Skier ad Wieberg (997) fid that idividual icomes drop by approximately 36 percet after retiremet, ad thereby move the idividual to lower margial tax rates. Thus for may idividuals, placig moey i a tax deferred accout has two beefits. First the beefit of tax deferral, ad secod the beefit of shiftig icomes to a time whe the idividual will be i a lower tax bracket. While the equatios developed i this paper are able to evaluate ay such situatios, this research is most beeficial to those idividuals that will either maitai or icrease their icome levels i retiremet ad those that have shorter periods of time to retiremet. With a large umber of baby boomers ow havig a short amout of time to retiremet, this research is particularly timely. The remaider of this paper focuses o how idividual ivestors ca make the tax deferral decisio based o their ow fiacial situatio ad expectatios about the future course of tax rates. Figure : The History of Uited States Margial Tax Rates from 93 through 2002 00 90 80 Margial Tax Rate 70 60 50 40 30 20 0 0 93 97 4. Methodology ad Results 92 925 929 933 937 94 945 949 953 957 Top Margial Tax Rate Year 96 965 969 Lowest Margial Tax Rate 973 977 98 985 989 993 997 200 The optimal tax deferral strategy depeds upo a ivestor s curret tax rate, expectatios about future tax rates, the time to retiremet, ad the expected rate of retur o ivestmet. I this paper, the umber of years to retiremet, the curret tax rate ad various estimates about future tax rates are take as give. With this iformatio, the idifferece before tax retur o ivestmet (IROI) is computed. This idifferece retur o ivestmet is the aual percetage retur o ivestmet that makes a ivestor idifferet betwee a tax deferred ivestmet ad a taxable ivestmet give curret ad expected future tax rates as well as a kow time util fuds
will be withdraw from the accouts. For simplicity, we assume that there are o withdrawals from a tax deferred accout that would trigger a pealty. It is also assumed that ivestmets produce the same before tax rates of retur i a tax deferred accout or o-deferred accout. To determie the retur o ivestmet required to be idifferet about tax deferral, it is ecessary to estimate the future course of tax rates. The aalysis here is completed for each of three differet assumptios about the future course of tax rates. I additio, a method for solvig the problem for ay other future tax rate ad ivestmet horizo combiatio is demostrated. As such, this research has a broad scope, beig applicable to ivestors with ay curret tax rate, expectatio about the future course of tax rates ad umber of years to retiremet. The first tax assumptio is that tax rates will make a permaet oe time shift. The idividual curretly faces some tax rate o icome from o-deferred ivestmets, which ca be ay combiatio of capital gais ad ordiary icome tax rates. A tax rate shift will occur i the year followig the iitial ivestmet to a ew rate, that agai may be ay combiatio of the capital gais ad ordiary icome tax rate. The ivestor s tax rate will remai at that level through retiremet o o-deferred icome. Fuds ivested i a tax deferred accout are subject to the future ordiary icome tax rate of the ivestor, which may or may ot equal the future tax rate o o-deferred ivestmets. Oe istace of this tax rate sceario ivolves a ivestor that has observed the U.S. Cogress make a tax rate chage which takes effective i the followig year. The secod assumptio also ivolves a ivestor that is curretly faced with ay combiatio of capital gais ad ordiary icome tax rates o o-deferred icome. Agai, tax rates will make a permaet oe time shift. However the secod assumptio is that the shift will occur after the last amout of iterest has bee eared, but before the fuds have bee withdraw from the accouts. Ay fuds ivested i a tax deferred accout are subject to the future ordiary icome tax rate, which may or may ot equal the future rate o o-deferred icome. As such, oly the withdrawal from the tax deferred accout will be subject to the ew rates. A ivestor that expects a tax rate chage i the distat future might base his decisios o the results of this secod aalysis. The third assumptio ivolves a ivestor that is curretly faced with ay combiatio of capital gais ad ordiary icome tax rates o o-deferred icome. This rate will remai costat at its curret level for oe year. After oe year, the rate will icrease i equal aual icremets util it reaches a ew higher or lower rate. This ew tax rate o o-deferred icome will be the future ordiary icome tax rate that prevails at the time fuds are withdraw from the accouts. Fuds ivested a tax deferred accout are subject to the future ordiary icome tax rate of the idividual. May idividuals are advised to gradually shift their portfolio from capital gais producig assets to icome producig assets as they age. These idividuals could fid themselves i a situatio at retiremet where both, returs from o-deferred assets ad withdrawals from tax deferred accouts are taxed at the same rate, the the prevailig ordiary icome tax rate. These three assumptios are ot exhaustive as ay umber of other assumptios about the future course of tax rates ca be cosidered. We provide aalysis tools to assist the ivestor i computig (IROI) uder ay other tax rate assumptio ot specifically solved for here. Moreover, while we use a specific combiatio of rates ad time to retiremet here, the problem ca be solved for ay other rate combiatio or times to retiremet that might occur. The three tax assumptios are illustrated i Table where curret tax rates o o-deferred icome faced by the ivestor i 2005, which ca be ay combiatio of ordiary ad capital gais rates, are 5 percet. These rates are expected to rise so that the future rate o icome from o-deferred ivestmets is 20 percet. The future ordiary icome tax rate is 25 percet i 2008. Usig the three assumptios outlied above, the future value of each, a Table : Future Course of Tax Rates Year Oe Time Shift Begiig Oe Time Shift Ed Icremetal Chage 2005 5% 5% 5% 2006 20% 5% 5% 2007 20% 5% 20% 2008 20% (25)% 5% (25%) 25 (25)%
ivestmet i a tax deferred accout ad a ivestmet i a o-tax deferred accout are computed. Next, these future values are equated ad the resultig equatio is solved for the IROI. This is doe for several combiatios of curret tax rates ad expected future tax rates. By examiig these tables ad formulas, ivestors ca determie if tax-deferral is appropriate give a curret tax rate, expectatio about future tax rates ad time to retiremet. For demostratio purposes, cosider a ivestor who has $30,000 from curret earigs to ivest today. Through various defermet vehicles, the idividual is able to defer the etire amout if he/she so chooses. The ivestor has a five year ivestmet horizo. His/her curret tax rate is 5% o o-deferred icome. The ivestor expects the future tax rate o o-deferred icome to be 20 percet. The ivestor expects the future tax rate o deferred icome, the ordiary icome tax rate, to be 25 percet. The ivestor expects to ear a 0 percet aual ROI either i a tax deferred, or o-tax deferred accout. Icome from the tax deferred ivestmet will be taxed at the future ordiary icome rate, while icome from the o-deferred accout will be taxed at the future o-deferred tax rate. The ivestor wishes to determie if it is preferable to ivest through a tax-deferred accout or pay taxes curretly ad ivest the remaiig proceeds. We complete the aalysis usig each of the assumptios about the course of future taxes outlied above. Oe Time Shift Begiig Recall that the first tax assumptio is that tax rates will make a permaet, oe time, shift. The shift will occur i the year followig the iitial ivestmet ad remai at that level through retiremet. First, the future value of the idividuals ivestmets are computed if taxes are deferred ad if taxes are ot deferred. The aalysis begis with the tax deferral case. The ivestor that defers taxes places all of his/her curretly saved retiremet fuds i a tax deferred accout. The idividual will leave the fuds i this accout util retiremet. At retiremet, the idividual removes the fuds from the accout. The idividual the pays taxes at the ordiary icome tax rate that prevails at the time fuds are withdraw from the accout. The idividual uses the fuds at this poit as desired. While the aalysis here assumes the idividual removes the fuds from the accout upo retiremet, the aalysis is also relevat for idividuals who wish to delay withdrawal of the fuds util some time after retiremet. Cosider a idividual that has curretly saved some moey which is iteded for use i retiremet, S. The ivestor expects to ear a aual rate of retur of i, o the ivestmets ad has a ivestmet horizo of. If the ivestor defers taxes, at the time of withdrawal, ad before payig taxes, the idividual will have the future value of his ivestmets BTFV, available as: BTFV ) = S( + i () The idividual will the pay taxes at the ordiary icome tax rate that prevails i the future, TOf, leavig the idividual with the after tax future value ATFV, which ca be used by the ivestor as desired. This amout is computed as: ATFV = BTFV ( TOf ) (2) Combiig equatios ad 2 gives: ATFV = S( + i) ( TOf ) (3) For the ivestor described above, at retiremet the idividual will have: ATFV 5 = $30,000( +.0) (.25) = $36,236.48 If the idividual does ot defer taxes, the ivestor pays taxes o the fuds today at the curret combiatio of capital gais ad ordiary icome tax rates that the ivestor is faced with, Tc, ad ivests the remaiig proceeds. The amout of moey available to ivest today after tax, FI is: FI = S( Tc) (4)
I additio to taxes o the pricipal amout, the ivestor pays taxes each year o the earigs at the rate TGf, which ca agai be ay combiatio of ordiary or capital gais tax rates that the ivestor is faced with i the future. The future value of the savigs after payig these taxes is computed as: ATFV )]} = FI{ + [ i *( TGf (5) Combiig Equatios, 4 ad 5 gives: ATFV )} = S( Tc){ + [ i *( TGf (6) For the ivestor described above the amout of moey available at the ed of the ivestmet horizo is: ATFV = $30,000( 0.5){ + [0.0*( 0.2)} 5 = $37,467.87 At the ed of the ivestmet horizo, the ivestor removes this $37,467.87 from the accout ad speds it as he/she chooses. I this example, the retur o the additioal fuds available by tax deferrig is ot sufficiet to offset the icrease i tax rates, so the ivestor should ot defer. The differece i future values is $,23.39 ($37,467.87- $36,236.48). However, this will ot always be the case. I the evet that the idividual is able to ear a higher retur, or has a loger time util retiremet, it may be better to defer taxes eve i the presece of icreasig tax rates. The aalysis here assumes that the idividual removes the etire amout of moey from the accout o a give day. I reality, may ivestors deposit ad withdraw fuds from their retiremet accouts i the form of auities or other multi-paymet patters. The equatios developed here ca accommodate such situatios. To do so requires a separate aalysis for each cotributio ad withdrawal date combiatio. For example, suppose that a 50-year old idividual deposits $4,000 ito a IRA for retiremet. He/she iteds to withdraw some of these fuds alog with the associated earigs from the accout at age 69 ad the remaider at age 70. I the curret framework this problem ivolves two idepedet decisios. To aalyze the problem it is ecessary to compute the solutio oce for each iteded withdrawal date. Similarly, a idividual with multiple deposit dates, would re-compute the solutio for each deposit date. To summarize the computatios, a formula is developed to solve specifically for the IROI. The solutio is obtaied by equatig, the future value of the tax deferral alterative to the future value of the o-tax deferral alterative as follows: S ( )]} + i) ( TOf ) = S( Tc){ + [ i *( TGf (7) Solvig Equatio 7 for i, gives Equatio 8, the retur o ivestmet at which the idividual will be idifferet betwee tax deferral ad o tax deferral (IROI): ( TOf ) Tc IROI ( ) = (8) ( TOf ) TGf ( Tc) Equatio 8 allows a idividual to easily compute the IROI give his specific tax situatio ad ivestmet horizo. The equatio ca easily be applied to ay combiatio of curret tax rates, expected future tax rates, ad time to retiremet. For the ivestor discussed above with a 5 percet curret tax rate, a 20 (25) percet future tax rate ad a five-year ivestmet horizo, the equatio is computed as:
IROI ( 0.25) 5 ( 0.5) = ( 0.25) 0.20 ( 0.5) = 5 0.40 If the idividual expects to ear a 4. percet ROI o his ivestmets, he will be idifferet about deferral. If the ivestor expects his retur to be above the rate computed by Equatio 8, the idividual is better off by deferrig taxes. If the ivestor expected his retur to be below the rate computed by Equatio 8, the idividual is better off without deferral. Give historical average returs o the U.S. stock market betwee 0- percet (Ibbotso ad Che, 2003), exceedig a 4. percet retur should ot to be take lightly. Table 2 demostrates the computatios for various combiatios of tax rates for a idividual with 5 years util fuds with be withdraw from the accouts. Because there are three tax rates ivolved, the table is preseted for three possible future tax rates o o-deferred icome, 0%, 5% ad 20%, i Paels A, B, ad C, respectively. I each pael, the IROI is solved for varyig combiatios of the curret tax rate ad expected future tax rate o ordiary icome. For example if the curret tax rate is 5 percet, the future ordiary icome tax rate is 25 percet, ad the future tax rate o o-deferred icome is 0 percet the idifferece ROI is 32.84 percet. If the ivestor expects to achieve a 32.84 percet ROI, he/she will be idifferet about tax deferral. Ay time the ivestor expects to ear above 32.84 percet o his ivestmets, tax deferral is preferable. If he expects to ear less tha 32.84 percet o his ivestmets, tax deferral is ot preferable. Additioal tables, coverig other times to retiremet ad tax rates, are available from the authors by request. However, i geeral it ca be said that as the umber of years to retiremet icreases, the IROI will declie. For example, if the above described ivestor had 20 years to retiremet, the IROI would be 6.65 percet. The careful reader will ote that some combiatios havig low curret tax rates ad high future tax rates are omitted ad labeled NM (Not Meaigful). These cells were labeled as such, as the equatio tured egative. While the rate is ot meaigful, the idividual would clearly ot wat to defer taxes i such situatios. Oe Time Shift at the Ed of the Period Recall that the secod tax assumptio was that the tax rate remais uchaged throughout the preretiremet years, but makes a sudde shift, after all icome has bee eared, but prior to withdrawig fuds from the accout. Uder this tax assumptio, the IROI is computed as: ( TOf ) Tc IROI ( ) = (9) ( TOf ) Tc ( Tc) Agai, usig the ivestor discussed above with a 5 percet curret tax rate, Tc, a 20 percet future ordiary icome tax rate, TOf, ad five years to retiremet, the equatio is computed as: ( 0.25) 5 ( 0.5) IROI = ( 0.25) 0.5 ( 0.5) = 5 0.973
The idifferece ROI is 9.73 percet. If the idividual ca ear above 9.73 percet o his ivestmets it is better to defer taxes. At rates below 9.73 percet it is best to avoid tax deferral. It is iterestig to ote i this case that the timig of the tax rate shift makes a 563 basis poit differece (.973-.40) i the IROI. Table 3 demostrates the computatios at various combiatios of tax rates for a idividual with 5 years to retiremet. The careful reader will otice that TGf is ot icluded i Equatio 9. This is o accidet. Ideed, all earigs from the odeferred accout would be taxed at the curretly prevailig rate of Tc, uder the secod tax assumptio. Table 2: Idifferece ROI for a 5-years to Retiremet ad a Oe-Time Tax Rate Shift at the Begiig of the Ivestmet Horizo Pael A: 0 % Future Tax Rate o No-Deferred Icome Future Tax Rate o Deferred Icome 0 5 0 5 20 25 30 35 40 45 50 5 0.00 2.05 28.20 5.03 85.80 45.39 27.60 720.3 NM NM 0-9.8 0.00 2.82 30.35 55.78 96.6 70.36 352.33 52.9 NM 5-8.36-0.3 0.00 3.70 32.84 6.52 09.38 205.72 50.73 NM 20-25.9-9.25-0.87 0.00 4.7 35.78 68.57 26.82 259.7 872.56 25-32.62-27.08-20.22 -.50 0.00 5.88 39.30 77.45 50.92 352.33 30-38.64-34.0-28.36-2.30-2.20 0.00 7.25 43.60 88.99 86.37 35-44.09-40.2-35.53-29.78-22.50-2.99 0.00 8.88 48.94 04.58 40-49.05-45.79-4.9-37.20-3.34-23.84-3.90 0.00 20.85 55.78 45-53.60-50.86-47.63-43.76-39.02-33.07-25.36-4.93 0.00 23.28 50-57.80-55.5-52.82-49.64-45.79-4.04-35.0-27.08-6.4 0.00 Pael B: 5 % Future Tax Rate o No-Deferred Icome Future Tax Rate o Deferred Icome 0 5 0 5 20 25 30 35 40 45 50 5 0.00 7.72 7.9 29.07 44.48 65.29 95.03 4.9 222.90 408.0 0-6.76 0.00 8.20 8.37 3.36 48.55 72.44 08.02 66.90 283.73 5-3.04-7.2 0.00 8.74 9.73 34.03 53.44 8.36 25.6 204.9 20-8.90-3.7-7.52 0.00 9.35 2.3 37.2 59.43 92.80 48.83 25-24.40-9.84-4.46-7.97 0.00 0.05 23.7 4.04 66.94 08.02 30-29.57-25.58-20.88-5.29-8.48 0.00 0.87 25.38 45.76 76.64 35-34.46-30.95-26.87-22.04-6.22-9.05 0.00.84 28.05 5.70 40-39.09-36.03-32.48-28.3-23.33-7.27-9.7 0.00 3.00 3.36 45-43.50-40.83-37.75-34.6-29.9-24.78-8.47-0.48 0.00 4.40 50-47.73-45.40-42.74-39.65-36.03-3.70-26.43-9.84 -.37 0.00 Pael C: 20 % Future Tax Rate o No-Deferred Icome Future Tax Rate o Deferred Icome 0 5 0 5 20 25 30 35 40 45 50 5 0.00 5.68 2.36 20.33 30.02 42.09 57.59 78.27 07.35 5.49 0-5.6 0.00 6.03 3.7 2.8 32.47 46.00 63.79 88.32 24.49 5-0. -5.44 0.00 6.4 4.0 23.52 35.35 50.70 7.50 0.39 20-4.88-0.65-5.75 0.00 6.85 5.8 25.53 38.80 56.49 8.35 25-9.49-5.66 -.25-6.0 0.00 7.36 6.42 27.92 43.0 63.79 30-23.95-20.49-6.53 -.92-6.50 0.00 7.94 7.90 30.79 48.24 35-28.28-25.6-2.60-7.49-2.68-6.95 0.00 8.63 9.66 34.34 40-32.49-29.69-26.5-22.85-8.58-3.54-7.47 0.00 9.44 2.8 45-36.6-34.0-3.26-28.0-24.24-9.8-4.52-8.07 0.00 0.42 50-40.65-38.4-35.89-33.0-29.69-25.82-2.22-5.66-8.78 0.00 Preset Tax Rate Preset Tax Rate Preset Tax Rate
Table 3: Idifferece ROI for a 5-years to Retiremet ad a Oe-Time Tax Rate Shift at the Ed of the Ivestmet Horizo Future Tax Rate o Deferred Icome 0 5 0 5 20 25 30 35 40 45 50 5 0.00 27.4 78.57 208.38 208. NM NM NM NM NM 0-9.8 0.00 2.82 30.35 55.78 96.6 70.36 352.33 52.92 NM 5-3.04-7.2 0.00 8.74 9.73 34.03 53.44 8.36 25.6 204.9 20-4.88-0.65-5.75 0.00 6.85 5.8 25.53 38.80 56.49 8.35 25-6.22-2.93-9.2-4.94 0.00 5.80 2.72 2.5 3.68 45.26 30-7.35-4.66 -.66-8.28-4.43 0.00 5.6.26 8.62 27.70 35-8.39-6.2-3.6-0.8-7.66-4.09 0.00 4.75 0.36 7.0 40-9.40-7.44-5.28-2.90-0.24-7.26-3.88 0.00 4.5 9.83 45-20.43-8.70-6.82-4.74-2.45-9.89-7.02-3.75 0.00 4.38 50-2.50-9.97-8.30-6.47-4.45-2.22-9.73-6.9-3.7 0.00 Preset Tax Rate Others Tax Rate Chages Uder the third assumptio, tax rates will remai costat at their curret level for oe year. After oe year, rates will icrease i equal aual icremets to a ew rate. This ew rate will equal the future ordiary icome tax rate. Fuds withdraw from a tax-deferred accout will also be subject to the future ordiary icome tax rate o withdrawal. The mathematics for developig a formula to solve for the IROI i this situatio is complex. May other possible combiatios ivolve complex mathematical solutios. I these istaces, it may be easier to solve for the IROI by usig the Solver fuctio i Microsoft Excel or other similar program as opposed to explicitly developig a formula for the IROI. This approach was suggested by Sibley (2002). The procedure for usig Excel Solver is demostrated usig the third tax assumptio. This procedure ca be easily adapted for ay other tax rate combiatios that a ivestor might expect to occur i the future. To use solver for computig the IROI, first the future value of the tax deferred cash flows ad the o-tax deferred cash flows are computed for a certai umber of years to retiremet, curret tax rate, future tax rate ad retur o ivestmet. Next the differece betwee the two future values is computed. Fially, the solver fuctio i Excel is used to vary the retur o ivestmet util the differece i future values is zero. For the ivestor with a 5 percet curret tax rate, 20 percet future tax rate o deferred icome or o-deferred icome, ad 5 years to retiremet, the idifferece ROI is 7.40 percet: Table 4 shows IROI computatios for a idividual with 5 years to retiremet at differet tax rate combiatios. Table 4: Idifferece ROI for a 5-years to Retiremet ad a Gradual Tax Rate Shift Future Tax Rate o Deferred Icome ad No-Deferred Icome 0 5 0 5 20 25 30 35 40 45 50 5 0.00 6.74 28.5 36.88 44.4 NM NM NM NM NM 0-2.66 0.00 0.00 8.36 25.67 32.33 38.62 NM NM NM 5-8.38-8.42 0.00 7.40 4.0 20.35 26.34 32.24 38.9 44.37 20-2.9-3.72-6.52 0.00 6.04.78 7.34 22.86 28.45 34.26 25-24.50-7.53 -.25-5.46 0.00 5.24 0.38 5.50 20.72 26.4 30-26.6-20.54-4.98-9.77-4.8 0.00 4.74 9.50 4.35 9.4 35-28.49-23.0-8.0-3.37-8.83-4.39 0.00 4.42 8.95 3.67 40-30.25-25.39-20.84-6.5-2.32-8.2-4.3 0.00 4.23 8.64 45-3.97-27.54-23.36-9.36-5.47 -.65-7.83-3.97 0.00 4.4 50-33.7-29.63-25.76-22.04-8.42-4.84 -.25-7.62-3.89 0.00 Preset Tax Rate
5. Cocludig Commets I this paper the cocept of a idifferece retur o ivestmet (IROI) is itroduced. This IROI is the rate of retur at which a ivestor is idifferet about tax deferral give a curret tax rate, expected future tax rate ad time to retiremet. This work exteds the work of others who have solved for idifferece tax rates ad idifferece ivestmet horizos. The sesitivity of the results to differeces i the timig of a expected tax rate chage are computed. Over a five-year horizo, differeces i the timig of a tax rate chage are foud to make a 563 basis poit differece i the IROI for a ivestor with a curret tax rate of 5 percet, a expected future tax rate o odeferred icome of 20 percet ad a future tax rate o deferred icome of 25 percet. Formulas ad tables are preseted to assist ivestors i determiig their IROI for various tax rate combiatios. Solvig for the IROI uder a variety of other tax rate ad year to retiremet combiatios are also demostrated usig Excel Solver. This research provides ivestors a more comprehesive uderstadig of the factors that determie optimal tax deferral choices ad will permit ivestors to make better choices about tax deferral. There are may ope research questios related to tax deferral, however; the research preseted here fills oe importat gap i the literature. The authors wish to thak Mr. Victor Hugo-Cordero ad Karla Jessica Cordero-Madriz for their valuable research assistace i solvig equatios 8 ad 9. 6. Refereces Berheim, B.D., Skier, J.S., ad Weiberg, S. (997) What Accouts for the Variatio i Retiremet Wealth Amog U.S. households? Mimeo (Staford Uiversity) Bureau of Public Debt Webiste: http://www.publicdebt.treas.gov/ dowloaded May 5, 2005. Burgess, R.D., ad Madeo, S.A. (980) A Simulatio study of tax Sheltered Retiremet Plas, Joural of America Taxatio, vol., p. 34-4. Crai, T.L ad Austi J.R. (997) A aalysis of Tradeoff Betwee Tax Deferred Earigs i IRAs ad Preferetial Capital Gais, Fiacial Service Review, vol. 6(4), p. 228-229. Hora, S.M., ad J.H. Peterso (200) A Reexamiatio of tax-deductible IRAs, Roth IRAs, ad 40(k) Ivestmets, Fiacial Services Review, vol. 0, p. 87-00. Hora, S.M. ad J.H. Peterso ad R. McLeod (997) A Aalysis of Nodeductible IRA Cotributios ad Roth IRA Coversios, Fiacial Services Review vol 6(4) p. 243-256. Hora, S.M. (2002) After-Tax Valuatio of Tax-Sheltered Assets, Fiacial Services Review, vol., p. 253-275. Ibbotso, Roger ad Peg Che (2003) Stock Market Returs i the Log Ru, Participatig i the Real Ecoomy, Fiacial Aalysts Joural, vol. 59(), Jauary/February p. 26-33. Krisha, S.V., ad Lawrece, S. (200) Aalysis of Ivestmet Choices for Retiremets: A New Approach ad Perspective, Fiacial Service Review, vol. 0() p. 75-86. Kuter, G.W., Doey, L.D., Trebby, J.P. (200) Ivestmet Performace compariso betwee Roth ad Traditioal Idividual Retiremet Accouts, Joural of Applied Busiess Research, vol. 7(), p. 55-60. Radolph, W.L. (994) The Impact of Mutual Fud Distributios o After-Tax Returs, Fiacial Services Review vol. 3(2) p. 38-42. Sailer, P.J. ad Nutter S.E. (2992) Accumulatio ad Distributio of Idividual Retiremet Arragemets, Iteral Reveue Service. 2002. P. 2. http://www.irs.gov/pub/irs-soi/00retire.pdf Samuel Terece (2005) The America Prospect, $7,782,86,546,352 i Debt, CBS News, http://www.cbsews.com/stories/2005/04/08/opiio/mai686839.shtml Sibley, M. (2002) O the Valuatio of Tax-Advataged Retiremet Accouts, Fiacial Services Review, vol. (3), p. 233-25. U.S. Cesus Bureau (2003) Special Editio-Social Security COLA: CB03-FF.9SE December. http://www.cesus.gov/pressrelease/www/releases/archives/facts_for_features/00583.html U.S. Iteral Reveue Service. Publicatio 590. 2004. http://www.irs.gov/publicatios/p590/ch0.html#d0e922 Wilso, Robert A. ad David E. Jorda (2002) Persoal Exemptios ad Idividual Icome Tax Rates, 93-2003, Rev. 6-02), Iteral Reveue Service Statistics of Icome Bulleti, Publicatio 36 (Sprig), p. 26-225.