Academic journal article Academy of Accounting and Financial Studies Journal

The Fallacy of the Roth

Academic journal article Academy of Accounting and Financial Studies Journal

The Fallacy of the Roth

Article excerpt

INTRODUCTION

All Roth retirement plans, whether they are a 401k, a 403b, a 457, or an individual retirement account (Roth) have the same basic tax structure. The taxpayer invests a portion of his/her salary and wages that have been taxed at the current rates in a Roth plan and all income derived from that plan is tax free as long as no withdrawals are made before the taxpayer reaches retirement age. All traditional defined contribution retirement plans, whether it is a 401k, a 403b a 457, or an individual retirement account (traditional plan), also have the same basic tax structure though different than the Roth. If a taxpayer contributes a portion of his/her salary and wages in the plan, then the taxes on the amount contributed into the account together with all earnings are deferred until the amounts are withdrawn at retirement. The popular press then concludes that if the marginal tax rate is higher at the time of retirement, the Roth is superior (Kohm, 2010; Brandon, 2010; Clements, 2006; Updegrade, 2008). Greene (2009) claims the Roth is a good hedge against higher taxes. Others conclude that if income tax rates rise, tax free retirement income would be a financial lifesaver (Anonomous, 2010). Franklin (2008) concludes that tax free income is better than taxable income. These are all true statements, however, none of these authors incorporated into their analysis the fact that the United States has a progressive tax system; your tax rate at retirement will not be one number but a combination of many rates. They also do not mention that most taxpayers will receive a social security benefit and that some or all of that income will not be taxed, which may result in the taxpayer being in a lower marginal tax bracket. These articles lack an in depth analysis of the factors affecting the decision to select a Roth or traditional plan, so this study will begin with the basic premise that follows.

If the marginal tax rate of the taxpayer at the time of the contribution into the retirement account is the same as when the withdrawal is made, the net amount received during retirement after taxes will be the same for both the Roth and the traditional plans. Since this is not intuitive because the amount of tax paid for the traditional account is generally much greater than that of the Roth, this fact will be proven mathematically. Assume that a taxpayer has X pre tax dollars available for his retirement. Assume further that the taxpayer invests it for n years, receives an annual rate of return r, and that the taxpayer's marginal tax rate at the time of the contribution to the account and at the time of withdrawal from that account is t. For the Roth, the taxpayer would invest X(1-t) in his retirement account in year one since the contribution into a Roth is post tax dollars. At retirement the taxpayer would have an amount equal to (X (1-t)) [(1+r).sup.n] available for withdrawal. However, for a traditional plan, the taxpayer would invest X in their retirement account in year one, since contributions to a traditional retirement plan are pre tax. (There are certain income limitations on an individual retirement account where contributions to an individual retirement account are not pre tax. For purposes of this analysis, amounts above that limitation are not included.) At retirement, the taxpayer would have X [(1+r).sup.n] available for withdrawal. The net proceeds after taxes would be (X [(1+r).sup.n]) (1-t) since he would have to pay the tax on the withdrawal. Based on the commutative property of multiplication, (X(1-t)) [(1+r).sup.n] = (X [(1+r).sup.n]) (1-t). Thus, if the marginal tax rate of the taxpayer at the time of the contribution into the retirement account is the same as when the withdrawal is made, the amount received will be the same for both the Roth and the traditional plans.

Using similar logic, it can also be shown that if the marginal tax rate of the taxpayer at the time of contribution into the retirement account is less than the marginal tax rate at the time of withdrawal from the plan, the Roth is superior. …

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