Friday, March 28, 2014

Roth versus Conventional IRAs -- results from my first model


This post was originally published at my blog www.economicmemos.com.  I hope to do more work on this topic soon.


Question:  Should workers allocate more funds away from deductible IRAS and towards Roth IRAS?

Modeling the Roth versus Deductible IRA contribution decision.

The decision on whether to contribute to a deductible IRA or a Roth IRA is a fascinating financial question.  Many people contribute to the deductible IRA in order to minimize their annual tax bill.   However, the desire to minimize tax obligations in the short term does not automatically lead to an optimal retirement plan, especially because there are substantial long term advantages in holding Roth IRAs.

I personally believe that a Roth IRA should be a standard part of every person’s retirement plan.  However, this allocation decision should be based on quantitative analysis rather than belief.  I am building  a model to help people evaluate the costs/benefits of different IRA contribution strategies.  This post describes the first version of the model and presents examples illustrating its use.

The IRA Contribution Model -- Version 1.0.

The IRA  Allocation Model considers the financial consequences of different allocations between Roth IRAs and Deductible IRAs.  The model is admittedly  a work in progress.

The model has three steps.

Step One:  Calculate IRA Balances at Retirement for different Deductible/Roth allocation strategies:

The first step involves the calculation of the balance of IRAs at retirement based on the contribution history and the rate of return on assets.

The model has been set up so that the after-tax cost of contributions for different IRA Allocation Scenarios are equal  (The after-tax cost of the IRA contributions are the contribution to the deductible IRA plus the contribution to the Roth iRA minus the tax savings from the contribution to the deductible IRA.

Three IRA allocations scenarios are generate — (1) 100% of the contribution to a deductible IRA, (2) Identical contributions to the Roth and deductible IRAS, and (3) 100% of contributions to the Roth IRA.

IRA balances at retirement are equal to the future value of all contributions.

Since the after-tax cost of IRA contributions in working years are identical in all three scenarios a comparison of IRA allocation strategies only requires examination of resources available in retirement.

Step Two:  Taxes Paid In Retirement Under The Three IRA Allocation Strategies

The model includes three sources of income — IRA disbursements, Social Security benefits and other income.  There are three different Roth assets can reduce tax burdens in retirement.  First, the Roth distribution does is not included as income when determining the amount of Social Security benefits subject to the income tax.  Second, the Roth IRAs themselves are not taxed.  Third, the  use of Roth IRAs can reduce the marginal tax rate for the taxpayer.

The tax component of the model has the following features.

I make assumptions on the size of the annual household Social Security benefit, annual household other income and an annual disbursement rate.

The model uses places income assumptions and deductible IRA disbursements into the IRS worksheet that determines how much of the Social Security benefit is taxable.

Information on the the three sources of income and the standard deduction are added to obtain taxable income. Taxes due are estimated based on taxable income and the 2013 tax rate schedules.

Step Three: Resources Available in Retirement

Resources available in retirement are the sum of IRA distributions, Social Security benefits, other income and taxes.  IRA disbursements are larger for the scenario with 100 percent of income in deductible IRAS because the contributions and balance in retirement are largest for this scenario. However, taxes are greater for scenarios that use deductible IRAs compared to scenarios that use Roth IRAs.

The Roth scenario is preferred if the tax savings from the Roth in retirement is larger than the incremental

I have created two spreadsheets — one for a single person the other for a married household.

The single tax payer example:

Our first example used to illustrate the new model involves assessing three different IRA contribution strategies for a single tax payer.  The three strategies are invest 100 percent in a deductible IRA, invest half of the contribution in a deductible IRA and half in a Roth IRA, and invest 100 percent of contributions in a deductible IRA.   The after-tax cost of total IRA contributions are identical ($7,500 per year) for all three scenarios.  The  assumed marginal tax rate is 25 percent; hence, the first scenario involve a $10,000 contribution to a deductible IRA.   The second scenario involves a contribution of $4286 to a deductible IRA and a $4286 deduction to a Roth IRA.  The third scenario involve a $7,500 contribution to a Roth IRA and no deduction to a deductible IRA.

The key assumptions used in this exercise are:
  • Contributions are made for 30 consecutive years until retirement.
  • Assets in the IRAs earn 5.0 percent per year
  • 4 percent of the IRA balances are distributed in retirement
  • The Social Security benefit is $19,200 per year
  • Other income is $20,000 per year
Below are the IRA contribution allocations matched with the model’s projections for IRA balance, taxes paid, and total resources


IRA Contribution Information
Conventional
$10,000
$4,286
$0
Roth
$0
$4,286
$7,500
Total Cost
$7,500
$7,500
$7,500
Output
Deductible IRA Balance
$587,374
$247,874
$0
Roth IRA Balance
$0
$247,874
$433,780
Taxes
$9,842
$4,849
$2,329
Resources
$52,492
$54,180
$54,222


It appears as though for this household (with the assumptions listed above) allocating some resources to the Roth IRA results in a modest increase in resources available in retirement.

Example Two:  The Married Household 

The second example involves a married household  Again three scenarios 100% deductible, 50/50 deductible/Roth, and 100% Roth are considered

The key assumptions in this example are -- 30 annual contributions, a 5.0 percent annual return, $48,000 in Social Security benefits, a 4.0 percent distribution rate, and other taxable income of $ 40,000.

The IRA allocations and output for each scenario are summarized in the table below.




IRA Contribution Strategies 
Married Household
Conventional 
$18,000
$7714
$0
Roth
$0
$7714
$13,500
Total
$13,500
$13,500
$0
Output
Deductible Balance
$1,248,387
$535,023
$0
Roth Balance
$0
$535,023
$936,290
Taxes Paid
$27,771
$19781
$9779
Resources



$110,164
$111,020
$115,672
Again, the results for a specific exercise suggest that allocations towards Roth IRAs away from deductible IRAs can increase resources available in retirement.

Concluding thoughts:  This is version 1.0 of the IRA asset allocation model. My model has not been independently reviewed.  Errors are always possible but I am a bit OCD, have checked, and will do so again.


The results presented here cannot be generalized to all households.  This example considers only one disbursement strategy --disburse 4.0 percent per year from all accounts.   Retirees have discretion over disbursements from IRAs and can schedule larger disbursements from Roth IRAs when such disbursements are most warranted.  I suspect these results understate potential benefits from allocating resources towards Roth IRAs.

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