Tuesday, January 26, 2010

IRAs: Traditional vs. Roth, Part 2

I'm always trying to learn more about investing, and although much of what I read covers material I already know and understand, sometimes I run across information that increases my understanding significantly.  I recently ran across a couple of articles on IRAs on moneychimp.com (mentioned in my last post on useful investing websites) that increased my understanding of the tradeoffs between traditional and Roth IRAs.  Based on what I read, I started working on a spreadsheet to further deepen my ability to analyze the tradeoffs.  Based on this work, I revised and added to my original post on IRAs: Traditional vs. Roth (December 16, 2009).  For those who may have already read it, I'm repeating the main additions to that post here, in case you don't want to reread the original article.  I'll also include some examples to demonstrate the tradeoffs.

One of the key points of the moneychimp.com article was that unless you can afford to contribute the maximum allowable contribution to your IRA ($5,000 if below age 50, $6,000 if age 50 or above), it makes no difference whether you use a traditional or Roth IRA.  The assumption, although not explicitly stated in the article, is that your tax rate upon withdrawal (e.g., in retirement) is the same as when you make your original contributions.  Based on my spreadsheet analysis, I determined that although the main idea is correct, the point at which the Roth IRA starts to be superior is somewhat below the maximum allowable contribution.

Here are the additions I made to the original post:

If you can't afford to reduce your take home pay more than $3,500 - $4,000 (the exact number depends on your federal and state marginal tax rates), and if you assume that your marginal tax rates upon withdrawal will be the same as your marginal tax rates upon contribution, then it can be shown that it makes no difference whether you use a traditional or Roth IRA.  This is because while you can afford to contribute more to a traditional IRA (because of the tax deduction), the taxes you pay upon withdrawal exactly offset the additional contribution and its compound growth.

However, if you can afford to reduce your take home pay by more than about $4,000 (again, the exact number depends on your tax rates), then additional tax free compound growth of the Roth IRA begins to give you a slightly higher net withdrawal

If you invest the traditional IRA tax savings in a taxable account, the benefit of the Roth IRA is somewhat reduced, but the Roth still comes out ahead!  You get the maximum benefit from a Roth over a traditional IRA if you are able to afford to reduce your take home pay by exactly the amount of the maximum allowed contribution ($5,000 if under age 50).  However, the benefit is greatly reduced by investing your traditional IRA tax savings in a taxable account.

All of the above conclusions are affected by the difference between your marginal tax rates upon contribution and upon withdrawal.  Significantly lower tax rates in retirement result in the traditional IRA being the better deal, while significantly higher tax rates in retirement result in the Roth IRA being the better deal.

(end additions to original post)

Let's look at a few examples to clarify the statements made above.  My starting point is someone who currently is making no contributions to an IRA or 401(k), but realizes she can afford to do so.  In the examples, we'll only consider the results of a single contribution, but the same principles would apply to multiple contributions over the years.

Example 1

First, let's assume that Ann, a single, California resident, age 25, feels she can afford a reduction in her take home pay (net pay) of $2,000 per year, and already has adequate short term reserves for emergencies or planned purchases.  Ann's taxable income is $50,000/year, so her marginal federal tax rate is 25% and her marginal state tax rate is 9.55% (so her combined marginal tax rate = 34.55%).  Ann is eligible to make a fully deductible traditional IRA contribution, or a non-deductible Roth IRA contribution.

Ann can afford to contribute $2,000 to a Roth IRA or $3,056 to a traditional IRA.  She can afford the larger contribution to the traditional IRA because she'll get a total federal and state tax deduction of $1,056 (34.55% X $3,056 = $1,056); i.e., since she'll pay $1,056 less in taxes, her net pay is only reduced by the $2,000 she can afford.

Assuming a 5% compound growth rate over 40 years, the $3,056 traditional IRA contribution would grow to $21,513, while the $2,000 Roth IRA contribution would grow to $14,080.  Since we're assuming the same tax rates upon withdrawal, Ann would pay taxes of 34.55% X $21,513 = $7,433 on the traditional IRA withdrawal, leaving her with $14,080 to spend.  Note that this is exactly the same amount as the $14,080 she would be able to withdraw tax-free from the Roth IRA.  Hence, based on our assumptions of no change in tax rates for Ann, and that she actually withdraws the money, it makes no difference which type of IRA she uses.

Ann might want to consider that with a Roth IRA, she is not required to make withdrawals, whereas with a traditional IRA, she would be required to make withdrawals starting at age 70 1/2.  If she thinks that she might be able to live without making IRA withdrawals, the Roth IRA would be superior, because she could continue to let her Roth IRA investments grow tax free, and even pass it on to her children who could then make tax free withdrawals while continuing to let the remainder grow tax free.

Ann also should consider that she can withdraw her original contribution ($2,000) from the Roth IRA at any time, penalty and tax-free (since she's already paid the taxes).  With a traditional IRA, she'd pay a 10% penalty plus taxes on any withdrawals before reaching age 59 1/2 (although there are a few exceptions that would allow her to make premature withdrawals penalty-free).

Example 2

Now let's assume Mary is in the exact same situation as Ann, but can afford a reduction in net pay of $5,000.  Since the maximum allowable contribution to either type of IRA is $5,000 for 2009 and 2010, the starting and ending values would be the same in either type of IRA, growing to $35,200 over 40 years at 5%.  However, with the traditional IRA, she would receive a current tax savings of $1,728, which she could then invest in either a 401(k) or a taxable account.

With the traditonal IRA, Mary would pay $12,162 in taxes upon withdrawal, leaving her with $23,038 to spend.  Note that this is $12,162 less than the tax free withdrawal of $35,200 from the Roth IRA.  This is where many examples stop, making the Roth seem like the clearly superior long term choice. 

However, let's not forget about the original traditional IRA tax savings of $1,728.  Assuming that Mary invested that in a 401(k), or in a taxable account where all of the growth was from appreciation (i.e., no dividends or interest that would be taxable along the way -- not realistic, but I haven't made the spreadsheet sophisticated enough yet to consider dividends and interest), the terminal value of the $1,728 (after 40 years at 5%) would be $12,162, on which Mary would pay $4,202 in taxes, leaving her with $7,960 to spend.

Adding the $7,960 from the taxable or 401(k) account to the $23,038 from the traditional IRA account gives Mary a total of $30,998, or only $4,202 less than the Roth IRA.  So, while the Roth IRA is still the superior long term investment, the benefit isn't nearly as dramatic as when we ignore what Mary might do by investing the tax savings from the traditional IRA.  Considering only the IRAs, the Roth provides 53% more spendable money, but considering the additional investment of the original traditional IRA tax savings, the Roth benefit is about 14% -- still significant, but much less impressive.

The Effect of Different Tax Rates

Let's reconsider the Mary scenario, but assume that her combined marginal tax rate in retirement is 25% instead of 34.55%.  In this case, it turns out that the traditional IRA plus tax savings invested in a 401(k) comes out slightly ahead ($35,521 vs. $35,200).  On the other hand, if Mary's combined marginal tax rate in retirement is 45%, the Roth is far superior ($35,200 vs. $26,049).


As I said in the original IRA article, one of the biggest unknowns is what our tax rates will be in retirement.  Considering this, plus the potential benefit of investing the traditional IRA tax savings in a 401(k) or even a taxable account, it still seems reasonable to consider using both a traditional and Roth IRA, perhaps with somewhat of a bias toward the Roth.  On the other hand, the complexity of managing more accounts may not be worth it to you, so you might just want to go with one or the other, after having considered the discussions above.

In making your decision, remember the two other advantages of the Roth IRA:
  1. You can withdraw your contributions at any time, penalty and tax-free.
  2. You aren't ever required to take withdrawals.
If you're nervous about locking up your money until age 59 1/2 (without paying a 10% penalty to get at it), the Roth IRA may be the better choice for you.  Of course, you should only take early withdrawals from a Roth IRA if absolutely necessary, since you can never put the money back in the Roth, and enjoy the benefits of the long term tax-free compound growth.

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