Thursday, February 24, 2005

For an individual, a tax-deferred account is at best only slightly better than non-deferred account, and a Roth IRA is almost never the best choice.

(Part 2 of 5)

In the United States today, there are three basic ways to save money.

Let’s imagine three people, call them Ted, Ralph, and Neal. Each of them has a $1000 bonus coming from his boss and decides to save it for retirement. Ted puts his $1000 into a traditional IRA, Ralph puts his into a Roth IRA, and Neal puts his in a non-tax-deferred brokerage account. To make this a bit simpler, I’m going to ignore state taxes, and assume that all three of them are in the 25% tax bracket. There is one more important rule:

Money placed into any of the three types of accounts will grow at the same rate; $1 placed into any of the three accounts will, after a certain amount of time, have grown to exactly the same amount (before any taxes and withdrawal penalties).

I will call this growth factor ‘g’. For example, if the underlying investments return 10% anually, then after one year, g=1.1, and after ten years, g=2.59.

Tax rates are unstable. Every few years, they move up or down a bit. Nobody knows what personal income taxes will be like 10, 20, or 50 years from now. For this analysis, I’m going to assume that they will be the same when our three guys hit age 59.5 as they are now.

Let’s start with Ted, who puts his money into a Traditional IRA (I’m going to ignore 401(k) accounts for the rest of this article. For tax purposes, they are almost identical to traditional IRAs.) If we imagine that his boss can put the money straight into his IRA, we can ignore the withholding and later tax refund, which cancel out. Over time, the balance printed on his monthly account statement is $1000 * g. However, if he wants to access his money after retirement, he has to pay 25% taxes on it, so the final withdrawable balance at retirement will be $1000 * g * 75%. If Ted withdraws the money early, there will be an additional 10% penalty, and the withdrawable balance will be $1000 * g * 65%.

Let’s move on to Ralph. He decides to put his money into a Roth IRA. Because Roth IRAs are funded with post-tax dollars, Ralph’s extra $1000 in income results in him having an extra $250 in tax liabilities, giving him only $750. At first glance, he seems to be at a severe disadvantage to Ted, because the balance printed on Ralph’s account statement is $750 * g. However, Ralph can access his original $750 tax-free. If he decides to access the entire account, the amount above $750 is considered taxable income. Further, if he accesses it in the first five years, there’s an additional 10% penalty. However, at retirement, the entire balance of the account will be withdrawable completely tax-free. Unfortunately, the various penalties make the formulas more complicated, but, Ralph’s withdrawable balance looks something like this:

Profit = 750 * (g – 1)
Withdrawable balance in the first five years = 750 + (Profit * 65%)
Withdrawable balance after five years = 750 + (Profit * 75%)
Withdrawable balance at retirement = 750 * g

The interesting thing to note is that Ralph’s withdrawable balance at retirement, (750 * g) is exactly equal to Ted’s, which is $1000 * g * 75%. At retirement, if Fred’s tax bracket at withdrawal is equal to Ralph’s tax bracket was when they received the $1000, then the actual value of their accounts will always be identical. The only difference between a Roth IRA and a traditional IRA is that the taxes are levied at the front instead of at the back. With no change in tax rates, the actual realizable value from the two accounts is identical.

Meanwhile, what happened to Neal? He doesn’t trust fancy accounting shenanigans, so he just puts his money into a non-tax-deferred account. Like Ralph, he can only fund his account with $750. Also like Ralph, the original $750 can be taken out tax-free. However, Neal has some important differences when compared to Ted and Ralph. There will never be any special penalties on Neal’s withdrawals. Nothing special happens to the true value of his account at retirement. Finally, the big advantage: Gains in Neal’s account can be taxed at the much-lower capital-gains rates instead of as regular income. If Neal buys stock with his $750, then his gains won’t be taxable until he sells that stock. Further, as of 2005, capital gains from any stock held more than a year, as well as all dividends, are taxed at only 15%. Because of this, the best option for Neal is to buy a non-dividend-paying stock and hold it until he is ready to withdraw the full balance. If he is able to do that, his numbers look like this:

Profit = 750 * (g – 1)
Withdrawable balance in the first year: 750 + (profit * 75%)
Withdrawable balance after one year: 750 + (profit * 85%)

Neal also has one other advantage: If g is negative, meaning that the underlying investments have lost value, then Neal gets to take that loss as a tax deduction. Neither Ted nor Ralph get to take losses in his account as a deduction.

Maximum Withdrawable Balance, Profit = ($750 * (g-1))

Ted (Traditional IRA)Ralph(Roth IRA)Neal (Non-Deferred)
After one year:$1000 * g * 65%750 + (Profit * 65%)750 + (Profit * 85%)
After five years:$1000 * g * 65%750 + (Profit * 75%)750 + (Profit * 85%)
After age 59.5:$1000 * g * 75%
(750 * g)
750 +(Profit * 100%)
750 + (Profit * 85%)

Again, this table assumes that tax rates will be stable, and that all three workers will stay in the same tax bracket, from deposit time to withdrawal time.

So, what does this table tell us? As noted above, once they hit age 59.5, Ted and Ralph have exactly the same withdrawable amount. However, I should note that Ralph and Neal have the advantage of being able to take the whole thing at once, whereas if Ted tries to take too much at once, it might push him into a higher tax bracket.

The next thing to notice is that Neal’s withdrawable balance is always higher than Ralph’s up until retirement, and always lower afterwards.

To recap: Before retirement, a non-tax-deferred account is better than a Roth IRA, and after retirement, there is no benefit to a Roth IRA over a Traditional IRA. The only time that a Roth IRA is better than the others is if tax law changes, and the withdrawals from the other accounts become more expensive. Assuming static tax rates, there is no situation where a Roth IRA will have the highest actual value of the three account types.

Finally, if g is high enough, Ted will have more money than Neal, even if they withdraw their money before retirement. With 25% tax rates, the crossover point comes at g=9, which will happen after 25 years at an 8% growth rate. If both Ted and Neal invest in an investment that will be worth 10x what it was before, then Ted’s higher starting position will cancel out his higher taxes, even before retirement. However, the difference between the accounts is very small. If (before retirement) g = 3, then Neal’s withdrawable balance will be less than 4% higher than Ted’s. On the other hand, if g=20, then Ted’s withdrawable balance will be barely 1% higher than Neal’s.

So, assuming reasonable investment growth rates and static tax rates:

  • Before retirement, The withdrawable balance in a non-deferred account will be very close to the withdrawable balance in a traditional IRA; N ~= T

  • Before retirement, the withdrawable balance in a Roth IRA will always be lower than the withdrawable balance in a non-deferred account; R < T

  • At retirement, the withdrawable balance in a traditional IRA and a Roth IRA will be identical; T = R

  • At retirement, the withdrawable balance in a Roth IRA will always be higher than the withdrawable balance in a non-deferred account. R > N

Or, again assuming static tax rates and reasonable growth:
  • Before retirement, R < T and T ~= N
  • After retirement, N < R and R = T

Unless tax rates go up in the future, a Roth IRA is almost never the best choice. There is one very important exception, which I'll discuss in my next post.