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# Roth Vs. Non Roth (401k, 403b, 457, Etc) & The Time Value Of Money

This topic has been discussed by many, over the years, but it is still very apparent to me that even a number of teachers and financial planners still have trouble with this subject. Much information is out there that can either tend to scare you away from the Roth account, or profess that it is the "greatest thing since sliced bread." Neither of these facts is really the truth, as you probably suspect.

Let's first try to discover what I call the "mathematical truth." To me this is the truth when I hold all the variables (such as tax rates and investment returns) constant for both accounts and I don't try to "profess" that I will know what your tax rate will be in the future. What I will assume is that the tax rate will be exactly the same now and in the future. If you want to argue differently, feel free, but I can make a case either way on tax rates.

I like to use an easy example of a lump sum onetime \$10,000, with 25% tax rate, and invested for 20 years at 10% but split the 401k money stream into two parts, one is your tax free and the other the taxman gets when distribution is taken. This would look something like this:

401(k) - \$10,000 investment

\$7500 @ 10% for 20 yr. = \$50,456 - your tax free money

\$2500 @ 10% for 20 yr. = \$16,819 - taxman takes this

Another way to look at this is you put \$10k into the 401k for 20years @ 10% at which time you had \$67,275, but then you cashed it out and the taxman took his 25% or \$16,819.

No matter what the return the taxman always gets his share - how much he gets depends on your return.

Roth - same \$10,000, but this time you have to pay the taxman up-front

\$10k x tax rate 25% = \$2500 for taxes - invest the rest

\$7500 @ 10% for 20 yr. = \$50,456

So as you can see (I hope,) there is really NO difference between a Traditional IRA account and a Roth account, as far as comparing the investment income between the two forms of investment accounts. As for the "Time Value of Money" which is sometimes used to refer to the fact that inflation eats away at our purchasing power, it does NOT apply to this math as no matter what inflation has turned out to be the Roth investor can buy exactly the same number of loafs of bread as the non-Roth investor in our example above.

So why would anyone choose one over the other? To see what might affect our decision let's look at some of the basic characteristics:

Traditional IRA - must start taking withdrawals at age 70 ½.

Traditional IRA - withdrawals are taxed at your ordinary income rate when money is withdrawn.

Roth - no taxes at all after the 5 year holding period.

Traditional IRA withdrawals - must be 59 ½ only, no minimum time that it is open.

Roth account withdrawals - must be 59 ½ and the account must have been open for 5 years.

Contributions can only be made to both types of accounts to the extent that you have "earned income." In other words, money you worked for, not money from Pensions, Social Security, or Rental Income from Real Estate. However, if you are married and file a joint tax return, you can open two accounts, one for each spouse, even though only one spouse works, as long as you have enough earned income to cover your contributions.

So what are a couple of the major reasons for having a Roth account if the returns are so equal?

Imagine that you had a "sizable" 401k account in retirement and you were forced to take all your income from this account, you would be losing a substantial amount to taxes as all this money is taxed as ordinary income at your maximum rate.

Now let's say you could lower that marginal tax rate by taking half your income from a tax-free Roth account. You have just saved yourself some money by possibly lowering your tax rate and the chunk of money that the tax man takes.

This is where I think the real advantage of the Roth account comes in - not from the fact that your money is going to come to you tax free, but to lower the total amount that the taxman will take over your lifetime. Remember the Roth money was taxed already at the maximum rate, so our only advantage is to get some of the 401k money taxed at a lower rate. Also if you need a large one-time distribution, the Roth can be the place to get it without affecting your taxes.

The other major advantage is that I do not have to take any money out of the Roth account at any particular time, while the Traditional IRA owner has to be constantly aware of the fact that a certain amount has to be taken out every year (whether the market is up or down) once the owner reaches the magic age of 70 ½. Therefore the traditional IRA is somewhat limited as an estate planning tool as it will most likely be liquidated by the time the owner dies, whether that was the intent or not.

A fun way to think of this is what I call the casino example:

Two gamblers walk into a casino with \$10,000 each. At the entrance they are given the choice of paying the casino ¼ of their cash on hand (which would be \$2500) or paying one quarter of their cash when they leave. Gambler A had been told to always pay any tax as far in the future as possible. Gambler B decided he didn't want to pay tax on all his winnings so he would pay the tax now, so he gave up \$2500 of his cash now and received a hand stamp indicating his "fee" had been paid in full.

Now the question is, if both gamblers double their money while in the casino, who (if anyone) will have more money by the time they get back to their car.

Note, this is a problem that most should be able to do on the back of a napkin without even using a calculator.

For extra credit, assume each gambler only played the slot machines - why did the casino not care whether the tax was paid up front or as the gambler left the casino? How much did each gambler cost the casino?

If they lost half their money instead of winning how does this change the results - in other words does one gambler get away with more money than the other and does the casino make more money off one gambler than the other?

Finally, I don't mean to imply people can't do this simple math, but what I have found is that people are lazy. They hear things and they don't check the math out on paper. With a pencil and a napkin you CAN verify this math. For the more sophisticated investor who does understand the time value of money and inflation it is quite easy to see that if two investors have the same amount of money 20 years in the future, whatever the inflation was in the meantime just does not matter.

Disclosure: I/we have no positions in any stocks mentioned, and no plans to initiate any positions within the next 72 hours.