Retirement Savings

(Last Mod: 10 March 2011 00:40:05 )


There are several different tax-favored retirement savings plans that are available, each with its own features, rules, pros, and cons. Some are employer-sponsored, others are individual in nature. The basic feature that they all have in common is that the funds placed in them are not taxed between the time they are deposited and the time they are withdrawn. Furthermore, they are either taxed before you put the funds into the account or when you pull them out, not both. In addition, they all impose tax penalties if you break the rules of that particular plan.

Traditional vs. Roth

Before we discuss the various plans, lets focus on the two common variants that most plans offer, namely a traditional tax-deferred plan or a Roth version of the same plan. In a traditional plan, the funds placed into the plan are not taxed when placed into the plan but are then taxed when the funds are withdrawn during retirement. In a Roth plan, the opposite is true -- funds are taxed before being placed into the plan but are then free of tax from that point on, including when they are withdrawn.

There are some general rule difference that usually, though not always, go along with the two options. For instance, in a traditional plan you are usually prohibited from withdrawing any of the funds before you reach the age of 59.5 without incurring taxes and penalties. In most Roth plans, on the other hand, you are generally able to withdraw the contributed funds -- but not the earnings on those funds -- after they have been invested for at least five years. However, while these differences in rules can be significant if they apply to your situation, the vast majority of funds fall into the basic situation in which none of these differences matter; namely, funds are invested into the plan, allowed to grow for the minimum amount of time, and then withdrawn after the person has reached the necessary age. Therefore, the remainder of this discussion will concern itself solely with the performance of the two variants in that situation.

If you listen to many 'professionals' discuss the differences between a traditional and a Roth, you will hear many really tout the Roth as the only plan you should consider, provided it is an option in your situation, because everything is tax free after you make the contributions. Others will babble on about how lots of factors influence which is the better choice, usually focusing on how long you will be able to let the money sit and grow. The claim here is that if you choose a Roth, then the money has to sit for some minimum amount of time in order to recover the upfront taxes and then, after that, you are money ahead.

Here's a newsflash: all of that is pure crap. Very seldom will you hear any of these 'professionals' even mention the one and only factor that matters: Which end has the higher tax? If the effective tax rate at the time you contribute the funds is the same as the effective tax rate when you withdraw the funds, then they will perform exactly the same whether you leave them in for five years or fifty years. The reason is very simple: multiplication is commutative.

Consider the following two cases:

Person A takes an amount of money, M, and invests it into a traditional plan. While invested, the money grows tax-deferred by a factor G. When it is withdrawn, it is taxed leaving the person with a fraction TA. The total funds they have at the end, FA, is therefore given by:

FA = (M*G)*TA

Person B, on the other hand, takes the same amount of money but invests it into a Roth account. As a result, it is first taxed, leaving them with a fraction TB to actually invest in the account. The invested amount then grows by the same growth factor G before being withdrawn with no further taxes. The total funds they have at the end, FB, is therefore

FB = (M*TB)*G

Since multiplication is both commutative and associative, this may be rewritten as:

FB = (M*G)*TB

Clearly, if TA = TB, then FA = FB and they are equivalent. On the other hand, TA > TB, then the traditional plan will outperform the Roth while, conversely, if TA < TB, then the Roth will be the better choice.

So how do we determine TA and TB? The simple answer is that each is 1 minus the effective tax rate applied to the funds at that end. So if the tax rate applied to the funds when they are deposited is 25%, then TA = 0.75, while if the tax rate during retirement is 15%, then TB = 0.85. For these example numbers, the traditional plan would be the better choice.

Now, notice that I was very careful to use the term 'effective tax rate' and not just 'tax rate'. To understand the distinction, it is important to understand the nature of the progressive tax system that is applied at either end. To have solid numbers to work with, let's look at the 2010 tax rate schedule for people that are single.

Between and taxed at
0 8375 10%
8375 34000 15%
34000 82400 25%
82400 171850 28%
171850 373650 33%
373650 higher 35%

For those that are married filing jointly, it is:

Between and taxed at
0 16750 10%
16750 68000 15%
68000 137300 25%
137300 209250 28%
209250 373650 33%
373650 higher 35%

It is next important to note that these rates apply to 'taxable income', which is 'Adjusted Gross Income' (AGI) less deductions and exemptions. For simplicity, we will assume that all of our filers only clam the standard deduction, which is $5700 for people that are single and $11400 for people that are married filing jointly, and the standard exemption, which is $3650.

Now, for simplicity, let's assume that our tax filer is single, earned $45,000, and has no adjustments to income. Their AGI is therefore $45,000 and their taxable income, notwithstanding any retirement contribution decision they make, would be $35650. This places them in the 25% marginal income tax bracket. The term 'marginal' means that it refers to the tax applied to small (i.e., marginal) changes in income. This is commonly described as, "the tax rate on the next dollar earned." However, it is NOT the effective tax rate that is applied to this person's income. To find this out, we simply need to determine the total tax they must pay and divide that by the total income they earned, which was the full $45,000. The tax they will pay is

10%*$8375 + 15%*($34000-$8375)+25%*($35650-$34000) =  $5094 (you round to the nearest dollar)

and thus their effective, or average, tax rate is only

$5094/$45000 = 11.32%

But this is still not the effective tax rate that we are looking for. This is the effective tax rate applied to all of their earnings. We need to know the effective tax rate that applies to the amount they wish to use for their retirement plan. Let's say that they want to take $4000 of their income and use it for this purpose.  and our married couple has an adjusted gross income (AGI) of