### The 401(k) match

I hardly know anything about 401(k) plans because the company I work for doesn't offer them (or any other type of retirement package). But one of the things you hear bantered around the PF world is the "company match." This is typically a scheme where the company will match 50% or 100% of the money you contribute up to a certain total amount of your salary (usually 6% or 3% respectively). People are advised to max out their matched amounts as the first step to retirement savings, followed by an IRA or more unmatched 401(k).

Anyway, what effect does a 50% match have on your savings? It's fairly substantial in the beginning, certainly, but what is the long-term effect? From what I've read, typical 401(k) plans have limited investment choices. Usually you can choose from a mix of mutual funds, perhaps ETFs, and money market funds, but it seems rather limited. Over a 30 year period, how much better do you have to be at investing to overcome the 50% match?

Let's look at how you calculate something like that.

The basic formula for simple compound interest is x = y * (1+z)^t, where t is time, z is your interest rate, y is the initial investment amount, and x is the total at the end.

Well with a 50% match, any y that you invest automatically becomes 1.5 * y. Let's assume that we want x, y, and t to be constant, and we'll see what happens to z. We'll use z for the first interest rate (in the matching 401(k) version) and z' for the second interest rate. Since we're looking for equality, our equation is

1.5 * y * (1+z)^t = y * (1+z')^t

Doing some math...

1.5 * (1+z)^t = (1+z')^t

ln(1.5) + t*ln(1+z) = t * ln(1+z')

z' = e^((ln(1.5) + t*ln(1+z))/t)) - 1

A little complicated. Let's plug in some numbers so we can get a feel for what this equation means. In a short timespan of 2 years (t = 2), if the matched fund returns 10% annually (z = 0.1), our little independent investor would need an annualized return of 34.7% to overcome his disadvantage in not having a match. Over a 10 year period, he would have to achieve 14.5%. Over a 30 year period, he would need 11.5%, a bit easier to achieve.

What does this mean? Well, confirming the obvious, having a company match is a significant advantage in terms of how well your money will grow. However, if you fancy yourself a better than average investor, your 401(k) doesn't provide enough freedom to invest how you like, AND you have a fairly long time horizon, then it may be worthwhile to *ignore the company match* and make a go of it on your own. As you get closer to retirement age, you would stop your own investments and start taking advantage of the company match. The crossover point could be determined by substituting guessed values for z and z' (based on historical performance perhaps, though remember that's no guarantee of future performance!) and then solving for t.

## 5 comments:

I have a great company match, and I'm horrible at investing...good thing I'm maxing out the match, huh? :) Good post!

That's a very interesting analysis. In my case, though, my match is 100%, not 50%. Also, 401(k)'s are offering more and more investing options. We have about 200 funds to chose from. Granted, most of them are far too expensive to take seriously, but it's enough to find some good choices.

I plan to stay at my job long enough to have the whole 401(k) with a match thing, but not for too long. I'll invest in some kind of "freedom fund" (which they offer) or an S&P 500 index-type if I can find one.

In the end, though, I can roll it all over into an IRA upon leaving. The good part of this? My options won't be limited anymore. I'm partial to Vanguard, so I'll probably invest it there.

For a person with limited 401(k) options, therefore, one consideration might be how long they're going to stay there. If it's not long and the program's not dreadful, then getting the match would almost definitely be worth it because they could roll it into the IRA soon anyway and do what they wanted. But they'd have the extra money.

That's definitely a good point to consider, Mrs. Micah. But at the same time, what is the vesting schedule for your 401(k)? In a lot of plans, I think if you leave before a year or two, you could lose all of the matched contributions.

I think you'd have to have particularly bad investment choices to be that much worse than other external funds. In this case, I'd say that a bird in the hand is worth more than two in the bush.

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