Summary

If you expect to retire early or transition from a high-earning job to a low-income job, then contributing to a 401k could be a good idea in order to avoid capital-gains taxes and reduce your income while you're in a higher marginal bracket. If you expect to earn a lot and donate a lot indefinitely, then contributing more than what your employer will match to a 401k probably still doesn't make sense. The magnitude of the importance of this argument is limited, especially if you don't earn much, so consider this an "advanced topic" in personal finance.

Caveats

The following post is speculation about a topic on which I'm not an expert, so don't treat what I say as established wisdom. Indeed, I wrote this post in order to collect feedback from friends on whether my analysis is correct and whether there are factors I've neglected. Also, alas, this analysis only applies in the US, although maybe similar ideas would be relevant elsewhere.

Why 401k?

I won't explain the full details of a 401k plan here because it's well-enough documented on Wikipedia and elsewhere. As I understand it, the advantage of a 401k is that you can avoid capital-gains tax on the income that your investments earn, so that when you withdraw the money after age 59.5, you only have to pay the original income tax, not additional capital-gains tax.

To explain more precisely: say you have X dollars of income now. Let your current income-tax rate be t_0. For example, t_0 = 0.25 means you're in the 25% bracket. If you take the X dollars as income now and pay tax on it, you have (1-t_0)X left over to invest. With that money, you buy a stock with an annual geometric-average return of r (e.g., r = 0.08) over N years (e.g., N = 20). After N years, your investment is worth (1-t_0)X(1+r)^N. However, before you can use the money to defray your costs of living, you need to pay capital-gains tax. Say your capital-gains rate is c_N = 0.18 (that is, 18%) at year N. (Right now the capital-gains rate is 15%, but unless Congress changes things, the rate is set to increase to 18% for 5-year long-term capital gains in 2013.) Then you have to pay c_N(1-t_0)X[(1+r)^N-1] of capital-gains tax, and the amount you have left over is

In contrast, say you instead put your X dollars of income into a tax-deferred 401k. Let N be big enough that you can withdraw at age 59.5 without penalties. All X dollars of your contribution grow tax-free, so after N years, the fund has X(1+r)^N dollars. When you take the money out, you have to pay income tax at some rate t_N. The amount you have left is

Let's take the ratio of equation (1) to equation (2):

For simplicity, say t_0 = t_N. Then we have

If N = 0, this equals 1, so it doesn't matter if you use the 401k or not; you have no capital gains. If N > 0, this ratio is always less than 1, which means you save on capital-gains taxes by using the 401k. When N is large, the capital gains on your investment swamp the principal, and the ratio becomes about 1-c_N, which says that you pay c_N of capital-gains taxes if you invest without the 401k but don't pay them if you use the 401k.

Why not 401k?

Until now, I personally have contributed only 6% of my yearly income to my 401k. The reason I contributed at all was that my employer matches every $1 I donate with an additional $0.50 free, but only up to 6% of contributions on my part. However, I could in fact contribute about $17K before hitting deferral limits. So why didn't I?

Money in your 401k is locked until you turn 59.5, so I figured that if I contributed more, I would be preventing myself from having the option to use that money for important projects in the shorter term. If the returns on animal-suffering meme-spreading are higher than those on mutual funds, then it would be a shame to lock away the money for all those years just to save 18% on capital-gains taxes. Indeed, in the next 34 years before I turn 59.5, the world may look very different. Maybe financial institutions as we know them won't exist any longer. I would put the chance of this around 18% or maybe higher.

Withdrawal penalties

However, one thing that I neglected is that money in a 401k isn't totally locked. You can make early withdrawals if you're willing to pay a 10% fee on top of income taxes from the distributions. If that's all you have to pay, and you don't have to pay anything else for capital gains, then it seems it could actually be more advantageous to withdraw early from a 401k than to invest on your own.

Here's the intuition. If you withdraw early, you pay 10% of everything that you put in: principal and capital gains. If you instead invest on your own, you pay 18% but only on the capital gains. After a long enough time, when the capital gains swamp the principal, it'll be advantageous to use the 401k approach (up to your annual tax-deferral limit). Is this right?

In particular, let p = 0.1 be the penalty for withdrawing early. Say you withdraw at year M. I think the 10% penalty is paid separately on the pre-tax amount you withdraw from the 401k, so equation (2) becomes

At what year M does it become advantageous to use the 401k strategy? Set equation (5) equal to equation (1).

Say r = 0.08, t_0 = 0.25, t_M = 0.25, c_M = 0.18, and p = 0.1; this gives M = 17.5. So if you plan to need living expenses 17.5 or more years down the road, it appears advantageous to put money into the 401k and then break out.

How the tradeoff varies with M

The algebra is getting messy, so I put together an Excel workbook to compute the ratio of wealth using the no-401k strategy to that using the 401k strategy as a function of M. Below are sample snapshots for different r. (I tried to make these images in the post directly, but they were too big to fit.)

r=0.05

r=0.08

r=0.12

What if you have significantly lower income later?

Say you have a lower-earning job in the future such that your marginal tax bracket drops to 15% (t_M = 0.15 even though t_0 = 0.25 still). In this case, it's always advantageous to use the 401k strategy, because even though you pay a 10% penalty, 15% + 10% = 25%, so you pay no more than you would have otherwise. This ignores the savings due to not paying capital-gains tax, so if we include those savings, the benefit is even higher. At the 15% marginal income tax bracket, your capital-gains rate would be 8% for five-year capital gains starting in 2013. Even with that low capital-gains rate, you get the results shown below.

15% bracket

What if you plan to keep earning a lot indefinitely?

If you plan to keep earning a lot indefinitely, then additional 401k contributions don't make sense, because you can keep using your current income to fund your costs of living (no need to dip into the 401k and incur the additional penalty), and you can donate all of your investments to avoid capital-gains taxes entirely (i.e., c_M = 0). You also won't expect your future income-tax rate to be lower than your current rate. In this case, the graph looks like the following.

Earn and donate indefinitely

If you expect to retire early or transition from a high-earning job to a low-income job, then contributing to a 401k could be a good idea in order to avoid capital-gains taxes and reduce your income while you're in a higher marginal bracket. If you expect to earn a lot and donate a lot indefinitely, then contributing more than what your employer will match to a 401k probably still doesn't make sense. The magnitude of the importance of this argument is limited, especially if you don't earn much, so consider this an "advanced topic" in personal finance.

Caveats

The following post is speculation about a topic on which I'm not an expert, so don't treat what I say as established wisdom. Indeed, I wrote this post in order to collect feedback from friends on whether my analysis is correct and whether there are factors I've neglected. Also, alas, this analysis only applies in the US, although maybe similar ideas would be relevant elsewhere.

Why 401k?

I won't explain the full details of a 401k plan here because it's well-enough documented on Wikipedia and elsewhere. As I understand it, the advantage of a 401k is that you can avoid capital-gains tax on the income that your investments earn, so that when you withdraw the money after age 59.5, you only have to pay the original income tax, not additional capital-gains tax.

To explain more precisely: say you have X dollars of income now. Let your current income-tax rate be t_0. For example, t_0 = 0.25 means you're in the 25% bracket. If you take the X dollars as income now and pay tax on it, you have (1-t_0)X left over to invest. With that money, you buy a stock with an annual geometric-average return of r (e.g., r = 0.08) over N years (e.g., N = 20). After N years, your investment is worth (1-t_0)X(1+r)^N. However, before you can use the money to defray your costs of living, you need to pay capital-gains tax. Say your capital-gains rate is c_N = 0.18 (that is, 18%) at year N. (Right now the capital-gains rate is 15%, but unless Congress changes things, the rate is set to increase to 18% for 5-year long-term capital gains in 2013.) Then you have to pay c_N(1-t_0)X[(1+r)^N-1] of capital-gains tax, and the amount you have left over is

Code: Select all

`(1-t_0)X(1+r)^N - c_N(1-t_0)X[(1+r)^N-1] = (1-c_N)(1-t_0)X(1+r)^N + c_N(1-t_0)X. (1)`

In contrast, say you instead put your X dollars of income into a tax-deferred 401k. Let N be big enough that you can withdraw at age 59.5 without penalties. All X dollars of your contribution grow tax-free, so after N years, the fund has X(1+r)^N dollars. When you take the money out, you have to pay income tax at some rate t_N. The amount you have left is

Code: Select all

`(1-t_N)X(1+r)^N. (2)`

Let's take the ratio of equation (1) to equation (2):

Code: Select all

`[ (1-c_N)(1-t_0)X(1+r)^N + c_N(1-t_0)X ] / [ (1-t_N)X(1+r)^N ]. (3)`

For simplicity, say t_0 = t_N. Then we have

Code: Select all

`1 - c_N + c_N/(1+r)^N. (4)`

If N = 0, this equals 1, so it doesn't matter if you use the 401k or not; you have no capital gains. If N > 0, this ratio is always less than 1, which means you save on capital-gains taxes by using the 401k. When N is large, the capital gains on your investment swamp the principal, and the ratio becomes about 1-c_N, which says that you pay c_N of capital-gains taxes if you invest without the 401k but don't pay them if you use the 401k.

Why not 401k?

Until now, I personally have contributed only 6% of my yearly income to my 401k. The reason I contributed at all was that my employer matches every $1 I donate with an additional $0.50 free, but only up to 6% of contributions on my part. However, I could in fact contribute about $17K before hitting deferral limits. So why didn't I?

Money in your 401k is locked until you turn 59.5, so I figured that if I contributed more, I would be preventing myself from having the option to use that money for important projects in the shorter term. If the returns on animal-suffering meme-spreading are higher than those on mutual funds, then it would be a shame to lock away the money for all those years just to save 18% on capital-gains taxes. Indeed, in the next 34 years before I turn 59.5, the world may look very different. Maybe financial institutions as we know them won't exist any longer. I would put the chance of this around 18% or maybe higher.

Withdrawal penalties

However, one thing that I neglected is that money in a 401k isn't totally locked. You can make early withdrawals if you're willing to pay a 10% fee on top of income taxes from the distributions. If that's all you have to pay, and you don't have to pay anything else for capital gains, then it seems it could actually be more advantageous to withdraw early from a 401k than to invest on your own.

Here's the intuition. If you withdraw early, you pay 10% of everything that you put in: principal and capital gains. If you instead invest on your own, you pay 18% but only on the capital gains. After a long enough time, when the capital gains swamp the principal, it'll be advantageous to use the 401k approach (up to your annual tax-deferral limit). Is this right?

In particular, let p = 0.1 be the penalty for withdrawing early. Say you withdraw at year M. I think the 10% penalty is paid separately on the pre-tax amount you withdraw from the 401k, so equation (2) becomes

Code: Select all

`(1-t_M-p)X(1+r)^M. (5)`

At what year M does it become advantageous to use the 401k strategy? Set equation (5) equal to equation (1).

Code: Select all

`(1-t_M-p)X(1+r)^M = (1-c_M)(1-t_0)X(1+r)^M + c_M(1-t_0)X`

(1-t_M-p) = (1-c_M)(1-t_0) + c_M(1-t_0)/(1+r)^M.

Say r = 0.08, t_0 = 0.25, t_M = 0.25, c_M = 0.18, and p = 0.1; this gives M = 17.5. So if you plan to need living expenses 17.5 or more years down the road, it appears advantageous to put money into the 401k and then break out.

How the tradeoff varies with M

The algebra is getting messy, so I put together an Excel workbook to compute the ratio of wealth using the no-401k strategy to that using the 401k strategy as a function of M. Below are sample snapshots for different r. (I tried to make these images in the post directly, but they were too big to fit.)

r=0.05

r=0.08

r=0.12

What if you have significantly lower income later?

Say you have a lower-earning job in the future such that your marginal tax bracket drops to 15% (t_M = 0.15 even though t_0 = 0.25 still). In this case, it's always advantageous to use the 401k strategy, because even though you pay a 10% penalty, 15% + 10% = 25%, so you pay no more than you would have otherwise. This ignores the savings due to not paying capital-gains tax, so if we include those savings, the benefit is even higher. At the 15% marginal income tax bracket, your capital-gains rate would be 8% for five-year capital gains starting in 2013. Even with that low capital-gains rate, you get the results shown below.

15% bracket

What if you plan to keep earning a lot indefinitely?

If you plan to keep earning a lot indefinitely, then additional 401k contributions don't make sense, because you can keep using your current income to fund your costs of living (no need to dip into the 401k and incur the additional penalty), and you can donate all of your investments to avoid capital-gains taxes entirely (i.e., c_M = 0). You also won't expect your future income-tax rate to be lower than your current rate. In this case, the graph looks like the following.

Earn and donate indefinitely