"My company offers an after-tax 401k. Should I contribute to it?"

I've spent a lot of time over the past few weeks educating myself on "after-tax 401(k)s." These are different than, and sub-optimal to traditional pre-tax 401(k)'s and IRAs as well as Roth 401k(s) and IRAs, which you should max out before considering contributions to an after-tax 401(k). To be clear: the topic of this post is "after-tax, non-Roth" 401(k)s.
The basic 401(k) salary deferral limit of $18,000 applies to pretax and Roth contributions. But there is a total contribution limit of $52,000 annually, which includes the $18,000 pretax or Roth contribution limit, employer matching contributions (which will probably not be more than $10,000), plus after-tax non-Roth contributions.[2016 numbers]. This means that more than $25,000 of after-tax 401k space may be available to you.
Unlike a Roth 401k, in which earnings are never taxed, earnings in an after-tax 401k will eventually be taxed at withdrawal at your marginal income tax rate. This will likely be higher than your long-term capital gains tax rate. For this reason many people would rather just invest in normal taxable accounts.
However, if you can quickly roll over your after-tax 401k contributions to a Roth IRA, any earnings it makes there are completely tax free. The IRS published an announcement in Sep 2014 (Source) that makes it easy to roll the contributions portion of an after-tax 401k into a Roth IRA, and the earnings portion in a traditional IRA.
For people that work at companies that allow in-service distributions (even with a short waiting period), or people that are planning to leave their company within a few years, an after-tax 401k may be an easy way to get a lot more money into a Roth IRA where it will continue to grow completely tax free, while only a small amount (the earnings) needs to be rolled over to a traditional IRA
See the following images which better explain the scenario:
I can take in-service distributions, or I will leave my company within a few yearsIn this situation, the after-tax 401(k) didn't accumulate much taxable "earnings" before I could roll it over into a Roth IRA where it will grow completely tax freeImage 1 
I will remain at my company for a long time still, and can't take in service distributionsIn this situation, my money spent a lot of time in the after-tax 401(k) gaining a substantial amount of earnings. When I withdraw the earnings (or roll them over to a traditional IRA and later withdraw it), I will owe my marginal income tax rate on it.Image 2 
Even if you cannot do in-service distributions and are not leaving your company very soon, there may be some people that would still benefit from after-tax 401(k)s instead of taxable investing. These are people that will have an extremely low marginal income tax rate in retirement (e.g. the Mad Fientist). Trading a 10% income tax instead of 0% LTCG tax on a big chunk of earnings may be a price worth paying to get a some more money into a Roth IRA above the annual contribution limit.


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