Comments on: Calculating Post-Tax 401(K) Contribution Cost

By: Chief Family Officer

Chief Family Officer — Thu, 13 Dec 2007 04:18:23 +0000

Thanks, Jim! This was timely for me because I was just thinking about increasing my 401(k) contribution and debating the amount with myself

By: jim

jim — Wed, 12 Dec 2007 22:03:56 +0000

I thought double discounting it looked a little wrong… thanks for clearing that up.

By: Dret

Dret — Wed, 12 Dec 2007 21:29:35 +0000

Kurt, Dave,

You were both correct. My mistake. $2007$113.12 is always $2007$113.12 at anytime.

By: Kurt

Kurt — Wed, 12 Dec 2007 19:06:16 +0000

“Instead you pay it ($2007$113.12) in 2047 which is equivalent to paying
$2007$23.56 in 2007.”
No. You pay $2007$113.12 in 2047 ($2047$543.11). The logic is utterly, completely, 100%, wrong. Open up a spreadsheet and see how much money you’d have to set aside to today to pay the tax bill in 2047 if it grew at 4% a year. It’s not $23.56.

By: Lord

Lord — Wed, 12 Dec 2007 18:28:32 +0000

As Kurt notes, the income tax only becomes relevant if the tax rate changes between now and then in comparing retirement accounts. There is a benefit from tax deferral by not having to pay capital taxes on the earnings that make them superior to a taxable account though. For your example, the net return would be (1+8%)/(1+8%*(1-15%)), using a 15% capital rate fully taxed each year, or 1.1% a year. This benefit can be cut in half by using capital gains deferral in a taxable account, but not eliminated.

By: Dave

Dave — Wed, 12 Dec 2007 17:59:13 +0000

Kurt’s math is correct. The final “net value” of both types of accounts are exactly the same, if the tax rate in 2007 and 2047 are the same. From a purely mathematical exercise perspecitive, the only thing that matters is your future tax bracket in dermining which type of account is better. If you will be in a higher tax bracket in the future, a Roth is better, because you will pay a lower tax now. If you be in a lower tax bracket in the future, a 401(k) is better because you will pay a lower tax in the future. (Note, if you can read the future, please give me a call)

There are other things to take into consideration when deciding between the types of accounts though, such as employer match, contribution limits ($15,500 vs. $5000), and other future income sources (weather they are tax free or not). For example, if you have a pretty good idea that you’ll be in a lower tax bracket in the future and have $15,000 to invest, it probably makes sense to invest it all in a 401(k). If you only have $4,000 to invest and you are pretty sure you’ll be in a higher tax bracket when you retire, it makes sense to put it into a Roth. If you are like the rest of us and don’t really know where exactly you’ll be in the future, it probably make sense to put some money into both, just to help diversify your future taxable earnings.

By: Dret

Dret — Wed, 12 Dec 2007 17:33:21 +0000

Kurt,

Let’s use a notation to explicitly convey the time-value meaning of
the money: $2007$1000 means $1000 in 2007 dollar, and similarly,
$2047$1000 means $1000 in 2047 dollar.

Blue was saying that
while $2047$543.11 = $2007$113.12 is more than 4 times of $2007$25.00,
you don’t have to pay it in 2007.

Instead you pay it ($2007$113.12) in 2047 which is equivalent to paying
$2007$23.56 in 2007.

By: Kurt

Kurt — Wed, 12 Dec 2007 17:31:30 +0000

“There is simply little chance I’ll be taxed less in 40 years than I am now. So, Roth it is.”
The issue then becomes does congress honor the tax-free distribution from Roths or do they tax them? If the budget crunch is as bad as you say, that would be a tempting golden goose.

By: Kurt

Kurt — Wed, 12 Dec 2007 17:29:56 +0000

It isn’t necessarily a math error. It’s a logic error. For instance, if I said: You agree to pay me $100 in 10 years, but that’s only $10 in today’s money! And $10 in 10 years is only $1 in today’s money! So you’re only really paying me $1.

You don’t discount the figure twice (as he does above):

That’s $543.11 in 2047 dollars, which is only $113.12 in 2007 dollars. That’s $113.12 you don’t pay today, you pay that in 40 years… the time value of money makes $113.12 in 40 years worth only $23.56 today.

See?

By: Dret

Dret — Wed, 12 Dec 2007 17:24:22 +0000

I double checked your math and found nothing wrong. I don’t know the subject of your friend’s debate. If it is about whether or not to contribute to 401k, then I certainly agree with you: contribute to 401k or other retirement accounts like IRA, taking full advantage of any matching.

But if the debate is between Roth vs Traditional accounts, then I prefer to recommend Roth for both 401k and IRA. I truly truly believe that my generation (I’m 30-ish) will have to pay for the current national debt ($9 trillions and growing) while many of those that incurred and are incurring it will be laying in comfort 6 feet under.

There is simply little chance I’ll be taxed less in 40 years than I am now. So, Roth it is.

By: Kurt

Kurt — Wed, 12 Dec 2007 16:01:02 +0000

Heheh, oops. In the post above, the figures reflect a 4% investment growth. I’ve updated the google spreadsheet however.

By: Kurt

Kurt — Wed, 12 Dec 2007 15:59:46 +0000

Whoah whoah whoah. What are you doing? You’re discounting the figure twice? Re-read that paragraph and you’re saying $543.11 is $113.12 in today’s dollars, but $113.12 in 2047 dollars is just $23.56 today. That’s logical nonsense.

Here’s the real math: you have $1,000 today under the above return assumptions (inflation is meaningless). If you dump it into a Roth IRA, you avoid $250 in taxes, but have to pay $1,200 in taxes after 40 years, but have total cash at that time of $3,600. If you put it into a Roth IRA, you pay $250 today (and invest the $750) and have the same $3,600 in 40 years, but pay no taxes in 40 years (no better or worse than the 401(k)). In a taxable account, you pay $250 in taxes now and 25% of the annual income of the portfolio each year, every year for 40 years. The end result is $2,447 in cash.

As you can see, the value of a 401(k) isn’t in the tax deduction if you expect to be in the same (or higher) tax bracket when you retire. You’ll have the same after-tax final-period cash regardless of whether or not you pay taxes on the front end or the back end, if your average tax rate doesn’t change.

The real value is in the tax-deferral. If you run the numbers, you can either pay the taxes on the front end (Roth IRA) or on the backend (401(k)/IRA) but either way, by not paying taxes along the way, you benefit versus a taxable account.

Here’s the data I used: http://spreadsheets.google.com/ccc?key=pKtugvMWCNdTT23RnaQ0uKw&hl=en