### Author Topic: Anyone know an engineer/math wiz?  (Read 4158 times)

• Walrus Stache
• Posts: 5200
##### Anyone know an engineer/math wiz?
« on: July 01, 2013, 11:57:32 AM »
Forgive me if this has already been posted, but I'm wondering about the math behind using a 401k vs a taxable account.  If I am at a marginal tax rate of 25%, and take my money out in 10 yrs  at which time my marginal tax rate is 10%, is there a way to compute my ROI from the tax status, all other things being equal?

#### mpbaker22

• Handlebar Stache
• Posts: 1095
##### Re: Anyone know an engineer/math wiz?
« Reply #1 on: July 01, 2013, 01:47:04 PM »
Forgive me if this has already been posted, but I'm wondering about the math behind using a 401k vs a taxable account.  If I am at a marginal tax rate of 25%, and take my money out in 10 yrs  at which time my marginal tax rate is 10%, is there a way to compute my ROI from the tax status, all other things being equal?

What is your question?  Do you want to know the capital gains savings of a taxable vs. a 401K or the income tax savings of a traditional vs. roth?
If you buy and hold for ten years, you'll pay 25% tax before buying, and capital gains of 15% (or w/e the rate is then) when you sell.
If you put it in a traditional 401K, you avoid tax now, don't pay the capital gains, and pay 10% at withdrawal.  However, if you aren't 59.5, you pay another 10% penalty.
In a roth IRA, you pay 25% now and no capital gains and no penalty, if you only withdraw contributions.

#### pom

• Bristles
• Posts: 288
• Location: Paris, France
##### Re: Anyone know an engineer/math wiz?
« Reply #2 on: July 01, 2013, 03:06:04 PM »
Sure you can see the equation as such

(1+return on assets)^10 = (0.9/0.75)(1+investment rate)^10
Return on assets= (1+investment rate)(1.0184) - 1

Which is about 1,9% higher than the investment rate.

#### velocistar237

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##### Re: Anyone know an engineer/math wiz?
« Reply #3 on: July 01, 2013, 03:15:21 PM »
You can punch the numbers into a spreadsheet and use IRR() if you're just looking at a particular case.

My understanding is that the difference between tax-deferred and regular investment is 1) current vs. future tax rates and 2) capital gains tax. If you buy and hold, then you only pay capital gains once, otherwise you generate churn which reduces your gains.

Why not just use net present value? Something like this?

Earnings*(1-FutureTaxRate)*(1+RealReturn)^Years
vs.
Earnings*(1-CurrentTaxRate)*[((1+RealReturn)^Years-1)*(1-CapitalGainsRate)+1]

So I suppose for comparison the two real rates of return would be
((1-FutureTaxRate)/(1-CurrentTaxRate)*(1+RealReturn)^Years)^(1/Years)-1
vs.
([((1+RealReturn)^Years-1)*(1-CapitalGainsRate)+1])^(1/Years)-1

Those might simplify.

#### mpbaker22

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##### Re: Anyone know an engineer/math wiz?
« Reply #4 on: July 01, 2013, 06:31:52 PM »
My understanding is that the difference between tax-deferred and regular investment is 1) current vs. future tax rates and 2) capital gains tax. If you buy and hold, then you only pay capital gains once, otherwise you generate churn which reduces your gains.

Theoretically, "church" won't reduce your gains.  If you start with \$1000 and buy and hold to an end point of \$2000, you pay taxes on \$1000 of gains.

The biggest threat to this type of investment would be losing a certain amount and selling, then re-gaining beyond the statute of limitations.  But I would say that's rather unlikely.

#### velocistar237

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##### Re: Anyone know an engineer/math wiz?
« Reply #5 on: July 01, 2013, 07:16:01 PM »
For individual stocks, churn can add up as trading fees eat into your profits. Obviously, this happens more with small portfolios and frequent trades. Even if you have no trading fees, if you buy/sell every year and pay capital gains tax on your earnings, then that taxed portion goes away forever and will not create any more returns, whereas leaving it invested allows it to compound until you finally do pay taxes. Over 10 years, this would create an annualized difference of about 0.2%/year.

"Church"? Church will reduce your gains, to the tune of 10% per year.

• Stubble
• Posts: 216
• Location: Baltimore
##### Re: Anyone know an engineer/math wiz?
« Reply #6 on: July 01, 2013, 08:17:54 PM »
And don't forget dividends, a significant fraction of the total return for equities. You'll have these every year even if you hold and they will be taxed.

#### mpbaker22

• Handlebar Stache
• Posts: 1095
##### Re: Anyone know an engineer/math wiz?
« Reply #7 on: July 02, 2013, 07:44:01 AM »
For individual stocks, churn can add up as trading fees eat into your profits. Obviously, this happens more with small portfolios and frequent trades. Even if you have no trading fees, if you buy/sell every year and pay capital gains tax on your earnings, then that taxed portion goes away forever and will not create any more returns, whereas leaving it invested allows it to compound until you finally do pay taxes. Over 10 years, this would create an annualized difference of about 0.2%/year.

"Church"? Church will reduce your gains, to the tune of 10% per year.

Ah yes, I was thinking of the formulas combating the common mis-belief that paying taxes later rather than now is better for compounding.  Paying taxes later is only better if your marginal tax rate on that income is lower.

Thanks for the correction.

#### velocistar237

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##### Re: Anyone know an engineer/math wiz?
« Reply #8 on: July 02, 2013, 10:52:44 AM »
Ah yes, I was thinking of the formulas combating the common mis-belief that paying taxes later rather than now is better for compounding.  Paying taxes later is only better if your marginal tax rate on that income is lower.

You caught it before. For a taxable account, paying taxes later rather than every year is slightly better in the long run, even with an unchanging tax rate. I've attached a spreadsheet in case I've made a mistake. Apologies if Excel botches the .ods.

#### grantmeaname

• Walrus Stache
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• Cast me away from yesterday's things
##### Re: Anyone know an engineer/math wiz?
« Reply #9 on: July 02, 2013, 11:28:07 AM »
Yay Libreoffice!