### Author Topic: The exact math behind using 401k loan to pay down debt  (Read 24416 times)

#### beltim

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• Posts: 2964
##### Re: The exact math behind using 401k loan to pay down debt
« Reply #100 on: May 22, 2015, 03:21:53 PM »
Your critique of my formula is correct.  I double counted the tax costs. Since the cost of eliminating the mortgage debt was already accounted for by using the net mortgage rate, it shouldn't have been counted again when paying back the 401k loan.
Exactly!

Quote
The formula should be:
Profit=Loan Balance*[Mortgage rate * (1-tax rate)] - (Loan Balance * Stable Value Rate) - PV of future tax pmt on 401k Interest
Profit = 100k*[.046125*(.75)] - (100k*.02)- 404
Profit= \$1,064.75

Or to make it even more eloquent:
Profit = (Loan Balance*aftertax mortgage rate) - (opportunity cost on investments) - PV of future tax pmt on 401k interest
Profit = (100k*.03459)-2,000-404
Profit= \$1,064.75

Agreed?

I hope so because the 3-day weekend is calling my name!

BTW, thanks for engaging in this banter.  I enjoyed it.

I agree with the formula.  I think you're overstating the PV of the future tax payment on the 401k interest – it could be that much, but it could also be much less.  I don't know if you care at this point, but that's the only remaining disagreement.

I enjoyed this too.  Frustrating at times, but overall quite enjoyable.

#### BBub

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##### Re: The exact math behind using 401k loan to pay down debt
« Reply #101 on: May 22, 2015, 04:03:13 PM »
Sure, figuring the future tax pmt involves a bit of guesswork & there's no way we could really know without a time machine.  But it can at least be estimated & I'd say its worth plugging in - even if it has to be projected using assumptions.  After all, the entire reason any of these formulas or models exist is to help us nerds plan for an uncertain future.

#### beltim

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• Posts: 2964
##### Re: The exact math behind using 401k loan to pay down debt
« Reply #102 on: May 22, 2015, 04:44:16 PM »
Sure, figuring the future tax pmt involves a bit of guesswork & there's no way we could really know without a time machine.  But it can at least be estimated & I'd say its worth plugging in - even if it has to be projected using assumptions.  After all, the entire reason any of these formulas or models exist is to help us nerds plan for an uncertain future.

I agree.  The modification I'd propose would include an offsetting amount for capital gains & dividends taxes.  So instead of subtracting (PV of future tax payments from 401k loan interest), I'd subtract:
(PV of future tax payments from 401k loan interest) - (PV of future tax payments of invested sum outside 401k)

For a \$4000 401k loan interest amount, assuming no short term capital gains, this can be approximated for short time periods by:
(n) * (average dividends * dividend tax rate) + \$4000 * [(1 + r)^n - 1] * marginal tax rate in retirement
where r = annual rate of return
n = number of years
Using current dividends would understate the amount over 20 years because dividends will increase substantially, but this can be fixed using an average:
If we assume a constant dividend yield = 2%, then average dividends can be approximated (but understated) as:
average dividends = dividend yield * \$4000 * (1+r)^(n/2)

Plugging in numbers, we get:
dividend tax rate =  15%
r = 9% (remember this is nominal returns)
n = 20
marginal tax rate in retirement = 15%
then
20* (.15 * .02 * \$4000 * (1.09)^10) + 4000 * (1.09^20 - 1) * .15
=568 + 2762
= 3330

Which isn't comparable because it's not a PV and also because you didn't assume any growth in the excess amount added to the 401k.  The first concern can be addressed by converting the \$3330 to a present value, which I'm going to ballpark (±10%) at \$2200.  The second concern can be addressed by re-figuring the PV of the future tax payment of the 401k by adding growth.  So:
PV of future tax payment = discounted (marginal tax rate in retirement * \$4000 * (1 + r)^n]
gives discounted(.15 * 22417) = 3362.
A future value of \$3362 discounts to ~ \$2242.

Now the number can be compared, so -(2242 - 2200) becomes -42.

The assumptions—or someone's individual tax situation—can make that value significantly different, though, so you can plug in your own numbers to see.

#### BBub

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##### Re: The exact math behind using 401k loan to pay down debt
« Reply #103 on: May 23, 2015, 10:16:45 AM »
LOL i'm kind of glad we get to keep going.

I didnt account for cap gains, interest, etc because the gain on the \$4k will be taxed in either situation: taxable or qualified.  So the gains are a wash - could be better or worse, depending on how the money is invested.  However, the \$4k principal would only be subject to back-end taxation in the 401k.  It would not be subject to taxation ever again if placed in a taxable account.

Furthermore, since we're talking about 2% gain, a case could be made for the OP buying a 10yr treasury and never being tax again on any of the \$4k plus gain if he went the taxable route.  In that situation, to get the 401k PV of future tax liability we'd have to account for the \$4k plus gains.

Make sense?

#### beltim

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• Posts: 2964
##### Re: The exact math behind using 401k loan to pay down debt
« Reply #104 on: May 23, 2015, 12:06:02 PM »
LOL i'm kind of glad we get to keep going.

I didnt account for cap gains, interest, etc because the gain on the \$4k will be taxed in either situation: taxable or qualified.  So the gains are a wash - could be better or worse, depending on how the money is invested.  However, the \$4k principal would only be subject to back-end taxation in the 401k.  It would not be subject to taxation ever again if placed in a taxable account.

Yes, the gains will be taxed either way - but the rate on those gains will be different, as will the number of times they are taxed.  In many cases, the gain from deferring taxes is more important than the difference between ordinary income or capital gains taxes.  That's why people used to use non-deductible IRAs instead of taxable accounts before a backdoor Roth was legal.

Quote
Furthermore, since we're talking about 2% gain, a case could be made for the OP buying a 10yr treasury and never being tax again on any of the \$4k plus gain if he went the taxable route.  In that situation, to get the 401k PV of future tax liability we'd have to account for the \$4k plus gains.

Make sense?

No, because treasuries are taxable.  Do you munis?  If so, yes, that's true - but buying municipal bonds in an IRA when you have stocks in a taxable account would be idiotic.

#### BBub

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##### Re: The exact math behind using 401k loan to pay down debt
« Reply #105 on: May 23, 2015, 04:09:12 PM »
LOL i'm kind of glad we get to keep going.

I didnt account for cap gains, interest, etc because the gain on the \$4k will be taxed in either situation: taxable or qualified.  So the gains are a wash - could be better or worse, depending on how the money is invested.  However, the \$4k principal would only be subject to back-end taxation in the 401k.  It would not be subject to taxation ever again if placed in a taxable account.

Yes, the gains will be taxed either way - but the rate on those gains will be different, as will the number of times they are taxed.  In many cases, the gain from deferring taxes is more important than the difference between ordinary income or capital gains taxes.  That's why people used to use non-deductible IRAs instead of taxable accounts before a backdoor Roth was legal.

Sure.  But in many cases, the deferred taxes would be higher than a tax efficient investment held outside a qualified account.  So, a wash.  Neither side could win on this because a sound argument can be made either way & there are far too many variables.
Quote
Furthermore, since we're talking about 2% gain, a case could be made for the OP buying a 10yr treasury and never being tax again on any of the \$4k plus gain if he went the taxable route.  In that situation, to get the 401k PV of future tax liability we'd have to account for the \$4k plus gains.

Make sense?

No, because treasuries are taxable.  Do you munis?  If so, yes, that's true - but buying municipal bonds in an IRA when you have stocks in a taxable account would be idiotic.
[/quote]

Ok, sorry, say munis.  Of course you wouldnt hold munis in a qualified acct.  But since we're assuming the stable value he is holding pays 2%,  I'd make the case he could find an investment with virtually no risk outside of a 401k to get 2%.  Like a AAA rated, insured tax free muni.

#### beltim

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• Posts: 2964
##### Re: The exact math behind using 401k loan to pay down debt
« Reply #106 on: May 23, 2015, 06:54:42 PM »
LOL i'm kind of glad we get to keep going.

I didnt account for cap gains, interest, etc because the gain on the \$4k will be taxed in either situation: taxable or qualified.  So the gains are a wash - could be better or worse, depending on how the money is invested.  However, the \$4k principal would only be subject to back-end taxation in the 401k.  It would not be subject to taxation ever again if placed in a taxable account.

Yes, the gains will be taxed either way - but the rate on those gains will be different, as will the number of times they are taxed.  In many cases, the gain from deferring taxes is more important than the difference between ordinary income or capital gains taxes.  That's why people used to use non-deductible IRAs instead of taxable accounts before a backdoor Roth was legal.

Sure.  But in many cases, the deferred taxes would be higher than a tax efficient investment held outside a qualified account.  So, a wash.  Neither side could win on this because a sound argument can be made either way & there are far too many variables.

Yes, this is why in the absence of specific tax information, I'd approximate the tax effect of putting extra after-tax money in a 401k as 0.

#### BBub

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• Age: 35
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##### Re: The exact math behind using 401k loan to pay down debt
« Reply #107 on: May 23, 2015, 08:15:21 PM »
I'd approximate the extra tax on the gains at zero.  The principal, however, is subject to taxation upon withdrawal  in the 401k scenario and is never subject to taxation if held outside of a qualified acct.  Therefore, that difference in tax treatment should be accounted for.

The only scenario for which it wouldn't be relevant is if the OP's income tax rate is 0% in retirement, a highly unlikely scenario given that he has rental income, presumably other investment income, social security, etc.  Only in this instance would it make sense to omit the PV of future tax pmt from the formula.

#### beltim

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• Posts: 2964
##### Re: The exact math behind using 401k loan to pay down debt
« Reply #108 on: May 26, 2015, 01:05:46 PM »
I'd approximate the extra tax on the gains at zero.  The principal, however, is subject to taxation upon withdrawal  in the 401k scenario and is never subject to taxation if held outside of a qualified acct.  Therefore, that difference in tax treatment should be accounted for.

If you're including that, you should include the extra tax on the gains, since my several examples show that they're of similar size to the taxation on the principal.