Author Topic: The exact math behind using 401k loan to pay down debt  (Read 24407 times)

beltim

  • Magnum Stache
  • ******
  • Posts: 2964
Re: The exact math behind using 401k loan to pay down debt
« Reply #50 on: May 21, 2015, 12:44:17 PM »
Can we pause the show while I make popcorn and go to the bathroom?

Can you get me a drink while you're up?

Sure! I've been meaning to try out my new Kuerig Kold;)

Thanks! I had to google Kuerig Kold, but now I'm excited!

BBub

  • Pencil Stache
  • ****
  • Posts: 774
  • Age: 35
  • Location: Deep South
Re: The exact math behind using 401k loan to pay down debt
« Reply #51 on: May 21, 2015, 12:49:37 PM »


As for this, the math is exactly the same as the current situation.  Whether Al repays a 401k loan or elects to contribute to a non-deductible IRA, the math is exactly the same.

And you "explicitly said:"
Quote
There isn't a situation where being subject to double taxation at ordinary rates is good.

My example directly proves that your statement is false.  My statement - that:
Quote
Yes, the extra $4k in your example is taxable at ordinary income tax rates upon withdrawal.  I said that in my response.  Whether that's bad, good, or neutral depends on your individual tax circumstances.
still holds true.  There are examples where deferring taxes is worth paying ordinary income tax, and there are examples where not deferring taxes is better.

1. No, it's not directly applicable to the OP because the OP is not buying a 5% bond on loan from a 401k. Al's a totally separate scenario that's entirely made up.

2. No, your example assumes that a nondeductible IRA is optimal for Al.  Under current tax laws Al could use a backdoor conversion to get that money into a roth, which would be most optimal.




BBub

  • Pencil Stache
  • ****
  • Posts: 774
  • Age: 35
  • Location: Deep South
Re: The exact math behind using 401k loan to pay down debt
« Reply #52 on: May 21, 2015, 12:51:40 PM »
I stopped reading after Seattle and Belt correctly esplained the analysis the third time each so I may have missed this discussion, but OP you should compare your after tax rate on the mortgage (I assume they are deductible/offsetting rental income) to the expected return on the foregone investment return on the principle you are withdrawing from 401(k).  Almost exactly the same as decision to pay down mortgage or invest as one of these smart cookies has already stated.

You should read the thread.  I'm not going to restate the whole argument, but you're simplifying the matter by failing to account for the double taxation on the 401k loan interest.

beltim

  • Magnum Stache
  • ******
  • Posts: 2964
Re: The exact math behind using 401k loan to pay down debt
« Reply #53 on: May 21, 2015, 12:51:59 PM »
For the true nerds, this is from the Federal Reserve on the lack of "double taxation" of 401k loans:

From Appendix 1 of http://www.federalreserve.gov/pubs/feds/2008/200842/200842pap.pdf

Edit: from the text of the paper:
Quote
Loan interest payments, on the other hand, can indeed be considered double-taxed under
traditional consumption tax principles—since interest payments are like new contributions,
they should be made with pre-tax dollars and then taxed upon withdrawal. In practice,
however, the double-taxation of loan interest relative to a consumption tax is offset by the
break borrowers get on the timing of their tax payments: recall that rather than paying
taxes on loan proceeds when they are distributed (i.e., consumed), borrowers pay the taxes
gradually over the following five years as they repay the loan with after-tax dollars. The
time value of these delayed tax payments offsets the double taxation of interest—perfectly
so, if the discount rate is the pre-tax rate of return; only partially if the discount rate is
lower.
An algebraic illustration of the taxation of 401(k) loans is provided in Appendix 1.

The bolded part is particularly interesting and cromulent to the discussion at hand.
« Last Edit: May 21, 2015, 01:04:21 PM by beltim »

beltim

  • Magnum Stache
  • ******
  • Posts: 2964
Re: The exact math behind using 401k loan to pay down debt
« Reply #54 on: May 21, 2015, 12:54:19 PM »


As for this, the math is exactly the same as the current situation.  Whether Al repays a 401k loan or elects to contribute to a non-deductible IRA, the math is exactly the same.

And you "explicitly said:"
Quote
There isn't a situation where being subject to double taxation at ordinary rates is good.

My example directly proves that your statement is false.  My statement - that:
Quote
Yes, the extra $4k in your example is taxable at ordinary income tax rates upon withdrawal.  I said that in my response.  Whether that's bad, good, or neutral depends on your individual tax circumstances.
still holds true.  There are examples where deferring taxes is worth paying ordinary income tax, and there are examples where not deferring taxes is better.

1. No, it's not directly applicable to the OP because the OP is not buying a 5% bond on loan from a 401k. Al's a totally separate scenario that's entirely made up.

2. No, your example assumes that a nondeductible IRA is optimal for Al.  Under current tax laws Al could use a backdoor conversion to get that money into a roth, which would be most optimal.

I'm not saying this is the math for the OP.  I'm saying that a nondeductible IRA can be better than a taxable account.  There are plenty of reasons that even under current tax laws this would be true, such as if Al already had a large (deductible) traditional IRA balance.

BBub

  • Pencil Stache
  • ****
  • Posts: 774
  • Age: 35
  • Location: Deep South
Re: The exact math behind using 401k loan to pay down debt
« Reply #55 on: May 21, 2015, 01:11:56 PM »
For the true nerds, this is from the Federal Reserve on the lack of "double taxation" of 401k loans:

From Appendix 1 of http://www.federalreserve.gov/pubs/feds/2008/200842/200842pap.pdf

Did you read the report?

Page 6: "Loan interest payments, on the other hand, can indeed be considered double-taxed under traditional consumption tax principles—since interest payments are like new contributions,
they should be made with pre-tax dollars and then taxed upon withdrawal."

The next paragraph describes how, in the real world applications the double taxation is usually offset due to the timing of repayments.  Not eliminated - offset.  Their formula to illustrate the actual taxation vs consumption tax is listed in appendix 1 on page 26.

Also, this paper is written to encourage consumers to pay down high interest credit cards with 401k loans.  Well, gee, there's an idea. 

I'm not saying it is always bad to take a 401k loan to pay off debt.  If OP was considering pulling his 401k to pay off a 25% credit card this discussion wouldn't have happened.  I'd have replied with a quick "hell yeah" & gone about my day.  But the OP is paying off tax deductible interest with nondeductible interest, then paying tax on that amount again in retirement.  That's not such a clear cut case, IMO.

beltim

  • Magnum Stache
  • ******
  • Posts: 2964
Re: The exact math behind using 401k loan to pay down debt
« Reply #56 on: May 21, 2015, 01:15:55 PM »
For the true nerds, this is from the Federal Reserve on the lack of "double taxation" of 401k loans:

From Appendix 1 of http://www.federalreserve.gov/pubs/feds/2008/200842/200842pap.pdf

Did you read the report?

Page 6: "Loan interest payments, on the other hand, can indeed be considered double-taxed under traditional consumption tax principles—since interest payments are like new contributions,
they should be made with pre-tax dollars and then taxed upon withdrawal."

The next paragraph describes how, in the real world applications the double taxation is usually offset due to the timing of repayments.  Not eliminated - offset.  Their formula to illustrate the actual taxation vs consumption tax is listed in appendix 1 on page 26.

Are you serious?  I literally quoted that exact paragraph.

BBub

  • Pencil Stache
  • ****
  • Posts: 774
  • Age: 35
  • Location: Deep South
Re: The exact math behind using 401k loan to pay down debt
« Reply #57 on: May 21, 2015, 01:21:34 PM »
Sorry - you went back in and edited it while I was typing my response.  As you can see, your initial post that I quoted from did not contain the paragraph addition.

Anyway, to go down that rabbit trail.  Here's your bolded sentence:

 "The time value of these delayed tax payments offsets the double taxation of interest—perfectly
so, if the discount rate is the pre-tax rate of return; only partially if the discount rate is
lower."


Today's discount rate is .25%.  Do you think this discount rate is higher or lower than the average pre-tax rate of return in a 401k - even a stable value fund like the OP's?  Because if it's lower then the double taxation is only partially offset.

BBub

  • Pencil Stache
  • ****
  • Posts: 774
  • Age: 35
  • Location: Deep South
Re: The exact math behind using 401k loan to pay down debt
« Reply #58 on: May 21, 2015, 01:26:03 PM »
Look, this is getting ridiculous.  The interest on a 401k loan is double taxed.  It just is, plain and simple.  This cost should be considered, among other factors, when evaluating whether or not to take out a 401k loan for any reason.  Especially in borderline cases where the loan is being used to pay down another tax-deductible loan.  Would you agree with that?

beltim

  • Magnum Stache
  • ******
  • Posts: 2964
Re: The exact math behind using 401k loan to pay down debt
« Reply #59 on: May 21, 2015, 02:00:52 PM »
Look, this is getting ridiculous.  The interest on a 401k loan is double taxed.  It just is, plain and simple.  This cost should be considered, among other factors, when evaluating whether or not to take out a 401k loan for any reason.  Especially in borderline cases where the loan is being used to pay down another tax-deductible loan.  Would you agree with that?

I agree that any cost of the 401k loan should be considered.  My issue hasn't been that - my issue is that you haven't been calculating that cost correctly, and denying that it's possible that there's even potentially a benefit.

BBub

  • Pencil Stache
  • ****
  • Posts: 774
  • Age: 35
  • Location: Deep South
Re: The exact math behind using 401k loan to pay down debt
« Reply #60 on: May 21, 2015, 02:10:42 PM »
I didn't mean to deny that there's possibly a benefit, and I'm sorry if I came accross that way.  There are definitely cases when it makes sense - no question.  This one seems borderline at best, but I wouldn't know without getting the exact figures from OP.

What calculation would you propose, if not the one I explained a bit earlier?  Here's my response to your issue with my formula.


So, the correct formula would be

Loan Balance*[4.625*(1-t) - (r)-(4.125*(t)^n], then run again for n+1, +2, and so on for the number of years on the 401k loan.

t = tax rate
r = rate of return on investments, or stable value
n = tims

Assuming a tax rate of 25% and a stable value of return, OP would gain 0.44% with this maneuver - as expected, slightly worse than my initial handwave of 0.5%. However, this figure still doesn't take into account the back end tax on the $4k interest.

No, this equation makes no sense.  Specifically, the (4.125*(t)^n term makes no sense.  That term would be the amount of taxes paid each year on the money you put into the 401k in excess of your original contributions (i.e. the "interest" on the 401k loan).  But that money is taxed this year regardless of what you use it for.

That money would not be taxed this year if used to pay the original investment loan interest, which is tax deductible.  For this reason I included it in the formula as an expense applicable to the OP's situation.

« Last Edit: May 21, 2015, 02:13:28 PM by BBub »

theoverlook

  • Bristles
  • ***
  • Posts: 283
Re: The exact math behind using 401k loan to pay down debt
« Reply #61 on: May 21, 2015, 02:20:53 PM »
I've been having trouble following the thread, with all the discussion of double taxation, etc.

But BBub, you do recognize his savings will be much higher than 0.5% right?  He's paying 4.625% right now, and after taking out the 401k loan the only actual cost to him will be his taxes - both those accrued due to not having the deductible loan interest and those paid upon withdrawing the money from his 401k later.  But even double taxes are not going to add up to the full amount of the loan interest.

Ie, he pays 4.625% now, but his net cost of funds would be - say he's in the 25% bracket - (4.625%*.25) + (4.125%*.25) = 2.19%, almost half of which is paid upon withdrawal from the 401k so not until much much later.  His immediate cost would just be the 4.625%*.25 = 1.16%.

As you said, it's a borderline case, it depends entirely upon the expected return of his stable value fund.

beltim

  • Magnum Stache
  • ******
  • Posts: 2964
Re: The exact math behind using 401k loan to pay down debt
« Reply #62 on: May 21, 2015, 02:34:19 PM »
What calculation would you propose, if not the one I explained a bit earlier? 

In broad terms I think you have the right idea.  That is, something like:
profit = loan balance * [ (mortgage interest benefit) - (return of alternative investment)] ± (cost/benefit of additional 401k contribution)

My previous example shows that additional, nondeductible 401k contributions can be a benefit or cost depending on the circumstances.  In this particular case, rmendpara gave a good conservative estimate of mortgage interest benefit of 4.24% (it's conservative because it assumes no other itemized deductions, but at a minimum the OP will have state income or sales taxes to deduct as well).  The return on the alternative investment is simply the return of the stable value fund - my guess would be between 2 and 3 percent. 

beltim

  • Magnum Stache
  • ******
  • Posts: 2964
Re: The exact math behind using 401k loan to pay down debt
« Reply #63 on: May 21, 2015, 02:42:14 PM »
That money would not be taxed this year if used to pay the original investment loan interest, which is tax deductible.  For this reason I included it in the formula as an expense applicable to the OP's situation.

Are you saying that if the OP didn't take out a 401k loan, instead of using after-tax money to pay back the 401k loan, they would instead pay down the mortgage?  If so, the calculation of that part of the benefit would be:
(cost/benefit of additional 401k contribution) = loan balance * (401k interest rate) * (effective after-tax interest rate of mortgage)

Using numbers of:
loan balance = 100K
401k interest rate = 4.125%
after-tax interest rate of mortgage = 4.24%
then (cost/benefit of additional 401k contribution) = 100k * .04125 * .0424 = $174.9

and the overall equation would be:

profit = loan balance * [ (mortgage interest benefit) - (return of alternative investment)] ± (cost/benefit of additional 401k contribution)
guestimating a return of stable value fund of 2.0%, then
profit = 100K * ( .0424 - .020 ) - 174.9
profit = $2065 per year

Gone Fishing

  • Magnum Stache
  • ******
  • Posts: 2814
  • So Close went fishing on April 1, 2016
    • Journal
Re: The exact math behind using 401k loan to pay down debt
« Reply #64 on: May 21, 2015, 02:44:39 PM »
Can we pause the show while I make popcorn and go to the bathroom?

Can you get me a drink while you're up?

Sure! I've been meaning to try out my new Kuerig Kold;)

Thanks! I had to google Kuerig Kold, but now I'm excited!

Don't feel bad, I had never heard of one until today...

http://forum.mrmoneymustache.com/antimustachian-wall-of-shame-and-comedy/make-your-own-tiny-soda-for-$1-29/?topicseen

BBub

  • Pencil Stache
  • ****
  • Posts: 774
  • Age: 35
  • Location: Deep South
Re: The exact math behind using 401k loan to pay down debt
« Reply #65 on: May 21, 2015, 02:46:47 PM »
I've been having trouble following the thread, with all the discussion of double taxation, etc.

But BBub, you do recognize his savings will be much higher than 0.5% right?  He's paying 4.625% right now, and after taking out the 401k loan the only actual cost to him will be his taxes - both those accrued due to not having the deductible loan interest and those paid upon withdrawing the money from his 401k later.  But even double taxes are not going to add up to the full amount of the loan interest.

Ie, he pays 4.625% now, but his net cost of funds would be - say he's in the 25% bracket - (4.625%*.25) + (4.125%*.25) = 2.19%, almost half of which is paid upon withdrawal from the 401k so not until much much later.  His immediate cost would just be the 4.625%*.25 = 1.16%.

As you said, it's a borderline case, it depends entirely upon the expected return of his stable value fund.

Yes I get it, but I'd suggest a few minor tweaks to your analysis above..

The 4.625% he is currently paying is tax deductible, so his effective rate is 3.46%.  That makes things much tighter.

Also consider that he will be taxed on the amount of his 401k interest again when he makes withdrawals in retirement.  Does this make sense?


brooklynguy

  • Handlebar Stache
  • *****
  • Posts: 2204
  • Age: 40
Re: The exact math behind using 401k loan to pay down debt
« Reply #66 on: May 22, 2015, 08:29:06 AM »
Don't tell me this thread is dead already?  That would be too anti-climactic.  I went to bed thinking this nerd-off had morphed into a nerd-fight-to-the-death, only to wake up this morning and find that it ended not with a bang, but a whimper.  You guys better get back in here and pick up where you left off -- if this thread doesn't end with at least one bloody nerd-corpse on the amphitheater floor, I'm going to demand my money back.  With (non-double-taxed) interest.

forummm

  • Walrus Stache
  • *******
  • Posts: 7389
  • Senior Mustachian
Re: The exact math behind using 401k loan to pay down debt
« Reply #67 on: May 22, 2015, 08:41:30 AM »
Yeah, by this point yesterday, there'd been at least 3 keyboards severely stressed from all the pounding. Pick up the pace, nerdstars! Let us summon our nerd armies and TYPE!

beltim

  • Magnum Stache
  • ******
  • Posts: 2964
Re: The exact math behind using 401k loan to pay down debt
« Reply #68 on: May 22, 2015, 08:46:38 AM »
Yeah, by this point yesterday, there'd been at least 3 keyboards severely stressed from all the pounding. Pick up the pace, nerdstars! Let us summon our nerd armies and TYPE!

I think my last two posts were a pretty good volley.  If someone wants to respond they should.

For an overall conclusion, I still like my post about the benefit vs. liquidity.

forummm

  • Walrus Stache
  • *******
  • Posts: 7389
  • Senior Mustachian
Re: The exact math behind using 401k loan to pay down debt
« Reply #69 on: May 22, 2015, 09:05:23 AM »
Yeah, by this point yesterday, there'd been at least 3 keyboards severely stressed from all the pounding. Pick up the pace, nerdstars! Let us summon our nerd armies and TYPE!

I think my last two posts were a pretty good volley.  If someone wants to respond they should.

For an overall conclusion, I still like my post about the benefit vs. liquidity.

Yes, this was a great conclusion. Perfectly stated. Amirite?

forummm

  • Walrus Stache
  • *******
  • Posts: 7389
  • Senior Mustachian
Re: The exact math behind using 401k loan to pay down debt
« Reply #70 on: May 22, 2015, 09:06:22 AM »
Yeah, by this point yesterday, there'd been at least 3 keyboards severely stressed from all the pounding. Pick up the pace, nerdstars! Let us summon our nerd armies and TYPE!

I think my last two posts were a pretty good volley.  If someone wants to respond they should.

For an overall conclusion, I still like my post about the benefit vs. liquidity.

Yes, this was a great conclusion. Perfectly stated. Amirite?

What? Are you kidding me? It was so wrong! Hey, let's all discuss!

BBub

  • Pencil Stache
  • ****
  • Posts: 774
  • Age: 35
  • Location: Deep South
Re: The exact math behind using 401k loan to pay down debt
« Reply #71 on: May 22, 2015, 09:30:03 AM »
I don't understand that last formula Beltim.   Can you explain the cost/benefit formula:

loan balance * (401k interest rate) * (effective aftertax interest rate of mortgage)

Doesn't make sense to me, but I would love to understand why you calculated it this way.  Honestly.



zephyr911

  • Magnum Stache
  • ******
  • Posts: 3624
  • Age: 42
  • Location: Northern Alabama
  • I'm just happy to be here. \m/ ^_^ \m/
    • Pinhook Development LLC
Re: The exact math behind using 401k loan to pay down debt
« Reply #72 on: May 22, 2015, 09:48:56 AM »
Even 4.625% is really cheap for an investment loan. I'm assuming your rental ROI is well above that, so unless your near-term goals require de-leveraging for risk-based reasons, why not pull the 401(k) loan for a down payment on another rental?
I mean, as long as we're doing all the comparisons based on the returns of various options, that's where I'd go with it....

beltim

  • Magnum Stache
  • ******
  • Posts: 2964
Re: The exact math behind using 401k loan to pay down debt
« Reply #73 on: May 22, 2015, 10:12:22 AM »
I don't understand that last formula Beltim.   Can you explain the cost/benefit formula:

loan balance * (401k interest rate) * (effective aftertax interest rate of mortgage)

Doesn't make sense to me, but I would love to understand why you calculated it this way.  Honestly.

Yeah, I'll give it a shot.  This is my attempt at calculating the cost of using funds to repay the 401k loan instead of using those funds to pay back the mortgage (in the absence of a 401k loan).  It's what I thought you were suggesting as an alternative use of funds, but I could easily be mistaken.  As to the math, [loan balance * (401 interest rate)] just give the amount of money that has to be paid back from other funds this year.  The benefit of using that money would be the amount multiplied by the effective after-tax interest rate on the mortgage (you used 3.46% assuming it's all tax-deductible, but it could be as high as the interest rate itself depending on other deductions).

That make sense?

Dicey

  • Senior Mustachian
  • ********
  • Posts: 13708
  • Age: 62
  • Location: NorCal
Re: The exact math behind using 401k loan to pay down debt
« Reply #74 on: May 22, 2015, 10:18:40 AM »
It sounds like I should take the loan and pay down debt instead of keeping it in a stable value fund.

NOOOOOOOOOOOO! I hope it's not too late, but there's another major consideration that I haven't seen mentioned, despite the nerd-off. If you separate from your employer, how long do you have to pay back the loan? What if you get a great offer and you can't take it because the market is in a down position and you can't pay the loan back? You must have this information before you take one more step!

I consider borrowing from my 401k my worst financial mistake. Did I lose money? No, the real estate I bought with the money doubled in value in less than four years. Did I miss out on market gains? Not to the extent that I made a metric shit-ton of non-taxable money on the RE deal and most likely wouldn't be FIRE now. So why? Because I felt like an indentured servant for every single second of the time that I was not in a position to leave my job. Hated every single minute of it, which is why I killed myself to pay it back in nine months. If you value your freedom, you must consider this factor in the decision to borrow from your 401k.

beltim

  • Magnum Stache
  • ******
  • Posts: 2964
Re: The exact math behind using 401k loan to pay down debt
« Reply #75 on: May 22, 2015, 10:22:52 AM »
It sounds like I should take the loan and pay down debt instead of keeping it in a stable value fund.

NOOOOOOOOOOOO! I hope it's not too late, but there's another major consideration that I haven't seen mentioned, despite the nerd-off. If you separate from your employer, how long do you have to pay back the loan? What if you get a great offer and you can't take it because the market is in a down position and you can't pay the loan back? You must have this information before you take one more step!

I consider borrowing from my 401k my worst financial mistake. Did I lose money? No, the real estate I bought with the money doubled in value in less than four years. Did I miss out on market gains? Not to the extent that I made a metric shit-ton of non-taxable money on the RE deal and most likely wouldn't be FIRE now. So why? Because I felt like an indentured servant for every single second of the time that I was not in a position to leave my job. Hated every single minute of it, which is why I killed myself to pay it back in nine months. If you value your freedom, you must consider this factor in the decision to borrow from your 401k.

Being one of the principals in the nerd off, I completely agree with you.  That said, I made this point at least twice before.  Of course, they probably got lost in the sea of my other posts.

forummm

  • Walrus Stache
  • *******
  • Posts: 7389
  • Senior Mustachian
Re: The exact math behind using 401k loan to pay down debt
« Reply #76 on: May 22, 2015, 10:54:46 AM »
It sounds like I should take the loan and pay down debt instead of keeping it in a stable value fund.

NOOOOOOOOOOOO! I hope it's not too late, but there's another major consideration that I haven't seen mentioned, despite the nerd-off. If you separate from your employer, how long do you have to pay back the loan? What if you get a great offer and you can't take it because the market is in a down position and you can't pay the loan back? You must have this information before you take one more step!

I consider borrowing from my 401k my worst financial mistake. Did I lose money? No, the real estate I bought with the money doubled in value in less than four years. Did I miss out on market gains? Not to the extent that I made a metric shit-ton of non-taxable money on the RE deal and most likely wouldn't be FIRE now. So why? Because I felt like an indentured servant for every single second of the time that I was not in a position to leave my job. Hated every single minute of it, which is why I killed myself to pay it back in nine months. If you value your freedom, you must consider this factor in the decision to borrow from your 401k.

I also borrowed from my 401k once. I also bought investment real estate with it. I also wouldn't do it again, but for different reasons. I don't like investing in real estate, it had a big opportunity cost for me (see below), I hated having my cash flow disrupted (stopping me from investing elsewhere and making me more vulnerable to an emergency), I hated having the money out of my account, there was some risk of my salary stopping temporarily (I'd have to make the loan payments anyway, on top of not having income), the concern of double taxation, etc.

All the Nerd-off math aside, it doesn't seem worth it to me. For a big savings (like buying my personal residence without a mortgage because they don't make loans that small--true story, and what I should have done instead of buying the investment real estate with the loan) I would do it. For a small amount of arbitrage, it doesn't seem worth it.

BBub

  • Pencil Stache
  • ****
  • Posts: 774
  • Age: 35
  • Location: Deep South
Re: The exact math behind using 401k loan to pay down debt
« Reply #77 on: May 22, 2015, 11:26:57 AM »
I don't understand that last formula Beltim.   Can you explain the cost/benefit formula:

loan balance * (401k interest rate) * (effective aftertax interest rate of mortgage)

Doesn't make sense to me, but I would love to understand why you calculated it this way.  Honestly.

Yeah, I'll give it a shot.  This is my attempt at calculating the cost of using funds to repay the 401k loan instead of using those funds to pay back the mortgage (in the absence of a 401k loan).  It's what I thought you were suggesting as an alternative use of funds, but I could easily be mistaken.  As to the math, [loan balance * (401 interest rate)] just give the amount of money that has to be paid back from other funds this year.  The benefit of using that money would be the amount multiplied by the effective after-tax interest rate on the mortgage (you used 3.46% assuming it's all tax-deductible, but it could be as high as the interest rate itself depending on other deductions).

That make sense?

Not sure.  Here's what I would do.  Like you, first figure up the Present net cost or benefit. Then determine profit.

Benefit is getting rid of the effective mortgage interest rate. 

Present Benefit = $100k*.0346 = $3,460

The present cost would be the taxes paid on the 401k interest (a cost the OP previously avoided due to the tax deductibility of mortgage). 

Present Cost = $100k*(.04125*.25) = $1,031.25

net benefit = $3,460-1,031 = $2,429 Net Benefit

profit = benefit - opportunity cost - PV of future tax liability on the 401k interest.

2,429 - (100k*.02) = $429

Finally, you'd need to subtract the PV of the future tax liability on the $4k interest that will be paid back into the 401k.  Let's assume his future tax rate will be 15%.  So, that's $600 owed ($4k*.15) in, say 20 years.  The present value of $600 owed in 20 yrs, assuming a 2% ror = $404. (the formula is complicated, but you can use a financial calculator.  FV=600, PMT=0, i=2, n=20, solve for PV)

$429-404 = $25

So, given these assumptions the OP would by my calcs come out $25 ahead.  Assuming the loan fee is probably at least that amount he'd probably break even.

The assumptions I used were:
Loan amount: 100k
Mortgage rate: 4.6125%
401k Int Rate: 4.125%
Stable Value Return: 2%
Current Tax Rate: 25%
Retirement Tax Rate: 15%
Years to Retirement: 20

Obviously modifying any of these assumptions will affect the outcome.  But the methodology, IMO, seems sound.  Any issues with this?  Am I missing something?  I have a degree in Finance, love numbers, and solve equations in my free time.  That doesn't mean I'm not dead wrong sometimes - I am.  But the methodology above seems clearly to be the best way to solve this problem.

beltim

  • Magnum Stache
  • ******
  • Posts: 2964
Re: The exact math behind using 401k loan to pay down debt
« Reply #78 on: May 22, 2015, 11:30:26 AM »

Present Cost = $100k*(.04125*.25) = $1,031.25

Yeah, this makes no sense at all.  That money is going to be taxed this year regardless, so it doesn't enter the calculation at all.

zephyr911

  • Magnum Stache
  • ******
  • Posts: 3624
  • Age: 42
  • Location: Northern Alabama
  • I'm just happy to be here. \m/ ^_^ \m/
    • Pinhook Development LLC
Re: The exact math behind using 401k loan to pay down debt
« Reply #79 on: May 22, 2015, 11:37:20 AM »
It sounds like I should take the loan and pay down debt instead of keeping it in a stable value fund.

NOOOOOOOOOOOO! I hope it's not too late, but there's another major consideration that I haven't seen mentioned, despite the nerd-off. If you separate from your employer, how long do you have to pay back the loan? What if you get a great offer and you can't take it because the market is in a down position and you can't pay the loan back? You must have this information before you take one more step!

I consider borrowing from my 401k my worst financial mistake. Did I lose money? No, the real estate I bought with the money doubled in value in less than four years. Did I miss out on market gains? Not to the extent that I made a metric shit-ton of non-taxable money on the RE deal and most likely wouldn't be FIRE now. So why? Because I felt like an indentured servant for every single second of the time that I was not in a position to leave my job. Hated every single minute of it, which is why I killed myself to pay it back in nine months. If you value your freedom, you must consider this factor in the decision to borrow from your 401k.
I once borrowed from a 401k to pay off high-interest debt (way above this example). Soon after, my position was terminated on short notice. I was insourced by the feds so I kept my seat, but I still had to pay thousands back very quickly. I also took a pay cut. It SUCKED. All my cash was tied up in investments, and I think I ended up using some kind of balance transfer deal to avoid getting totally fucked on interest. It did cost me a bit regardless.

I have two active TSP loans now for at least 15k total. Both of them funded high-yielding real estate investments, so I can't regret them from a long-term financial standpoint, but the feeling you describe above is very real. I'm about to dramatically accelerate my payoff efforts for that exact reason.

In fact, I meant to reamortize this week and this would be a good time to go do that. Thanks for the reminder. ;)

BBub

  • Pencil Stache
  • ****
  • Posts: 774
  • Age: 35
  • Location: Deep South
Re: The exact math behind using 401k loan to pay down debt
« Reply #80 on: May 22, 2015, 12:07:36 PM »

Present Cost = $100k*(.04125*.25) = $1,031.25

Yeah, this makes no sense at all.  That money is going to be taxed this year regardless, so it doesn't enter the calculation at all.

No, the OP is currently not being taxed due to the deduction on the mortgage interest.  Once he gives up that tax deductible mortgage it becomes taxed.

If OP was paying off a credit card, or buying counters or whatever - you would be correct and that money would be taxed regardless.  However, the OP is paying off a tax deductible interest with the money.  So, now he will incur taxes that he previously wasn't.
« Last Edit: May 22, 2015, 12:10:51 PM by BBub »

beltim

  • Magnum Stache
  • ******
  • Posts: 2964
Re: The exact math behind using 401k loan to pay down debt
« Reply #81 on: May 22, 2015, 12:53:05 PM »

Present Cost = $100k*(.04125*.25) = $1,031.25

Yeah, this makes no sense at all.  That money is going to be taxed this year regardless, so it doesn't enter the calculation at all.

No, the OP is currently not being taxed due to the deduction on the mortgage interest.  Once he gives up that tax deductible mortgage it becomes taxed.

If OP was paying off a credit card, or buying counters or whatever - you would be correct and that money would be taxed regardless.  However, the OP is paying off a tax deductible interest with the money.  So, now he will incur taxes that he previously wasn't.

This is giving me a headache.  It looks to me like you're calculating the opportunity cost of using the money to pack back the 401k loan instead of just using it to pay the mortgage directly in the absence of a 401k loan.  Is that right?

If so, then you're missing a step.  The benefit of paying back a mortgage is not equal to the amount that you pay back.  The value of paying back a mortgage is the amount that you pay back, multiplied by your interest rate.

So that opportunity cost should be what I said before:
loan balance * (401k interest rate) * (effective after-tax interest rate of mortgage)

BBub

  • Pencil Stache
  • ****
  • Posts: 774
  • Age: 35
  • Location: Deep South
Re: The exact math behind using 401k loan to pay down debt
« Reply #82 on: May 22, 2015, 01:05:22 PM »
Let's say he was going to refinance a 10% mortgage with a 5% 401k loan.  By your formula his opportunity cost would be $100k*.05*.10= $500

wtf? That has no meaning at all.  It's just a bunch of numbers multiplied together for no reason.
« Last Edit: May 22, 2015, 01:35:50 PM by BBub »

beltim

  • Magnum Stache
  • ******
  • Posts: 2964
Re: The exact math behind using 401k loan to pay down debt
« Reply #83 on: May 22, 2015, 01:38:26 PM »
That makes no sense.  Let's say he was going to refinance a 10% mortgage with a 5% 401k loan.  By your formula his opportunity cost would be $100k*.05*.10= $500

wtf? That has no meaning at all.  It's just a bunch of numbers multiplied together for no reason.

$500 would be the opportunity cost of the 401k interest, yes.

If someone pays down $5k mortgage at 10%, the annual benefit to that person is $5k * .1 = $500. 

By your formula, paying back $5k of mortgage would be a benefit of $5k * (1 - marginal tax rate).  At a 25% interest rate, your formula says that paying back $5k on a mortgage is a net benefit of $3750.  That makes no sense.  It is obviously wrong.

BBub

  • Pencil Stache
  • ****
  • Posts: 774
  • Age: 35
  • Location: Deep South
Re: The exact math behind using 401k loan to pay down debt
« Reply #84 on: May 22, 2015, 02:00:33 PM »
Ok, you just applied your formula to a paying down $5k on a mortgage.  We are talking about paying $100k on a mortgage.

Ignore the taxes entirely.

1. Pay off a $100k mortgage at 10%.  Annual Benefit is $10,000.  Is it not?

2. Now refinance the $100k at 5%.  Annual Cost is $5,000.  Is it not?

3. Net benefit is $5,000.  Is it not?

I'll stop here.  Is there any problem with the above logic?

frugalnacho

  • Magnum Stache
  • ******
  • Posts: 4122
  • Age: 37
  • Location: Madison Heights, Michigan
Re: The exact math behind using 401k loan to pay down debt
« Reply #85 on: May 22, 2015, 02:01:01 PM »
That makes no sense.  Let's say he was going to refinance a 10% mortgage with a 5% 401k loan.  By your formula his opportunity cost would be $100k*.05*.10= $500

wtf? That has no meaning at all.  It's just a bunch of numbers multiplied together for no reason.

$500 would be the opportunity cost of the 401k interest, yes.

If someone pays down $5k mortgage at 10%, the annual benefit to that person is $5k * .1 = $500. 

By your formula, paying back $5k of mortgage would be a benefit of $5k * (1 - marginal tax rate).  At a 25% interest rate, your formula says that paying back $5k on a mortgage is a net benefit of $3750.  That makes no sense.  It is obviously wrong.

I think you guys are getting mixed up. If I understand correctly beltim is saying using 5k from 401k to pay mortgage at 10% saves them $500 in interest.  I agree with that.  I think bbub seems to be agreeing that you will save $500, but that $500 now becomes taxable income (because you can't deduct mortgage interest if you don't pay any).  So if you do that, when you file your tax forms you will have $500 less in deductions, effectively making you have $500 more to pay your marginal tax rate. 

BBub

  • Pencil Stache
  • ****
  • Posts: 774
  • Age: 35
  • Location: Deep South
Re: The exact math behind using 401k loan to pay down debt
« Reply #86 on: May 22, 2015, 02:07:57 PM »
Ok, you just applied your formula to a paying down $5k on a mortgage.  We are talking about paying $100k on a mortgage.

Ignore the taxes entirely.

1. Pay off a $100k mortgage at 10%.  Annual Benefit is $10,000.  Is it not?

2. Now refinance the $100k at 5%.  Annual Cost is $5,000.  Is it not?

3. Net benefit is $5,000.  Is it not?

I'll stop here.  Is there any problem with the above logic?


Ok, I'll pretend there isn't a problem and continue working through this, accounting for the taxes and 401k loanthis time..

Since the original 10% was deductible, we are losing out on $2,500 by refinancing.  $10k-2,500 = 7,500 in benefit.

Since the 5% 401k loan is being paid to ourself, now we are only losing out on the taxes.  The interest rate itself is inconsequential, but the tax applied to it is a true cost.

Benefit of the transaction simply = $7,500 for the net interest saved.

Now to get profit, we'd take  $7,500-stable value rate on the 100k - PV of future tax payment on the 401k interest.

« Last Edit: May 22, 2015, 02:13:15 PM by BBub »

BBub

  • Pencil Stache
  • ****
  • Posts: 774
  • Age: 35
  • Location: Deep South
Re: The exact math behind using 401k loan to pay down debt
« Reply #87 on: May 22, 2015, 02:09:14 PM »
That makes no sense.  Let's say he was going to refinance a 10% mortgage with a 5% 401k loan.  By your formula his opportunity cost would be $100k*.05*.10= $500

wtf? That has no meaning at all.  It's just a bunch of numbers multiplied together for no reason.

$500 would be the opportunity cost of the 401k interest, yes.

If someone pays down $5k mortgage at 10%, the annual benefit to that person is $5k * .1 = $500. 

By your formula, paying back $5k of mortgage would be a benefit of $5k * (1 - marginal tax rate).  At a 25% interest rate, your formula says that paying back $5k on a mortgage is a net benefit of $3750.  That makes no sense.  It is obviously wrong.

I think you guys are getting mixed up. If I understand correctly beltim is saying using 5k from 401k to pay mortgage at 10% saves them $500 in interest.  I agree with that.  I think bbub seems to be agreeing that you will save $500, but that $500 now becomes taxable income (because you can't deduct mortgage interest if you don't pay any).  So if you do that, when you file your tax forms you will have $500 less in deductions, effectively making you have $500 more to pay your marginal tax rate.

I agree with that too.  But using Beltim's formula, he is saying that using $100k to pay a mortage at 10% saves them $500.  That is incorrect.  See my above post.

beltim

  • Magnum Stache
  • ******
  • Posts: 2964
Re: The exact math behind using 401k loan to pay down debt
« Reply #88 on: May 22, 2015, 02:10:44 PM »
Ok, you just applied your formula to a paying down $5k on a mortgage.  We are talking about paying $100k on a mortgage.

Ignore the taxes entirely.

1. Pay off a $100k mortgage at 10%.  Annual Benefit is $10,000.  Is it not?

2. Now refinance the $100k at 5%.  Annual Cost is $5,000.  Is it not?

3. Net benefit is $5,000.  Is it not?

I'll stop here.  Is there any problem with the above logic?

No problems here.

BBub

  • Pencil Stache
  • ****
  • Posts: 774
  • Age: 35
  • Location: Deep South
Re: The exact math behind using 401k loan to pay down debt
« Reply #89 on: May 22, 2015, 02:11:20 PM »
Ok awesome.  Go back up a few posts.  Then let me know what you think.

beltim

  • Magnum Stache
  • ******
  • Posts: 2964
Re: The exact math behind using 401k loan to pay down debt
« Reply #90 on: May 22, 2015, 02:12:23 PM »
That makes no sense.  Let's say he was going to refinance a 10% mortgage with a 5% 401k loan.  By your formula his opportunity cost would be $100k*.05*.10= $500

wtf? That has no meaning at all.  It's just a bunch of numbers multiplied together for no reason.

$500 would be the opportunity cost of the 401k interest, yes.

If someone pays down $5k mortgage at 10%, the annual benefit to that person is $5k * .1 = $500. 

By your formula, paying back $5k of mortgage would be a benefit of $5k * (1 - marginal tax rate).  At a 25% interest rate, your formula says that paying back $5k on a mortgage is a net benefit of $3750.  That makes no sense.  It is obviously wrong.

I think you guys are getting mixed up. If I understand correctly beltim is saying using 5k from 401k to pay mortgage at 10% saves them $500 in interest.  I agree with that.  I think bbub seems to be agreeing that you will save $500, but that $500 now becomes taxable income (because you can't deduct mortgage interest if you don't pay any).  So if you do that, when you file your tax forms you will have $500 less in deductions, effectively making you have $500 more to pay your marginal tax rate.

I agree with that too.  But using Beltim's formula, he is saying that using $100k to pay a mortage at 10% saves them $500.  That is incorrect.  See my above post.

Maybe this is the miscommunication.  That's not what I'm saying.  Where did I say that?

frugalnacho

  • Magnum Stache
  • ******
  • Posts: 4122
  • Age: 37
  • Location: Madison Heights, Michigan
Re: The exact math behind using 401k loan to pay down debt
« Reply #91 on: May 22, 2015, 02:14:01 PM »
That makes no sense.  Let's say he was going to refinance a 10% mortgage with a 5% 401k loan.  By your formula his opportunity cost would be $100k*.05*.10= $500

wtf? That has no meaning at all.  It's just a bunch of numbers multiplied together for no reason.

$500 would be the opportunity cost of the 401k interest, yes.

If someone pays down $5k mortgage at 10%, the annual benefit to that person is $5k * .1 = $500. 


By your formula, paying back $5k of mortgage would be a benefit of $5k * (1 - marginal tax rate).  At a 25% interest rate, your formula says that paying back $5k on a mortgage is a net benefit of $3750.  That makes no sense.  It is obviously wrong.

I think you guys are getting mixed up. If I understand correctly beltim is saying using 5k from 401k to pay mortgage at 10% saves them $500 in interest.  I agree with that.  I think bbub seems to be agreeing that you will save $500, but that $500 now becomes taxable income (because you can't deduct mortgage interest if you don't pay any).  So if you do that, when you file your tax forms you will have $500 less in deductions, effectively making you have $500 more to pay your marginal tax rate.

I agree with that too.  But using Beltim's formula, he is saying that using $100k to pay a mortage at 10% saves them $500.  That is incorrect.  See my above post.

Huh?  I quoted him saying exactly that.

BBub

  • Pencil Stache
  • ****
  • Posts: 774
  • Age: 35
  • Location: Deep South
Re: The exact math behind using 401k loan to pay down debt
« Reply #92 on: May 22, 2015, 02:15:47 PM »
So that opportunity cost should be what I said before:
loan balance * (401k interest rate) * (effective after-tax interest rate of mortgage)

Your formula said it.

Apply the following numbers to your formula:
Loan balance = $100k
401k interest rate = 5%
Effective after tax interest rate of mortgage= 10%

$100k*.05*.1=$500

beltim

  • Magnum Stache
  • ******
  • Posts: 2964
Re: The exact math behind using 401k loan to pay down debt
« Reply #93 on: May 22, 2015, 02:18:33 PM »
So that opportunity cost should be what I said before:
loan balance * (401k interest rate) * (effective after-tax interest rate of mortgage)

Your formula said it.

Apply the following numbers to your formula:
Loan balance = $100k
401k interest rate = 5%
Effective after tax interest rate of mortgage= 10%

$100k*.05*.1=$500

That was the opportunity cost of the repaying the 401k loan, not the total benefit.  I said the total benefit earlier:

In broad terms I think you have the right idea.  That is, something like:
profit = loan balance * [ (mortgage interest benefit) - (return of alternative investment)] ± (cost/benefit of additional 401k contribution)

beltim

  • Magnum Stache
  • ******
  • Posts: 2964
Re: The exact math behind using 401k loan to pay down debt
« Reply #94 on: May 22, 2015, 02:19:41 PM »
Ok, I'll pretend there isn't a problem and continue working through this, accounting for the taxes and 401k loanthis time..

Since the original 10% was deductible, we are losing out on $2,500 by refinancing.  $10k-2,500 = 7,500 in benefit.

You've switched to talking about a 401k loan, not a mortgage now, correct?

Quote
Since the 5% 401k loan is being paid to ourself, now we are only losing out on the taxes.  The interest rate itself is inconsequential, but the tax applied to it is a true cost.

Benefit of the transaction simply = $7,500 for the net interest saved.

Now to get profit, we'd take  $7,500-stable value rate - PV of future tax payment on the 401k interest.

This is all correct as well.

BBub

  • Pencil Stache
  • ****
  • Posts: 774
  • Age: 35
  • Location: Deep South
Re: The exact math behind using 401k loan to pay down debt
« Reply #95 on: May 22, 2015, 02:30:11 PM »
So that opportunity cost should be what I said before:
loan balance * (401k interest rate) * (effective after-tax interest rate of mortgage)

Your formula said it.

Apply the following numbers to your formula:
Loan balance = $100k
401k interest rate = 5%
Effective after tax interest rate of mortgage= 10%

$100k*.05*.1=$500

That was the opportunity cost of the repaying the 401k loan, not the total benefit.  I said the total benefit earlier:
It's not correct though.  How could it be correct that the opportunity cost of repaying the 401k loan is $500.  That is a totally irrelevant figure.  The proper way to solve the equation is laid out in my post.. You just said so.


Ok, I'll pretend there isn't a problem and continue working through this, accounting for the taxes and 401k loanthis time..

Since the original 10% was deductible, we are losing out on $2,500 by refinancing.  $10k-2,500 = 7,500 in benefit.

You've switched to talking about a 401k loan, not a mortgage now, correct?

Yes
Since the 5% 401k loan is being paid to ourself, now we are only losing out on the taxes.  The interest rate itself is inconsequential, but the tax applied to it is a true cost.

Benefit of the transaction simply = $7,500 for the net interest saved.

Now to get profit, we'd take  $7,500-stable value rate - PV of future tax payment on the 401k interest.
This is all correct as well.

I know.  It's the same formula I've proposed all along.

beltim

  • Magnum Stache
  • ******
  • Posts: 2964
Re: The exact math behind using 401k loan to pay down debt
« Reply #96 on: May 22, 2015, 02:37:56 PM »
Benefit of the transaction simply = $7,500 for the net interest saved.

Now to get profit, we'd take  $7,500-stable value rate - PV of future tax payment on the 401k interest.

I know.  It's the same formula I've proposed all along.

This is not what you said earlier.  Specifically, it differs in that in your earlier equation you subtracted a term that doesn't appear in this one:

Benefit is getting rid of the effective mortgage interest rate. 

Present Benefit = $100k*.0346 = $3,460

The present cost would be the taxes paid on the 401k interest (a cost the OP previously avoided due to the tax deductibility of mortgage). 

Present Cost = $100k*(.04125*.25) = $1,031.25

net benefit = $3,460-1,031 = $2,429 Net Benefit

profit = benefit - opportunity cost - PV of future tax liability on the 401k interest.

This is the term that I have a problem with.

beltim

  • Magnum Stache
  • ******
  • Posts: 2964
Re: The exact math behind using 401k loan to pay down debt
« Reply #97 on: May 22, 2015, 02:40:31 PM »
That was the opportunity cost of the repaying the 401k loan, not the total benefit.  I said the total benefit earlier:
It's not correct though.  How could it be correct that the opportunity cost of repaying the 401k loan is $500.  That is a totally irrelevant figure.  The proper way to solve the equation is laid out in my post.. You just said so.

Sorry, I was using a shorthand.  The $500 is the opportunity cost of the amount that you pay back the 401k instead of using the same amount of money to pay down the mortgage.

Edit: That means it's not the total benefit of taking the 401k loan, which you seem to think is what I mean.
« Last Edit: May 22, 2015, 02:42:45 PM by beltim »

BBub

  • Pencil Stache
  • ****
  • Posts: 774
  • Age: 35
  • Location: Deep South
Re: The exact math behind using 401k loan to pay down debt
« Reply #98 on: May 22, 2015, 03:14:49 PM »
Still not understanding your opportunity cost calc, but whatever.  Moving on...

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.

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.


adamwoods137

  • 5 O'Clock Shadow
  • *
  • Posts: 68
Re: The exact math behind using 401k loan to pay down debt
« Reply #99 on: May 22, 2015, 03:16:07 PM »
Thanks to all who responded

It sounds like I should take the loan and pay down debt instead of keeping it in a stable value fund.

We already have equity index investments in other tax deferred and taxable accounts, I am simply trying to optimize this very specific stable value part of our asset allocation

Hey one important point I haven't seen mentioned is that the fees involved in the 401k loan can eat the benefit.  Most 401k loan documentation I've seen includes large fees based on the size of the loan. Make sure they don't apply in your case!