Prioritizing tax-advantaged accounts over debt paydown

[drachma]

I have a fairly simplistic mathematical analysis that shows a slight advantage to prioritizing 401k contributions over aggressive debt paydown in certain scenarios. It shows this advantage even if I assume the 401k investments grow 0% real returns ( it would even work in a money market account), so I am talking about hard, guaranteed savings on tax dollars.

Im wondering if anyone can tell me if I'm making any mathematical errors or unrealistic assumptions. Here goes:

tax bracket now: 25%
tax bracket in retirement: 10&15% ~= 12.5%
30k debt @ 6.5% = $1950 in interest paid this year
401k contrib. max = $18000
taxes paid on 18k if not contributed = $4500
taxes paid on 18k if contributed and withdrawn in retirement = $2250
$2250 - $1950 = $300
so I come out $300 ahead by contributing to my 401k instead of aggressively paying down debt.

I think the error here is that if I was using the 18k to pay the loan faster, I'd end up paying less than 1950 in interest. The other error though, which works in my favor, is that I still have to pay the minimum on the 30k, so the 1950 is still an overestimate of interest paid this year.

Now, that's a hypothetical situation that's right on the line of worth it vs. not.

My reality is I have a relatively high income and am ALREADY paying quadruple the minimum payment while still maxing my 401k. The loan will be gone after this year (12 months from now). To me it just doesn't seem right to pay that loan off in 8 months at the expense of not maxing my 401k. (I'm also maxing a Roth IRA and HSA which further complicates things). The difference overall is probably pretty insignificant but I'm interested in the proper analysis out of curiosity.

[vexed87]

Not sure about the details on the 401k because we don’t have them in the UK, but you really need a better model that calculates the total cost of interest as you pay the debt down. At 6.5%, I know which I’d choose!

If you are only $300 up before you have factored in the reduced interest savings over the repayment period, for me it’s a no brainer, I’d opt for the peace of mind and be done with the debt. I do recall reading there are penalties for withdrawing from 401k so in the event you lose your job and need to raid your 401k to pay your minimum balance on the debt, you’ll be glad you paid off the debt first. Real life has a habit of gettin in the way of repayments at a later date so drop that debt like it’s hot. Because debts are liabilities and can make life difficult when the unexpected happens, I avoid them at all costs.

From a mathematicians point of view, you could be better off with the tax advantaged contributions, so it's about weighing up the pros and cons of both approaches. What happens if the markets implode tomorrow and you lose your job?

I'd rather have the freedom from debt than be small potatoes ($300) better off.

[JL13]

You theory is pretty solid, you could draw out a 10 year scenario in Excel (compare scenario A versus B).

The $18,000 tax-deferral is so powerful I think it's, in most cases, the first thing you should put your money into if you're in a decent tax bracket. (of course, pay off credit cards/high interest cards first).

two things I would note: one, make sure you've got some safety net, i.e. ability to pay on the note balance as well as rent and food were something to happen. Two, don't forget about state income tax as well, my state income tax is 6% so I get a 31% current tax reduction (25% fed plus 6% state).

[drachma]

you really need a better model that calculates the total cost of interest as you pay the debt down.

yeah, I'm just not sure how to calculate it other than iterating on every compounding period for the life of the loan for both scenarios. excel time...

raid your 401k to pay your minimum balance

i agree with "peace of mind" arguments for debt reduction but I already have a sizeable emergency fund capable of paying the minimums (+ living expenses) on the debt for 8-12 months.

[Scott 2]

This is solved math. You are looking for net present value equations that factor in the current value of the asset or liability, a rate of return, and a payment stream.

The functions exist in excel. Calculate the net present value of both the asset and the liability, splitting the payment stream as you prefer. You can maximize the resulting value by playing with the numbers.

In your situation, I would kill the debt before maxing the Roth. The return is certain, possibly better, and it removes immediate demands on cash flow. There's also a good chance you could get ahead and still be able to max the Roth by the end of the tax year. Qualitatively, I don't like the feeling of owing something. My mortgage is at a really low rate, and I know carrying it is financially optimal, but I consider paying it off at least once a month.

[henrik]

If you're talking about the full tax year
and are only concerned about the tax and not the potential investment gains
and you say you'd be able to pay off the 30k loan in 12 months,
then that should mean you are saving at least (30k+18k)/12=4k per month?

To me the logical thing to do would be to pay off the loan in the first 7.5 months of the year, saving a bunch on interest, and then catch up with the retirement contributions during the rest of the year with no loan payments to worry about.

[George the original one]

> The return is certain, possibly better, and it removes immediate demands on cash flow.

Yes, that would be my recommendation. On the other hand, you can guarantee the return of investments by taking a rather poor rate (gov bonds or CDs), so it's possible to have mathematical certainty instead of a fuzzy solution set.

[GandK]

In your situation, I would kill the debt before maxing the Roth.

Me too, OP. Debt carries risk. It may not be much risk in your specific situation, but it exists, and I'd personally prefer less risk over that block of time to the $300. I'm sure there are some math whizzes here that can fix a sum to your particular amount of risk; I'm not one of them. But I know those formulas exist, and I'm equally certain they would not return $0.

[JL13]

Let's be careful not to project our emotions onto OP. It sounds like he is not afraid of carrying a loan balance over a year (which is also BTW, immaterial relative to his income).

Paying down the debt saves $2,000 in interest, but forgoing the 401(k) contribution loses minimum $4,500 in tax benefit. You can pay down the debt anytime, but you can't ever put that $18,000 in the 401(k). If you pay off the loan this year, next year you can't do $36,000 in 401(k) to catch up.

The order matters in this case, and interest expense is not the only factor influenced by time.

[drachma]

In your situation, I would kill the debt before maxing the Roth.

Me too, OP. Debt carries risk.

As for the roth, I realize that is not optimal but there is another risk factor e.g. job loss. Roth contributions can be withdrawn in a (super) emergency so in effect that acts like a backup of my cash emergency fund. Not to mention the Roth's usefulness for ER.

Let's be careful not to project our emotions onto OP.

thank you. I've posed this question in a few other places and got a huge emotional response + little analysis. So far this board has given me the most useful and rational set of responses (no big surprise).

I think the key is in Scott 2's response about using NPV formulas. I'm not familiar with that style of analysis so I'm currently trying to learn how it works and construct an excel sheet that encompasses my scenario.

[Scott 2]

Due to unknowns, emotion always enters the picture. These are reflected in the assumptions your calculation uses, as all as the complexity of your chosen model. The inflation adjusted rate of return is probably the most obvious in our scenario.

This is one of the reasons an engineer can't just go win the stock market because they are good at math. Qualitative factors determine both the inputs and the approach. Getting those right is the hard part, not doing the actual calculations.

[JL13]

@Scott2

Definitely agree with you. I think it's best to pin down a number (or a range of numbers), and then introduce the qualitative aspects - i.e. assigning risk or % likelyhood for each scenario, and then just a final gut check for what your comfortable with.

@drachma

Probably don't need to go overboard with NPV analysis. Just do a spreadsheet with the following columns:

Month(or year)
401K contribution
401k balance
tax savings (from 401k)
Earnings on 401(k) (3%? 5%? -10%? play with it)
Debt payment
Debt interest
Debt balance

Create the first couple rows then copy the formulas down as far as you want to go into the future. Copy the columns over and change a couple things for a side by side A and B comparison.

[dalralmi]

You mention wanting possible mathematical flaws in your analysis. here is the question I have. You say you are currently quadruple paying your mortgage which is great, but that implies you were always already contributing to your 401k too. (I'm assuming but could be wrong here on this next part). If your company offers a "matching" contribution to the 401k I would presume from a financial standpoint of being "awesome" and smart like most people on this board you would no doubt not at least contribute enough money to get the matching from your company. This is me basing on assumptions.

If that is the case then you would not necessarily be putting the FULL 18000 towards the mortgage. I realize you wanted a simple calculation, but I find it interesting to say you would immediately cease all contributions to the 401k. I'm making some assumptions here but that would lead me to believe that depending on your income you will always be at least putting a small portion into the 401k and that limits the ACTUAL amount you should be subtracting from the 1950. The other thing to consider is does your tax bracket stay 25% whether or not you contribute. I personally contributed more to my 401k because I was on the tipping point of two brackets.

Basically the real thing I see possibly flawed in your calculation (not that it is flawed but possibly) is if the max contribution to the 401k is based on that number and if you would actually use all the money (18k) towards the mortgage. If instead you would still contribute the minimum to get a company match (or minimum to lower your tax bracket just enough) then the amount you effectively save in taxes is a different number entirely then based not he 18k.

Just my initial observation based on my debt savings. I've done this calculation many times similar to you have to pay off my mortgage, but there is always a number I start with that isn't quite the maximum based on company match.

[dalralmi]

Also mathematically the value of money in the future is less than the value of money today so it "appears" you save 2250 cause that's your taxes in the future, but that money could be more comparative to 1500 dollars today in future money (there is a formula for this somewhere based on how many years in the future the hypothetical tax is taken out compared to paying the tax in today's dollars). Also depending on how far in the future the risk of the unknown taxes may rise significantly or decrease obviously. Lots of unknowns. It becomes difficult to compare future value of money to today's value of money. Otherwise the calculations do seem fairly solid if we are talking ~5 years or so. Once you get beyond five years it becomes a little less significant.

[JL13]

@dalralmi

You could account for this by adding a deferred tax liability figure to the 401k balance @ whatever your expected future income tax rate is. That's how accountants do it anyway.

The time frame, in this particular situation, is too short to consider future value of money IMHO. Inflation rates and market fluctuations in the short term can be anywhere.

[drachma]

@dalrami

you are correct. my company matches 5% so for my PERSONAL situation I would only be re-routing 13,500 from the 401k to the loan (its a student loan, not a mortgage). This does complicate the calculation somewhat. And yes I have been contributing max to my 401k in addition to the extra payments. if we want to get more specific to my situation my effective interest rate isn't 6.5% and my debt isn't exactly 30k.

this was more of a back-of-the-napkin analysis that gave me an unexpected result, so I posted it to see if my analysis method was correct. It largely is, albeit a bit too simplified, and the responses here have given me some great suggestions for how to approach this problem in a general sense. I'm more interested in nailing down a general algorithm for analyzing this problem with any set of inputs than I am interested in having others calculate out my personal results for me.

[dalralmi]

In that case the basic algorithm is indeed correct. I was just inputting the few things i noticed. I assumed there was some rounding involved just not sure how much. For a general algorithm though those are the types of things I would worry about if scaling it to other people. For personal use though looks good.

[jacob]

The biggest advantage of tax-deferred accounts is not that it eliminate taxes in the present but that you eliminate capital gains and capital income taxes until you start withdrawing in the far future giving you many years of non-taxed transactions. This certainly does depend on the specifics of the particular investment strategy. Believe you me, some strategies actually work better in a taxable account. For example, one could imagine a security that mostly declines because out its equity in qualified dividends (many CEFs, for example). In that case, for a low income, one can get the dividends tax free AND take a $3000 capital loss each year to boot. Another taxable account advantage is that you can get the foreign tax credit. Not happening in tax-deferred accounts. In general, though, these are special cases, and most styles would be best in tax-deferred accounts.

I think the best strategy for any projection is a spreadsheet that iterates/inducts forward because it's super flexible.

Methinks using discounting merhods (NPV or IRR) is a bit iffy since it either depends on you setting some discount rate (which requires a serious amount of fudging) or requiring the ability to reinvest at your IRR which usually isn't realistic. Also, neither accounts for risk. They're good for ballparking though. As far as I understand, they're usually used to compare similar strategies, e.g. should we go with project A or project B. Not whether we should go with project A or not at all.

[IlliniDave]

Since life isn't a math problem the proper analysis goes beyond the math. In your math you make a favorable assumption about your future tax rates which is probably its biggest weakness given you are looking for "hard, guaranteed savings in tax dollars". There are none of those that you can know apriori because tax rates will likely change by the time the money in question is withdrawn.

In the non-tax realm you also neglect the possibility of a substantial investment loss.

At 6.5% I'd pay off the debt in 8 months. You'd only have a fraction of 1 year where you might miss maxing the 401, and the quadruple payments could be diverted to taxable investing accounts and quickly make up the difference in any tax differential in that one year.

Another way to frame the question: if someone were to offer to loan you $30,000 at 6.5%, would you take the loan and invest the money in the stock market? Not many people would at that interest rate. By prolonging the loan in order to invest, that is effectively what you are doing.

[JL13]

@Illinidave

I think regarding tax-deferred accounts it's a bit more nuanced. You're also borrowing interest free from the government with no set payback schedule. In my case it would be:

Borrow $30,000 (or whatever number) at 6.8%
Borrow $9,300 from the gov't (at 25% fed and 6% state) at 0%

The student loan interest is tax deductible, so becomes 4.7% net of tax. Which would equal $1,410 in expense in year 1. So $1,410/$39,300 = 3.6%

Borrow at 3.6% to invest in the market? with no risk of a margin call? Essentially this is what everyone with a mortgage does if they own any stocks. Additional items to consider:

1.) The money in the 401(k) is protected in most states from bankruptcy.
2.) You are likely to be in a lower tax bracket at retirement, absent any statutory changes.
3.) The government will loan you additional money at 0% as the account balance grows (deferred taxes)
4.) Student loans disappear upon death, leaving more money to the estate (a grim thought, sorry)

The biggest issue, which I think it non-financial, is the liquidity risk. You really can't pull the money back out of the tax-deferred account. and the additional required payments on the loan on top of living expenses could put you in a short term crisis.