Pay Off House Before Early Retirement?

[AJ]

Thoughts?  Does my analysis miss anything?

Here are the numbers I get:

Scenario #1: Buy house outright, invest $477 a month in stock market
Start with $0
End with $404k ($477 a month for 30 years at 5%, compounded quarterly)
Zero interest paid

Scenario #2: Get mortgage with $477 monthly payment
Start with $100k in stocks
End with $459k* in stocks
$71k interest paid

The only thing I see missing in your calculation is what you would do with the extra money every month that you are no longer spending on a mortgage payment (I assume we would put it into the market). It looks to me like you would come out ahead in scenario #1, so I must be missing something...

*I get $459k when I plug the numbers into a calculator, compounded quarterly.

[sol]

Not exactly relevant to the original poster, but an additional wrinkle for some to consider: we're looking at carrying our 30 year mortgage for as long as possible even though we'll have the money to pay it off in like four more years, because we have a bunch of money locked up in our 401k that can be used to pay off the mortgage when it becomes available under a lower tax bracket.

In short, paying off your mortgage while working means paying your marginal tax rate on your mortgage balance.  Paying it off after you quit working and have a much lower income will cost you more in mortgage interest, but less in taxes.  Coupled with the desire to keep liquid funds outside of the 401k so we can live off them before we hit retirement age, this situation works out in favor of keeping the mortgage, for us.

[skyrefuge]

Thoughts?  Does my analysis miss anything?

Yep, like AJ said, in the no-mortgage scenario, you didn't account for the $477 in monthly income that you would be required to have in order to pay the mortgage in the mortgage scenario.  In the no-mortgage scenario, you would still have that income, and should assume that money gets invested every month.  Given those assumptions, if the mortgage rate is equal to your expected investment return, then there is no difference.  With a mortgage at 4%, you lose $71,870 in interest payments, and without a mortgage, you lose $71,870 in gains if you had left that money invested at 4%.

You can try it out in spreadsheet-math.  We really want to see what your investment account total is at the end to compare.  The formula is:
=FV(Rate, Number of periods, Amount added per period, Starting Value)

Our period will be months, so there are 30*12=360 of those, and our rate is also per-period, so we divide 4% by 12.

In the no-mortgage scenario, we drain $100k out of our account at the beginning, leaving us with $0, and adding it back at $477/mo:
FV(.04/12, 360, $477, $0)

In the mortgage scenario, we start with $100k in the account, but never add anything, since that money is going to pay the mortgage:
FV(.04/12, 360, $0, $100000)

Both come to the exact same result, $331,349 (actually the first is slightly off, because the mortgage payment is really $477.4153)

I don't know what most people are actually referring to when they use a predicted 7% (or 5%, or whatever) return rate in the stock market, but I assume it's a Compound Annual Growth Rate, in which case the compounding is already taken into account.  That means you don't get any "bonus" from the power of compounding, because it's already baked into the prediction.

[skyrefuge]

In short, paying off your mortgage while working means paying your marginal tax rate on your mortgage balance.

Hmm, I'm not exactly sure what you're saying here, but it sounds like this could be something that applies only if you were making early mortgage payments in lieu of 401(k) contributions?  But if you're already maxing out your tax-advantaged accounts and still have unused income left over (not a terribly unheard-of situation amongst Mustachians), then it's getting taxed at your marginal rate regardless of whether you put it towards your mortgage or towards investments, right?

[sol]

if you're already maxing out your tax-advantaged accounts and still have unused income left over, then it's getting taxed at your marginal rate regardless of whether you put it towards your mortgage or towards investments, right?

Right, I was just saying you pay taxes on all of the income you take now, and that's not always obvious what's a better deal.

In our case, it makes more sense to contribute less than the 17k tax deferred match in order to have that cash taxed immediately, because we have a bunch of money locked up in the 401k that we won't need after we're eligible to withdraw it, and a shortage of available cash before then.  So we're basically using our mortgage like a loan, in that we're borrowing against our future 401k income in order to live off the money that would have gone to paying down the mortgage, in the years between retiring early and being eligible to withdraw the 401k.

Totally clear, right?

[Dicey]

Totally fucking brilliant, Sol. Awesome Mustachian thinking.

[jpo]

if you're already maxing out your tax-advantaged accounts and still have unused income left over, then it's getting taxed at your marginal rate regardless of whether you put it towards your mortgage or towards investments, right?

In our case, it makes more sense to contribute less than the 17k tax deferred match in order to have that cash taxed immediately, because we have a bunch of money locked up in the 401k that we won't need after we're eligible to withdraw it, and a shortage of available cash before then.

This was going to be my next question about this topic. It seems like the consensus is to not pay down the mortgage, and there are compelling arguments on why not to above. But when investing that extra money, do I max out the 401k and save on taxes while I'm in a higher bracket or take the tax hit now and invest in a regular brokerage account?

Haven't given this too much analysis/thought, but eventually will be figuring out which is the better option...

[grantmeaname]

I believe the issue sol is referring to is the difficulty of getting 401k money out of the account early. There are two relevant ways to do that: you can take substantially equal periodic payments (SEPPs, governed by rule 72t) until you're 59.5, but they have a tiny value (try the calculator here to get a feel for the amount) and aren't sufficient to support even a Mustachian way of life.

You can also rollover your 401k to a Roth IRA, but you're paying income tax on the amount rolled over in the year that you do it unless you had a Roth 401k. Either way, the rolled-over sum then has to 'season' in the Roth for five years before you can access it penalty-free. If I remember correctly, the problem sol is dealing with is planning for the five years between the rollover and the rollover's withdrawal eligibility. You can contribute to regular brokerage accounts to get you through that period, but sol's technique decreases the need to do so... he's simply waiting until his five year seasoning period is up to pay off the mortgage with his gobs of TSP cash (gov't employees 401k equivalent), which decreases the amount of money he needs to have before the end of the seasoning period.

Sol/everyone else, did I miss something there?

[sol]

Sol/everyone else, did I miss something there?

Sounds about right, but I should point out that I think mine is a somewhat unusual circumstance so this may not be the right choice for other people.

In addition to forestalling the need for that income until we can access the TSP, by carrying the mortgage longer, we also push those withdrawals out until we're in a lower tax bracket after retirement.  It's kind of a little side bonus, but one that is offset for us by deferring less money into the TSP now and thus taking a larger tax hit up front.  Which we're doing because the TSP doesn't appear to allow the 5 year rollover plan to a Roth IRA, so we need more money in taxable accounts than most folks.

[velocistar237]

This was going to be my next question about this topic. It seems like the consensus is to not pay down the mortgage, and there are compelling arguments on why not to above. But when investing that extra money, do I max out the 401k and save on taxes while I'm in a higher bracket or take the tax hit now and invest in a regular brokerage account?

Haven't given this too much analysis/thought, but eventually will be figuring out which is the better option...

Usually the tax-advantaged option is better. One conservative check is to compare what would happen if you withdrew it early. If you're in the 25% tax bracket, and you drop down into the 15% tax bracket in retirement, then the worst that could happen on withdrawal is that you pay 15% plus the 10% penalty, and you're right back with the brokerage account, except you didn't have to pay capital gains taxes, etc. In reality, you can avoid the 10% penalty through a few different (possibly difficult) avenues, and even if you didn't, as MMM showed with his recent post on taxes, your tax burden would be lower than 15%, so you would come out ahead tax-wise anyway. Since you're not considering a Roth, I assume that you're in a high tax bracket.

[jpo]

This was going to be my next question about this topic. It seems like the consensus is to not pay down the mortgage, and there are compelling arguments on why not to above. But when investing that extra money, do I max out the 401k and save on taxes while I'm in a higher bracket or take the tax hit now and invest in a regular brokerage account?

Haven't given this too much analysis/thought, but eventually will be figuring out which is the better option...

Usually the tax-advantaged option is better. One conservative check is to compare what would happen if you withdrew it early. If you're in the 25% tax bracket, and you drop down into the 15% tax bracket in retirement, then the worst that could happen on withdrawal is that you pay 15% plus the 10% penalty, and you're right back with the brokerage account, except you didn't have to pay capital gains taxes, etc. In reality, you can avoid the 10% penalty through a few different (possibly difficult) avenues, and even if you didn't, as MMM showed with his recent post on taxes, your tax burden would be lower than 15%, so you would come out ahead tax-wise anyway. Since you're not considering a Roth, I assume that you're in a high tax bracket.

I also have a Roth that I max out each year. I am in the 25% bracket now.

I am contributing to the 401k enough for the employee match and saving my extra income after 401k and Roth for a house down payment. After I buy a house I will redirect that extra income towards ER savings - the question is whether to put it into a brokerage account or to max out the 401k above and beyond the match.

So, I will be in one of two scenarios:

• $5k to Roth, 6% to 401k, extra to brokerage
• $5k to Roth, $17k to 401k, negligible to brokerage

I suspect maxing out the 401k would be better, as well as being a little more "forced" of savings since it won't ever flow through my checking account, but haven't run any hard numbers.

[WageSlave]

Yep, like AJ said, in the no-mortgage scenario, you didn't account for the $477 in monthly income that you would be required to have in order to pay the mortgage in the mortgage scenario.  In the no-mortgage scenario, you would still have that income, and should assume that money gets invested every month.  Given those assumptions, if the mortgage rate is equal to your expected investment return, then there is no difference.  With a mortgage at 4%, you lose $71,870 in interest payments, and without a mortgage, you lose $71,870 in gains if you had left that money invested at 4%.

Ahh, OK.  In my mind I was actually thinking about a slightly different scenario than I proposed: what if your income was exactly the amount of your monthly expenses?  In other words, your income differs by $477/month depending on whether or not you take the mortgage.  (But I now think that's just a roundabout version of the same question: a difference in income over 30 years is obviously going to make a difference.)

I don't know what most people are actually referring to when they use a predicted 7% (or 5%, or whatever) return rate in the stock market, but I assume it's a Compound Annual Growth Rate, in which case the compounding is already taken into account.  That means you don't get any "bonus" from the power of compounding, because it's already baked into the prediction.

Can you elaborate on this a bit?

I was thinking about it like this (and this may be wrong!): let's say you have a $100k 30-year CD that pays 5% annually.  The balance after...

• 1 years: 105,000 (100,000 + 100,000*0.05)
• 2 years: 110,250 (105,000 + 105,000*0.05)
• 3 years: 115,763 (110,250 + 110,250*0.05)
• ...
• 30 years: 432,194 (411,614 + 411,614*0.05)

My understanding is that you can use the P(1+i)^N formula to express this kind of calculation.  And in this case, it works out: 432,194 = 100*1.05^30.

Using the "FV" formula (with 0 for payment) yields the same result: FV(0.05, 30, 0, 100000) = 432,194.

When somebody says, "the stock market has returned an average of X% over a 30-year period" (where X=5 in the example we've been discussing), is it safe to look at it like a CD paying 5%, as I did above?  Note that I'm ignoring the characteristics (e.g. risk) of the investment, just wondering if the computations are correct?

In other words, does "Compound Annual Growth Rate" mean the same thing as "average returns"?  If not, what is the difference?

[sol]

In other words, does "Compound Annual Growth Rate" mean the same thing as "average returns"?  If not, what is the difference?

Sadly no, totally not the same thing.  Very few people recognize the difference though, and it makes a huge difference.

If you start with 100k and have a +50% year and then a -50% year, you will end up with $75k.  Your average return is zero (+50-50/2) but your compound annual growth rate is clearly negative.

There was a good description of this distinction linked here recently, from some other blog.  Don't remember where, sorry.

[grantmeaname]

The compound annual growth rate is the geometric mean of your yearly returns, while the average return is the arithmetic mean. Wikipedia has a good explanation of the difference.

I'm not totally sure what skyrefuge means about compounding being "baked in" to CAGR. If you have a CAGR of 7% and four years, your final amount will be given by 1.07⁴*P=1.31*P.  A four-year investment grows by 31%, not 28%. The only difference with CAGR instead of average return is that it's a more meaningful measure of central tendency, because when you're comparing things like annual growth you want to use the geometric mean.

[skyrefuge]

I'm not totally sure what skyrefuge means about compounding being "baked in" to CAGR.

Yeah, I'm not totally sure what I mean either.  I think the whole CAGR-vs.-average thing may be completely unrelated to matt's original question.  I was just reaching for a way to disabuse him of his notion that "investing still comes out ahead due to the magic of compound interest".  It probably would have been better to say that mortgages and investments (they're really two sides of the same coin) both use the same magic of compound interest, so the magical effects cancel each other out.

Anyway, regarding the CAGR stuff, http://www.moneychimp.com/features/market_cagr.htm lets you actually compare "average returns" of the historical S&P 500 vs. "annualized/CAGR returns", which is a good practical way to see the difference.

And yeah matt, your assumptions/calculations regarding CD returns are correct, and can be applied the same way to predicting stock market returns, as long as it's a CAGR value you're using.  In the case where the rate is the same for every period, like a CD, the "average rate" is the same as the "CAGR rate", but if the rate varies over time (as it does in the stock market), then the "CAGR rate" will be lower than the "average rate".