MATH HELP re recent blog post: Loan payoff vs. Invest

[ChristopherMD20]

I know this is a hot button topic and I do not want to start a debate in that regard because there are multiple forum posts and blog comments that hash this debate out. What I am asking for help with is figuring out the math to determine how much one would need to invest in a taxable account to make it "mathematically correct". I do not want to fall into the trap (if my wife and I choose to invest) of not actually investing the money necessary for it to be the smart move.

 

Situation

Payoff Amount: $44,511.10 (Current Prinicple: $44,433.79)

Interest rate: 2.74% variable via Laurel Road (term 5 years ending 12/2022)

Monthly Payment at current rate: $810.58

AGI after maximizing tax advantaged retirement accounts for FY2018 (start first attending job 8/2018): $185,966.63

 

We could payoff the balance by the end of my fellowship in 6/2018. Before taking an interest in financial education, I was always frugal and a saver. My wife is the same way but to a slightly lesser degree. Our goal was to max out her 403b which had a match (mine did not in residency) but other than that throw extra money at my student loans. The lack of financial knowledge cost 3-4 years of Roth IRA contributions!

Now that we have a low interest rate, it makes sense to me that investing would yield a greater return (in theory). However, after reviewing many of the threads that mathematically derive the benefit of investing (compounding) vs. debt repayment I get lost and realize that I am not actually able to do the math myself to calculate how much to put into the taxable account to get an expected positive ROI when compared to paying off my student loans.

Thanks.

[Zaphod]

There are lots of moving parts here so there is no one formula that will fit every situation. There are compound growth and loan calculators online which would serve your purposes well. Most of the loan/invest calculators are really bad and only compare rates, not terms or time to retirement which is whats important. Also what your extra payments would be.

Most important is when you plan to retire. That becomes your end point for investment calculations. We already know the loan terms so thats set. To see your 'hurdle rate' of interest just look on your loan paper and it will say somewhere cost of the loan, etc...and give an exact dollar amount. If you pay it off on time that is the most you will pay in interest.

In your situation you only have about 3000 dollars in interest left, so depending on how much extra and how fast, thats all the money you could 'make' by paying off your loans. So in your case if you decided to double your monthly payment vs. invest it, you would need a CAGR of 0.35% to basically break even by investing over a 20 year period (1507 for loans vs. 1565 invested).

[Ryan]

Number shcnumbers. Kill the student loan debt. You didn't state the rate, but assuming it's > 3% and you're not going for PLSF, there's literally nowhere else you can get equivalent non-taxed returns with 100% safety of principal "invested."

[cgossage]

ChristopherMD20 wrote:

I know this is a hot button topic and I do not want to start a debate in that regard because there are multiple forum posts and blog comments that hash this debate out. What I am asking for help with is figuring out the math to determine how much one would need to invest in a taxable account to make it “mathematically correct”. I do not want to fall into the trap (if my wife and I choose to invest) of not actually investing the money necessary for it to be the smart move.

 

Situation

Payoff Amount: $44,511.10 (Current Prinicple: $44,433.79)

Interest rate: 2.74% variable via Laurel Road (term 5 years ending 12/2022)

Monthly Payment at current rate: $810.58

AGI after maximizing tax advantaged retirement accounts for FY2018 (start first attending job 8/2018): $185,966.63

 

We could payoff the balance by the end of my fellowship in 6/2018. Before taking an interest in financial education, I was always frugal and a saver. My wife is the same way but to a slightly lesser degree. Our goal was to max out her 403b which had a match (mine did not in residency) but other than that throw extra money at my student loans. The lack of financial knowledge cost 3-4 years of Roth IRA contributions!

Now that we have a low interest rate, it makes sense to me that investing would yield a greater return (in theory). However, after reviewing many of the threads that mathematically derive the benefit of investing (compounding) vs. debt repayment I get lost and realize that I am not actually able to do the math myself to calculate how much to put into the taxable account to get an expected positive ROI when compared to paying off my student loans.

Thanks.

Click to expand...

I sense a lot of stress in your post, but you really shouldn't be.  Sure you could have contributed to a Roth earlier, but having the ability to pay down your loans by the end of your fellowship is amazing.

Really, the only math is having a higher-after tax rate of return on your investments.  This is simply to say, if you expected a 7% return and had long-term capital gains rate of 15%, your after-tax rate of return would be 5.95%.  In reality, there is more to it than that.  You will pay taxes on any dividends and interest income.  You may also go years without selling anything within the taxable account which will push your return close to 7% then it would to 5.95%

This isn't really what you were asking, but I would max out your 401k and Backdoor Roth since both are both tax sheltered, and use any additional money you have to pay down the debt.

[Ryan]

cgossage wrote:

Really, the only math is having a higher-after tax rate of return on your investments. This is simply to say, if you expected a 7% return and had long-term capital gains rate of 15%, your after-tax rate of return would be 5.95%. In reality, there

Click to expand...

And that intentionally optimistic 7% taxable gain assumes it's 100% deferred capital gains and 0% dividends/distributions. In reality, 1% or more of that gain will be taxed _each year_ in distributions, reducing compounding and further lowering the after-tax return. And, built into that optimistic return is the risk premium-- sometimes stocks go up 20% in a year, sometimes, less commonly, they go down 20%. By paying off loans I guess there's some risk-- namely inflation-related (you also forgo having saleable assets in case of emergency), but swings are much less.

On the other hand, it takes guts to stay out of a bull market. Can you sleep at night knowing you went the safe route when stock prices might keep climbing >10%/year? I can and do every night.

[ChristopherMD20]

@Ryan I think to @Zaphod point, I would be paying $45k to save $3000. When in the long run I would probably "make more" than that in a taxable account.

Zaphod wrote:

Most important is when you plan to retire.

Click to expand...

I am 30 and my wife is 29. We plan to retire at age 60-65, so we are in this for the long haul.

Ryan wrote:

You didn’t state the rate, but assuming it’s > 3% and you’re not going for PLSF,

Click to expand...

Rate is variable but currently at 2.74%. No PSLF we refinanced after we got married when I was a PGY-3.

cgossage wrote:

I sense a lot of stress in your post, but you really shouldn’t be.

Click to expand...

I will have to adjust my tone, I am not stressed. My wife and I fist pump every night because we are far ahead of most people our age. We are just trying to build an empire now .

The anxiety that you likely have astutely pointed it is a mixture of paralysis analysis and neuroticism. To hearken back to my poker playing days as a teen, I always want to make positive equity plays at the table. Now the poker table is life and the financial well being of my family, so the stakes are bigger.

cgossage wrote:

This isn’t really what you were asking, but I would max out your 401k and Backdoor Roth since both are both tax sheltered, and use any additional money you have to pay down the debt.

Click to expand...

We are maximizing 403b (x2), my 457, HSA, both have already completed backdoor Roth for 2018. The AGI I quoted was subtracting out the contributions to those pre-tax retirement accounts. Combined pre-tax income before contributing to any tax shelters should be ~$400k in 2019.

 

Thanks for the responses.

[Zaphod]

ChristopherMD20 wrote:

@ryan I think to @zaphod point, I would be paying $45k to save $3000. When in the long run I would probably “make more” than that in a taxable account.

Zaphod wrote:

Most important is when you plan to retire.

Click to expand…

I am 30 and my wife is 29. We plan to retire at age 60-65, so we are in this for the long haul.

Ryan wrote:

You didn’t state the rate, but assuming it’s > 3% and you’re not going for PLSF,

Click to expand…

Rate is variable but currently at 2.74%. No PSLF we refinanced after we got married when I was a PGY-3.

cgossage wrote:

I sense a lot of stress in your post, but you really shouldn’t be.

Click to expand…

I will have to adjust my tone, I am not stressed. My wife and I fist pump every night because we are far ahead of most people our age. We are just trying to build an empire now .

The anxiety that you likely have astutely pointed it is a mixture of paralysis analysis and neuroticism. To hearken back to my poker playing days as a teen, I always want to make positive equity plays at the table. Now the poker table is life and the financial well being of my family, so the stakes are bigger.

cgossage wrote:

This isn’t really what you were asking, but I would max out your 401k and Backdoor Roth since both are both tax sheltered, and use any additional money you have to pay down the debt.

Click to expand…

We are maximizing 403b (x2), my 457, HSA, both have already completed backdoor Roth for 2018. The AGI I quoted was subtracting out the contributions to those pre-tax retirement accounts. Combined pre-tax income before contributing to any tax shelters should be ~$400k in 2019.

 

Thanks for the responses.

Click to expand...

You only save the 3k if you have a lump sum today to pay it off. You will for sure pay some interest, so your savings are <3k.

Rate does not need to be higher to win out. Terms are different, thats what matters.

[Donnie]

It really doesn’t matter what you do regarding paydown versus invest. The expected difference in the outcomes is not large enough to worry about it. Just do one or the other (or a combination), whatever feels better, and don’t sit on the cash.

[DMFA]

The principal, rate, and term are not enough to make a big enough difference. Just make sure that any money in question that is not put toward the loan actually has to be invested for this argument to be valid.

The early payoff argument is also only valid if you put everything that would have gone toward your now paid-off loan now goes into investments.

The percent-vs-percent argument ignores several factors: the simple amortizing (non-compound) term-limited nature of the loan thus yielding a fixed cost or "loss," and the compound, open-ended nature of the investment, as well as any possible tax advantage you might get on those investments if they'd be pretax or Roth (hence why retirement accounts are generally advised to be prioritized ahead of well-structured debt). Yes, there is market risk and loss-of-income risk, but for it to be so catastrophic that you can't liquidate your investment to pay the debt is unlikely.

In the end, you're talking 3 grand or so over five years, here. If you pay off earlier than 5 years (already fairly aggressive), you're not missing out on that much investment principal, and if you invest in equities instead of paying over the schedule, then you're not losing much to finance charges.

The only way you really "lose" is if you take that extra money, look at your low-rate, short-term loans and say "meh," and put your extra money into anything other than investments. If that debt is not used as investment leverage, then it's just debt complacency and lost money (which should not be acceptable). And if you don't need that leverage anymore, then just pay it. If you've won the game, stop playing.

[cgossage]

ChristopherMD20 wrote:

@ryan I think to @zaphod point, I would be paying $45k to save $3000. When in the long run I would probably “make more” than that in a taxable account.

Zaphod wrote:

Most important is when you plan to retire. 

Click to expand…

I am 30 and my wife is 29. We plan to retire at age 60-65, so we are in this for the long haul.

Ryan wrote:

You didn’t state the rate, but assuming it’s > 3% and you’re not going for PLSF, 

Click to expand…

Rate is variable but currently at 2.74%. No PSLF we refinanced after we got married when I was a PGY-3.

cgossage wrote:

I sense a lot of stress in your post, but you really shouldn’t be. 

Click to expand…

I will have to adjust my tone, I am not stressed. My wife and I fist pump every night because we are far ahead of most people our age. We are just trying to build an empire now .

The anxiety that you likely have astutely pointed it is a mixture of paralysis analysis and neuroticism. To hearken back to my poker playing days as a teen, I always want to make positive equity plays at the table. Now the poker table is life and the financial well being of my family, so the stakes are bigger.

cgossage wrote:

This isn’t really what you were asking, but I would max out your 401k and Backdoor Roth since both are both tax sheltered, and use any additional money you have to pay down the debt. 

Click to expand…

We are maximizing 403b (x2), my 457, HSA, both have already completed backdoor Roth for 2018. The AGI I quoted was subtracting out the contributions to those pre-tax retirement accounts. Combined pre-tax income before contributing to any tax shelters should be ~$400k in 2019.

 

Thanks for the responses.

Click to expand...

That's great.  I would just pay it down and be done with it then.  You might beat the interest rate in a taxable account, but you really can't beat the feeling of being debt free.

[ChristopherMD20]

cgossage wrote:

you really can’t beat the feeling of being debt free.

Click to expand...

It seems like in the grand scheme of things from everyone's input even if I make the "wrong" mathematical choice it isn't going to move the needle much in the grand scheme of things. Therefore, I will do whatever will make my wife happier.

The bigger lesson here is learning how to analyze these situations myself so I do not have to keep bugging you fine folks. Thanks for the input and education everyone.

[cgossage]

Ryan wrote:

cgossage wrote:

Really, the only math is having a higher-after tax rate of return on your investments. This is simply to say, if you expected a 7% return and had long-term capital gains rate of 15%, your after-tax rate of return would be 5.95%. In reality, there

Click to expand…

And that intentionally optimistic 7% taxable gain assumes it’s 100% deferred capital gains and 0% dividends/distributions. In reality, 1% or more of that gain will be taxed _each year_ in distributions, reducing compounding and further lowering the after-tax return. And, built into that optimistic return is the risk premium– sometimes stocks go up 20% in a year, sometimes, less commonly, they go down 20%. By paying off loans I guess there’s some risk– namely inflation-related (you also forgo having saleable assets in case of emergency), but swings are much less.

To clarify, the 7% (with 15% capital gains) was just a simple example. The 5.95% after tax return assumes annual capital gains taxes every year which is highly unlikely.  Any deferral at all, will improve upon the return.

[DMFA]

cgossage wrote:

you really can’t beat the feeling of being debt free.

Click to expand...

I can. My balance sheet makes me feel good. You don't get to tell me what feels good and what doesn't.

I don't buy this "debt slavery" argument. I know Clint didn't use that specific nomenclature, and I don't mean to put words in his mouth, but it's in the same vein.  Someone with a mortgage at <2% after tax over 15-30 years (below historical inflation rate in some cases) who is earning 5% a year compound in their investments over that same period must be in the cushiest bondage imaginable. That's a massive emotional overstatement. The debt is the debt and the gain is the gain. You get to decide how to feel about it.

Now, no one should be taking out needless debt or debt on which they can't reliably cover the payments over time; that's just not smart. If you don't need the leverage because you can afford what you need/want without it, don't take it. Also, you should definitely be structuring your existing necessary debt to the lowest rate and shortest term possible (think 5-year, 3% range for student loans). Just doing that alone is an "aggressive" move to limit your debt to a fixed cost over a short term which should henceforth make long-term equity investing superior.

But don't delude yourself into thinking you're putting yourself into the Chains of Mephistopheles over $3,000 of finance charges over 5 years, or a mortgage loan with a rate approximating historical inflation which is backed by an insured, protected, (likely) appreciating asset, especially if the alternative is open-ended compound (likely) growth and even more so if it's tax-advantaged.

The subjective criterion which cannot be right or wrong is risk tolerance. What is the expected return of the alternative to reducing your fixed finance charges over how long? Is that worth taking the market risk? Is your income to cover the monthly payments on your simple amortizing loan at risk (going part-time, retiring)? If you consider that and you *want* to pay your well-structured debt, then pay your debt. That's never wrong, especially if you have a robust portfolio and have no use for leverage. But don't emotionally aggrandize a static numerical entity. It's ontology over semantics.

[ChristopherMD20]

cgossage wrote:

To clarify, the 7% (with 15% capital gains) was just a simple example. The 5.95% after tax return assumes annual capital gains taxes every year which is highly unlikely.  Any deferral at all, will improve upon the return.

Click to expand...

I follow the example that you illustrated. After tax return (%) = % return x (1- capital gains %).

 

The part I do not follow is the statement: "The 5.95% after tax return assumes annual capital gains taxes every year which is highly unlikely." If funds are in a "taxable account" then why wouldn't taxes be applied yearly? Probably a basic question, but I do not follow (still a rookie ).

 

[DMFA]

ChristopherMD20 wrote:

cgossage wrote:

you really can’t beat the feeling of being debt free. 

Click to expand…

It seems like in the grand scheme of things from everyone’s input even if I make the “wrong” mathematical choice it isn’t going to move the needle much in the grand scheme of things. Therefore, I will do whatever will make my wife happier.

The bigger lesson here is learning how to analyze these situations myself so I do not have to keep bugging you fine folks. Thanks for the input and education everyone.

Click to expand...

Making your spouse happy is way more valuable than a couple thousand dollars gained or lost over five years.