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# Opportunity Cost of Paying Down Debt

This blog is to make the case that investing extra savings may more beneficial financially than paying down debt.

I can explain this best through illustrating an example. In my example I am using a mortgage, but this can be applied to any form of debt, taking into account the cost of debt and the opportunity cost of paying off debt.

Quantitative Example

Here is a snapshot of the modeling I did in a Google Sheet that outlines my assumptions. For this case scenario, I assumed a \$350k mortgage at 3% net interest rate over 30 years, starting 6/1/2021. I say “net interest rate” meaning I am not making any assumptions around tax deductibility, so we will assume this 3% is after tax deductions, if applicable.

Second, I made the assumption that this individual is going to get a 5% return if they invest this money. Again, assumption is this is an after-tax assumption since this can be saved in a taxable or tax-deferred account.

Finally, I assume this individual has an extra \$500 that they want to save. This is solely modeling the decision of payoff debt vs. invest, so we will assume this person has set a strong financial foundation including an emergency fund, getting the company 401(k) match, no consumer debt, making all minimum payments on debt, etc.

Here is a screenshot of the first year of paying down debt. You see that on the left side “Mortgage Paydown”, the mortgage is declining at a faster rate, while the right side “Invest” is taking the extra money to grow its “Investment Account”:

This continues on for 30 years. In the screenshot below, you’ll see that an extra \$500/mo will pay off the mortgage at the end of 2040, or about 10.5 years early - awesome! From there in column “Mortgage Paydown”, I show the full mortgage payment + the \$500 and start putting it all into the investment account growing at 5%.

But you’ll notice that by the time you START your investment account in “Mortgage Paydown”, your “Invest” column has already built an account worth almost \$200k. With this balance already there, the amount of money the \$200k is earning is almost as much as the full mortgage payment in “Mortgage Paydown”.

One last point this example illustrates is that after about 18 years and 2 months, if you chose team “Invest”, your after-tax investment balance will be large enough to pay off the mortgage, which is sooner than team “Mortgage Paydown” of 19.5 years.

If we continue on to the end of 30 years, or when the mortgage is paid off, clearly team “Invest” has brought a higher ending investment balance than team “Mortgage Paydown”:

Qualitative Explanation

It is easy to say to yourself that getting a 5% return in the market is better than paying down debt that costs you 3%; if you paid 3% to get a 5% return then you end up ahead. But in the grand scheme of things, is saving this 2% worth the added “risk” of the stock market?

It may not sound like it when you put it that way, but that is the point in putting numbers into this example. The discrepancy in ending investment balance isn’t because you are getting an extra 2% in a year by making this decision. It’s because you are making this decision over the span of 30 years (in my example) - and not only are you gaining an extra 2% each year, but that 2% is also compounding on top of itself over that long time period.

Starting the investment account right at the start helps to fuel the compounding interest. And as we know, time is the most valuable resource when it comes to investing, which is illustrated in this example.

Finally, this example ends after both mortgages are paid off. If we continued, the higher investment balance would continue to compound faster and create a bigger gap between the two balances until you were ready to start spending that money. This really goes to show what time can do for your investments!

Other Benefits

There are also a few benefits of holding a mortgage that I can think of which include:

1. Credit score. You will continue to carry “installment debt” for an extra 10.5 years which may help to show your credit worthiness by responsibly carrying debt over the long-term.

2. Lock in inflation. There is concern right now about inflation, but increased inflation will help costs that are locked in. In other words, your mortgage payment isn’t affected by inflation because it doesn’t change (unless you refinance) - therefore as inflation rises and the dollar is worth less, the real cost of your mortgage payment goes down.

3. Conversion to rental. Although not as likely, in the instance you decide to convert your property into a rental property, that mortgage can be beneficial. The full amount is deductible as a business expense and can be used to magnify your investment returns from the rental.

Drawbacks

There are risks to everything! This strategy can certainly be seen as riskier, since instead of paying down debt which is a guaranteed 3% savings, you are investing money for an uncertain return (in my case I am assuming 5%, but that is an assumption). Here are some things to consider:

1. Emotions. This is the biggest drawback. I am honestly not sure what will be more important to some individuals reading this blog - that you’ll have no mortgage 10.5 years earlier or you’ll have an extra \$87k. For some, knowing you are debt free is worth more than the extra money.

2. Cash Flow. Some may find having extra cash flow is important to their financial stability and would rather have that 10.5 years sooner by prepaying the mortgage.

3. Administration. Some may hate sending a check to their mortgage company every month, or they may hate it if their mortgage gets sold and they have to set up a payment to a new company, etc. It may be easier to pay off the mortgage ASAP and control the funds as you please.

4. Leverage. This is a fancy term for using debt: in this example it is to buy a home. But, the value of your home may go down and put you “underwater” in the sense that you owe more to the bank than your house is worth. To my “benefits” point above, leverage can magnify investment gains but can also magnify losses.

5. Risk of the stock market. The crux of this decision is arbitrage - borrowing money at a lower rate than that borrowed money can make you. My example is very peachy because it assumes every year that your investments go up 5%, but that may not always be the case. If it goes down, then you were charged 3% to lose value on your extra \$500/mo. This may be hard to stomach in the short-term, so it is important to keep a long-term focus on this strategy.

Final Thoughts

My example was mortgage focused but this can also be used in any form of debt - by recognizing the cost of debt vs. the opportunity cost you would be giving up by paying down that debt. The hard part about this decision is that the opportunity cost is an unknown variable, and that can be seen as risky.

My point was not to convince you to take out or hold debt, but to understand there are two sides to every story. The media will have you believe that being debt free is the best determinant of your financial health - and I couldn’t disagree more. “Learn how Sally paid down \$150k of debt in 3 years” - good for Sally, but I don’t think that is the right decision for everybody.

Personal finance is personal and you should assess your own goals, financial status, risk tolerance, etc. to make an informed decision that makes the most sense for you. You can always implement balance as well - it is not always one or the other. You could consider taking your extra \$500 and splitting it between the two so you can pay off the mortgage a few years early and still have a nest egg growing for you.

At the end of the day, the feeling of being debt free may be worth the \$87k for some - but don’t you want to find out what that number is to you to make sure it is worth it?

P.s. to flex my Google Sheets modeling, here is the formula (in cell D8) to get me the correct number in the “Investment Account” column of the “Mortgage Paydown” illustration. “Sheet 2” is a second tab that calculates a new mortgage amortization based on the available monthly savings:

=if(C8<’Sheet 2’!\$E\$33,if(C8>0,’Sheet 2’!\$E\$33-C8,(D7+’Sheet 2’!\$E\$33)*(1+(\$J\$9/12))),0)

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