Every few months I receive the same bill in the mail that tempts me to start calculating future value and expected returns. This single sheet of paper that arrives quarterly like clockwork is an invoice for the King County Sewage Treatment Capacity Charge that is charged to the owner of a new home for 15 years after hooking up to the sewer system. I suppose this prevents new builders from incurring a large “sewer hook-up fee” from the county right off the bat, but slowly charging the fee over 15 years seems like more of a hassle to me. For us, it doesn’t matter where it came from or why because at this point we’re stuck with it. Even though we didn’t build the home, this capacity charge happily passes from one owner to the next until those first 15 years are up. The purpose of this post is to focus on a single line that exists in the invoice right below the “Remaining Balance”, an “Early Discount Payoff” price.

Instead of continuing to make the quarterly payment of $87.42 for the next 7 years, we can choose to pay it all off in a lump sum at a discount of over $200 on the full balance. It might seem like a decent deal at first, but if you know anything about inflation, you’ll understand that $200 today is not worth the same as $200 7 years from now. So how do we determine if paying something off early for a discount is worth it (sewer capacity charge or anything else for that matter)? Let’s find out.

## Comparing Our Two Options

When presented with an opportunity to pay something off early for a discount or pay it off over time, we first have to look at whether or not we can afford to pay it off immediately. For our most recent capacity charge invoice, we would need to pay $2,303.20 in order to close out the balance today. We have a solid emergency fund (not that this is an emergency in any way) and solid cash flow thanks to our jobs, so making the early lump-sum payment is certainly an option for us. If paying something like this early would cause financial stress or force you to dip into emergency funds, it’s probably not worth it.

So assuming we can comfortably come up with $2,303.20 before this payment is due, we have two comparable options.

- Make the lump-sum payoff for the $231.98 discount.
- Invest the $2,303.20 and make all of the future $87.42 payments out of that investment.

There is also the third option of spending it all, but if we knew of a way to make our lives significantly better by spending a couple grand, we’d already be doing it. Beyond that point it would just be wasteful spending, so let’s stick to the two smart investing options above.

Now that we have our two options, let’s explore which one is the better investment.

## Similar, but Not the Same As Invest vs. Pay Off Debt

A common question in personal finance is whether or not debt should be paid off before investing money. In order to properly ask this question at all, you should already be in a pretty solid financial position. Before investing OR paying extra towards debt, you should have money set aside in a savings account for emergencies and make sure you’re taking advantage of any employer matches available to you in a 401k or similar plan. Once you’ve got that out of the way, then you can start looking at the trade-offs between investing and paying off debt.

Once you’ve established a solid financial base and have some money left-over, the invest vs. pay off debt question becomes rather simple. Do you expect to receive better returns from the investment than the interest rate on your debt? If yes, invest. Otherwise, pay off the debt first, then invest.

There are a few caveats such as the value of guaranteed returns versus expected returns and tax deductions on certain types of interest, but the basic comparison remains the same. Looking at the interest rate of the debt compared to the expected return of your investments should point you towards which one is better.

In the case of paying off something early for a discount, the comparison is similar, but reversed. For my example of the sewer capacity charge, there is no interest rate on the “loan”. Instead, the county will essentially pay me some interest in order to get the payment sooner! Determining that amount of interest is the tricky part, but once we do, comparing it to the expected return of our investments will help us determine the right move to make.

## The Math Behind A Discounted Early Payoff

In order to determine the effective interest rate the early payout is offering, we need to see how our investment would perform if we didn’t choose to pay it off early. In my example, we would look at the growth of the $2,303.20 over the next 29 quarters that we would normally be making payments during. It’s not as simple as just calculating compounding interest on the total amount though, because we can’t forget about the quarterly $87.42 payments we will have to make along the way.

We can model this by compounding interest quarterly, subtracting out $87.42 from the balance, and then repeating 29 times to get the final value of our investment. If the final number is positive for the growth rate used, then it’s better to invest. If the final number is negative, it would be better to pay off the loan quicker.

Instead of going through all of those steps manually, we can use a simple excel formula to do it for us! Essentially what we’re trying to calculate is the future value of a shrinking investment, so we can use the built-in future value (FV) function.

=FV(rate of growth, number of payments remaining, payment amount, -1 * early payoff amount, payments made at end/beginning of period (0/1) )

For our capacity charge example, the equation would look like this if we expected to receive 5% growth annually from our investments:

- rate of growth = 5% annually, but the payments are made quarterly (4 times per year), so we divide by 4
- number of payments remaining = 29 (total balance of $2,535.18 divided by the $87.42 payment)
- payment amount = $87.42
- -1 * early payoff amount = -$2,303.20 (negative because it represents present value and we’re starting down by the early payoff amount)
- payments made at end/beginning = 1 (we can’t wait until the end of the quarter to decide whether or not to pay it off because the payment is due now, so we set this to payments being made at the beginning of each period)

=FV(0.05 / 4, 29, 87.42, -2303.20, 1)

By typing that into an excel cell and hitting enter, we will come up with a value of **$231.10**! As the value is positive, it means that we should invest the money in something that yields 5% annually rather than choose the early payoff amount. At the end of the 29 payments (~7 years), we would end up $231.10 ahead by investing in a 5% annual growth product rather than paying off the capacity charge early.

But just how poor of an investment would the early payoff be?

To answer that question and for easier comparison, what we really care about is the break-even point. What interest rate on our investments is necessary to make investing equal to paying it off early?

## Using the Rate Function to Find the Break-Even Point

Rather than try to estimate what the return on our investment is, let’s instead see what rate of return makes the two choices equal. The RATE function is similar to the FV function discussed above, but instead calculates the interest rate necessary for an amount of money now (that may grow or shrink) to grow to a different amount of money over time.

=RATE(number of payments remaining, -1 * payment amount, early payoff amount, future value, payments made at end/beginning (0/1) )

For our capacity example, most of these values are the same that we input above:

- number of payments remaining = 29 (total balance of $2,535.18 divided by the $87.42 payment)
- -1 * payment amount = -$87.42 (negative because we’re subtracting it from the starting amount)
- early payoff amount = $2,303.20 (present value of investment)
- future value = 0 (this will give us the break-even of when investing equals paying off early)
- payments made at end/beginning = 1 (same reason as above, payments are due at the beginning of the quarter)

=RATE(29, -87.42, 2303.20, 0, 1)

After typing that into a cell in excel, we find out the interest rate required is 0.7% per quarter. To find the annual rate, we multiply by the number of payments per year (4) to get 2.8% as the break-even point for investing versus paying it off early.

## Comparing All The Options

In our personal situation, we also have the option of paying off debt to consider in addition to simply investing the money or paying off our sewer capacity charge early. Now that we’ve calculated the break-even point of paying off the capacity charge early to be 2.8%, it’s easy to see that simply putting extra towards our mortgage principal which carries an interest rate of 4% would be a better use of the money. Knowing that, there is no way we’re going to pay this capacity charge off early!

Now that we’ve removed PMI from our mortgage, we’ve decided it no longer makes sense to commit any extra money to paying off the mortgage early. Since our mortgage interest rate is 4% and we expect our investments to grow around 7-10% annually (on average), it makes financial sense to simply keep investing while making the minimum monthly payments.

Others will speak to the emotional benefit of reducing mortgage debt and eventually paying it off versus growing investments, but I think I’ll feel just as emotionally safe with $100k in investments and $100k remaining on the mortgage as I would with both balances being $0. To each his own though, anyone who find themselves in a position of choosing between the two is already ahead of the game financially and either choice certainly beats blowing the extra money in Vegas!

## Try It Yourself and Apply It To Other Situations

I created a public Google Sheet that will allow you to enter your own Early Payoff information to see what your break-even point or potential profit for investing instead of paying off early could be.

Link to Money Metagame Early Payoff Calculator

Use **File->Make a copy…** if you want to put in your own values and test it out.

Here’s the sewer capacity charge example I discussed above in google sheets:

Another situation that’s come up in my life is whether or not to pre-pay membership dues. For example, let’s say a group charges a $70 annual rate for membership, but also offers the option of pre-paying 5 years of membership for a $40 discount. Should you do it?

According to the calculation above, we would need our investments to grow over 6.46% annually in order to beat out simply pre-paying the membership dues! This is a situation where it might be worth it to take the “guaranteed return”.

I put guaranteed return in quotes, because even a situation like pre-paying dues isn’t necessary a guaranteed return. Maybe after 4 years, you decide to part ways with the club and would never have paid that 5th year to begin with. Not only are you now down $30 right off the bat, but you’ve also lost out on investment gains on top! Even for the sewer capacity charge example, there’s no guarantee we’ll have to pay it down to $0. We weren’t the first people to live in this house and it’s entirely possible we’ll sell the place and move in the next 7 years. A quarterly $87 charge certainly didn’t make or break our decision to buy the house and I’m sure it wouldn’t for the next buyer either. That means if we pay it off early, but don’t stick around for the full 7 years, we’ll have most likely lost out by paying early, investment gains or not!

Hopefully this is helpful in the case you ever find yourself in the dilemma of whether or not to pre-pay for a discount. The answer might surprise you once you actually crunch the numbers! Does anyone else calculate future value when faced with an early payment discount or do you just go off of your gut feeling?

Great analysis as always, easy to follow and very illuminating. Really appreciating the value of this blog in terms of day to day financial decisions. People are so quick to think that financial advisors or “business people” know some magic trick, but at the end of the day it’s simple (but now so intuitive) math. Thanks!

Thanks for the kind words!

plus you may not keep the house for 7 years for any reason and pass the payments to the next owner.

2nd to last paragraph:

“Even for the sewer capacity charge example, there’s no guarantee we’ll have to pay it down to $0. We weren’t the first people to live in this house and it’s entirely possible we’ll sell the place and move in the next 7 years. A quarterly $87 charge certainly didn’t make or break our decision to buy the house and I’m sure it wouldn’t for the next buyer either. That means if we pay it off early, but don’t stick around for the full 7 years, we’ll have most likely lost out by paying early, investment gains or not!”

It’s very rare to ever have true “guaranteed returns”. Thanks for reading!

This is what has always led me not to do the calculations. Paying it off may or may not be better, but if I pay it off, i gained no equity because it does not ever play into any future buyers price they are willing to pay.