Running through payback time on a mortgage refinance

Five Cent Nickel posted on how to calculate the payback period for a potential mortgage refinance.  It's indeed important to figure this out before paying for a refinance that might never save any money.  (There are plenty of ways to blow money that are more fun than going through a mortgage refinance.  Trust me!)

Nickel got my attention on this one because he posted this formula:

Payback Period (in months) = Closing Costs / Monthly Savings

The costs of closing the mortgage refinance can be added up (and should be able to be added up, meaning that these shouldn't be a secret).

But what is this “monthly savings” amount?  Getting this right is important.  It's not just taking the difference of your payments before the refinance and after the refinance, because you could have exactly the same payment, or higher, after a refinance, and still come out ahead after a relatively short period of time.

Here is how I'd do the calculation instead.

1. Get the amortization schedule for your current loan, one that breaks down the principal and interest payments.
2. Create another one for your new loan terms.
3. Call your next payment on your current loan “Old Payment #1.”
4. Call your first payment on your (proposed) new loan “New Payment #1.”
5. Subtract the principal part of Old Payment #1 from the principal part of New Payment #1.  This is the amount extra that you're paying your loan down on Payment #1.
6. Subtract the interest part of New Payment #1 from the interest part of Old Payment #1.  The is the amount of interest savings that you accomplished on Payment #1.
7. Add these two differences to a running total.
8. Repeat Steps 5 through 7 with subsequent payments until the running total exceeds your closing costs.  The payment at which this happens is (roughly) your payback period.

Let's try an example.  Say I was five years into a 30-year loan with original principal of $100,000 and a rate of 6.5%.  Using the mortgage calculator, my monthly payment (principal and interest) is $632.07 and I'd have $93,610.81 left on the loan after payment 60.

Now let's say I could refinance for a total cost of $4,000 to a 15-year loan at a rate of 4.75%.  If I refinance all of my principal at that time ($93,610.81) then my payment will increase to $728.13.

Payment #61 on my current loan becomes Old Payment #1.  Payment #1 on the refinanced loan becomes New Payment #1.  The amount extra I'm paying down principal is $357.59 – $125.01, or $232.58.  The amount of interest I'm saving is $507.06 – $370.54, or $136.52.  Adding these two differences gives me $232.58 + $136.52, or $369.10.

Now, if we just use this one amount ($369.10) to make a quick and dirty estimate, we can say that this amount will be the lowest monthly amount that we'll save.  This is true; it just gets better.  So, now we can use Nickel's formula to get a conservative estimate of the payback time:  $4,000 divided by $369.10 is almost 11 months.

In fact, this quick and dirty estimate is pretty good.  If I go through and add up all of the savings through Payment #10, I get $3,757.82, which is just a little shy of $4,000.  So the quick and dirty estimate got it right to within a week or two.  This is so, because the monthly saving doesn't change much over the course of the payback period (the first payment's savings was $369.10, and the average over the first ten payments was $375.78).

There are other factors that could affect evaluation of the payback period:

• Lost federal income tax deduction if you itemize. Since you're paying about $1,500 less in mortgage interest after the refinance during the payback period in the example above, your tax bill will be a few hundred dollars more than if you hadn't refinanced.  This will effectively add a month or so to the payback period.
• What about just paying more principal on the current loan? The payment after the refinance in the example above is higher after the refinance.  What would throwing an extra $95 per month at the principal do?  This speeds things along, too, and costs nothing.  Ultimately, though, refinancing wins out if you keep the loan more than a year, but making the same dollar payments on the current loan and the new loan extends the payback period of the refinance a few months.
• Lost interest, but only slight. You might say, “Well, my payment is higher, and I could have had that money working for me in a savings account.”  The difference in this case would be $20 total — not worth worrying about.

These last three are probably small corrections.

In short, you can get a very good idea of the payback period by calculating the first month's savings (using Steps 1 through 7), plugging it into the formula, and adding a few months for good measure.

(Note:  Thanks to Pecuniarities for including this post in the Carnival of Personal Finance!)