Larry Swedroe posted an **interesting article** on how to do the math on a mortgage refinancing to find out whether or not it’s to your benefit to refinance. He used the following example:

• 12 years left on a 15-year mortgage.

• Current mortgage rate is 4.75%.

• Current monthly payment $1,369

• Current balance on the mortgage around $150,000 (this is the amount to be refinanced).

This couple is looking to refinance into:

• 15-year mortgage.

• $150,000 loan.

• $3,000 in closing costs (to be paid upfront).

This couple is in the 25% income tax bracket.

So…based on those numbers, would it be a good idea to refinance?

Well, as Larry points out, there are a lot of things to consider before jumping into a refinance.

1. In this example, the spread between the two interest rates is less than a 100 basis points (less than one percent). Naturally, the bigger the spread, the more advantageous it is to refinance.

2. There is more to the calculation than simply looking at the difference in payments since the payment includes principal, which is your own money. So, we have to look at the difference in the interest portion of the payment.

3. As Larry also points out, interest payments are tax deductible (if you itemize your deductions). Larry uses the 25% income tax bracket for his example. Based on that, the couple is paying $.75 for each $1.00 of interest. Basically, what this means is that this makes the refinance less advantageous (you’ll see this in the spreadsheet).

4. This couple is already three years into their loan. They are looking to refnance into a new 15-year mortgage. That means they have paid 3 years of interest on the old loan and will be paying 15 years of interest on the new loan for a total of 18 years of interest.

5. The closing costs are paid upfront.

After running the example, I came to the conclusion that refinancing this loan will cost an additional $702 in after-tax interest. I arrived at this number by adding up the three year’s of interest paid on the original loan plus the 15 year’s of interest on the new loan. Were they to continue with the old loan, they would have paid a total of $70,417 in interest ($52,812 after-tax in a 25% income tax bracket).

What Larry leaves out, in my opinion, is a discussion of the opportunity cost between the two loans. By choosing to refinance, this couple would be freeing up cashflow that could be put to work elsewhere (unless they are using the cashflow to shore up their budget). The payment difference of $296 per month could be invested elsewhere for the next 12 years. Using a monthly total return on the S&P 500 Index of .75% (including a management fee), that $296 per month payment difference could grow to more than $112,000 in 15 years. If they invested the $3,000 plus the entire $1,369 monthly payment for 3 years after the end of the original mortgage, they would have over $60,000 at the end of 15 years. Another thing worth mentioning is that all of the $296 per month could be put into a Roth IRA where only a portion of the $1,369 payments could be put in a Roth because they would exceed the Roth limits.

Based on those numbers, the refinance looks like a no-brainer. But, I left out three things: 1. Investing in the stock market is not a sure thing and 2. I didn’t make adjustments for taxes, which favored the refinance. 3. In order for the scenario to work, the payment difference MUST be invested and not spent.

With that said, I am making available the spreadsheet I used for this post, which you can download here: **Mortgage Amortization Comparison (Two 15-year Mortgages)**. I didn’t spend a lot of time making it user-friendly but if you understand the basics of Excel, you can get in there and change up the variables yourself.

I haven’t checked out the sheet, but two points:

1. The tax-deductibility of the interest payment is partially cancelled out by the taxability of the dividends and capital gains generated by the laternative investment. (Possibly more than cancelled out if you account for the standard deduction.)

2. You should not just add up the total interest paid to conclude that one scenario is better or worse than the other. You should do a discounted cash flow.

In my case, I found that taking a 30-year instead of a lower-interest rate 15-year reduced my monthly PAYMENT (not only interest). I calculated that if I invested that money and achieved a 5% return, I would have enough saved after 15 years to continue payments for the remaining 15 years, depleting the saved amount and it’s compounded earnings over that 15-year period.

I decided that 5% should be achievable over the next 15 years, so I went with the 30-year. If we experience rampant inflation I will be even better off.

Good point, Mark.

Mark,

Regarding discounting…if you discount both examples at the same discount rate, aren’t the results the same–just different numbers?

I have a question about the tax deductibility of the interest. The standard deduction is $11,400. Depending on the couples income and other deductions, they may never get to itemize deductions and get the tax break for the interest. Am I missing something?

EZ,

True. However, property taxes, state and local taxes, and charitable contributions might be enough to get them over the threshold.

I think Mark (and you too JLP) are both talking about using the house as leverage/debt to invest in the stock market for a potentially higher return.

Nothing wrong with that as long as everyone understands the risk involved with this type of plan.

There are a lot of people in California that did just this: maxed out the mortgage debt only to see house prices plummet (along with stocks), leaving them upside down on the mortgage and a bunch of (unrealized) losses in the stock market.

Either way, you are comparing apples & oranges: I don’t think the decision on whether to refinance or not should include what-if scenarios of potential returns in the stock market — when looking at whether to refinance.

For me to refinance, the refinancing numbers need to stand on their own. Is loan A better or worse than loan B, after adjusting the payment amounts to match. This means that the new 15-year mortgage (B) needs to have less interest paid to the bank than loan A, assuming that loan B will be pre-payed just enough to match the original loan A’s payments. Also, assume that loan B’s principle is higher than loan A due to the closing costs for the refinance (or you just prepay loan A with the closing costs and don’t do the refinance).

BTW, JLP: you didn’t state what the new loan’s interest rate is. Checking the linked article the new loan is @3.875%.

EZ, no you’re not missing anything. You’re correct that sometimes the interest doesn’t benefit people from a tax-standpoint, most likely found in the latter years of a mortgage when most of your payment is princ. rather than int. The only time it might make a difference is if you have a home office and are splitting your mortgage interest and real estate taxes between tax forms–Sch A and Sch C.

To respond to JLP’s #3 comment: Interest, dividend or cap gain income from the “investing” the difference would increase one’s AGI. Thus anything dependent on AGI would be impacted: IRA contribution eligibility, the deductibility of medical expenses, phasing out of itemized deductions or personal exemptions, etc.

If the plan was to pay down the mortgage as quickly as possible and not invest the difference then your 1040 would obviously have both decreased AGI (b/c you’re not investing the diff) and decreased mortgage interest deduction. If you don’t have enough mortgage interest deduction (and other deductions) to itemize, then paydown of mortgage w/no investment would appear to be the better tax choice.

Mark,

First, thanks for your blog – love what you post.

I replied on the Wise Investing site – the following>

Nice article.

2 comments:

Spending $3K to refi, saves $269/month. Simplisticly, it takes about 11 months to pay for itself, then added benefits.

Key is to continue paying the current payment, after the refi, so the loan will payoff in less than the current 12 years remaining. I don’t like lowering the payment and paying more years. Never ending cycle if you keep refinancing every 2 yrs because rates are 1% lower.

Example: In 5 yrs, it will be a 1.875% rate and you’ll still have 15 years left on the loan…

**My most recent refi, I went from a 30yr to a 20yr, so I got to cut years, and interest.

Just ran some numbers:

Original loan: $150k loan @4.750 for 12-years: $47,078 interest

Refi loan: $153k @3.875 for 15-years: $48,988 interest

Refi loan + prepay diff: $153k loan @3.875 for 15-years, prepaying $246.44/month: $37,115 interest

Original loan + prepay closing costs (by not refinancing): $150k loan @4.750 for 12-years, prepaying $3k in first month: $44,809 interest

The best move, IMHO, would be to refinance the loan, roll in the closing costs, and prepay the new 15-year mortgage by $246.44/month (hence keeping your payments the same). You would earn $7,694 over the second best move.

Now, if the couple is already prepaying their existing mortgage (like I do), then that changes the numbers and these calculations would need to be redone with that new information.

Oops, technically the earning is $4,694, not $7,694. I mistakenly forgot the $3k principal that was added to the refi’s balance.

@BG:

I wasn’t necessarily talking about sticking money in the stock market. I suspect that some time in the next 30 years, even a federally-insured CD at a bank will earn more than my mortgage interest rate.

Even those silly Californians you refer to are only in trouble if they over-extended themselves or have short-term needs. The mortgage being underwater is irrelevant – the only relevant question is whether in the long run it was cheaper to borrow money and pay it off slowly or quickly. And that depends on future interest rates and inflation, not the value of their homes.

You also said that the refinance decision has to stand on it’s own. You may not want to base it on potential stock-market returns. But I think you DO have to consider potential future inflation, your own future earnings, etc. You may have the opportunity to repay with money that is worth significantly less to you (either really less due to inflation, or notionally less due to your own higher income).

Looking back at my own experience: I have been exceptionally fortunate and I now earn 4 times what I earned 20 years ago (in nominal dollars). I paid extra principal to knock off my first mortgage back then, but now I realize how easy it would be today to write that little check each month. To understand the feeling think of your house-payment. Now think of it divided by 4 – is that an easy number or what!

I think it is 100% wrong to simply add up the total interest payments and take the loan with the lower number. That’s like saying you value a dollar 15 years from now equal to a dollar today. As soon as you are willing to assume a dollar may buy less 15 years from now, you have to make another assumption: How much less? And as soon as you do that, the refinance decision no longer stands alone.

If you had the money available, and plenty of other money to cover other expenses, would you pay cash for your house? My answer was yes on past mortgages, and would be yes today IF interest rates were higher. but right now it is NO. We are living in a time of very low inflation and interest rates, and I don’t believe either will last 30 years.

In the 1980’s my IRA was invested in a 1-year CD, paying 10%. I also lived through a period when inflation was higher for an extended period. Not hyper-inflation, “just” 8%. Nine years of 8% inflation halves the value of a dollar, which halves the pain of the mortgage payment.

@JLP: Re discounting: I am looking at saving money over the first 15 years which I spend over the second 15. You can think of a 30-year mortgage as a partially amortized 15-year. At the end of 15 years, you have a sum of money saved up. Depending on the rate of return you have earned in 15 years of saving/investment, you may have enough to either pay off the remaining principal (probably not) or make payments for the next 15 years using that money. Not sure if discounting both is the same due to the 15-year time-shift.

Mark) All good points you make. The point I was making is that it still makes sense to do the refinance, and keep the risk levels the same. Basically the couple could earn almost $5k just from an accounting trick (take out the refi, and prepay the difference). The risks are the same, and they make money — it’s guaranteed!

All of the ways you mention, require taking on more risk to get that ‘potential’ higher-return — it’s not guaranteed. What you are doing is leveraging your house to amplify the gains/losses in the other investment.

If you think that inflation is a sure thing, and also thing that stock returns will beat mortgage rates — then opt for the interest only mortgage. (go all in).

Another idea to get guaranteed money (with no extra risk). Refi the house into a 30-year fixed — this should free up a bunch of monthly cashflow.

With that extra monthly-cashflow, either prepay the mortgage, or buy FDIC-insured CDs: depending on which is paying the higher rate that month.

Simple as that — easy money management, for the risk adverse. This strategy should handle your inflation concerns nicely.

@BG: I agree with you on both the points you made above:

1. I would defintely take the interest-only loan if I could get it at the same low interest rate, fixed for 30 years. (Unfortunately many of the interest-only loans are not fixed-rate nor for 30 years. Bankers have to eat too you know, and sometimes they have to eat your children!) I would have to have the discipline to save the principal and have it ready at the end.

2. Re-fi into a 30-year fixed is almost certainly the best option for many people.