In a recent article on lifestyle mistakes by mortgage borrowers, I gave an example of such a mistake that touched a nerve on the part of some readers. I said in the article that many borrowers would find irresistible the deal I labeled a mistake, and I was right. Some readers did find the deal I described as irresistible, and were completely convinced that I was wrong in saying that it was a loser.

The borrower in my example had a 6 percent loan with a $200,000 balance and 10 years to go. She is offered a 5.75 percent refinance for 30 years that will reduce her monthly payment from $2,220 to $1,267. Although the borrower was not required to put up any cash, upfront charges amounting to $17,000 had to be financed — that is, included in the loan amount.

In a recent article on lifestyle mistakes by mortgage borrowers, I gave an example of such a mistake that touched a nerve on the part of some readers. I said in the article that many borrowers would find irresistible the deal I labeled a mistake, and I was right. Some readers did find the deal I described as irresistible, and were completely convinced that I was wrong in saying that it was a loser.

The borrower in my example had a 6 percent loan with a $200,000 balance and 10 years to go. She is offered a 5.75 percent refinance for 30 years that will reduce her monthly payment from $2,220 to $1,267. Although the borrower was not required to put up any cash, upfront charges amounting to $17,000 had to be financed — that is, included in the loan amount.

The readers who said that this deal would have been irresistible to them focused on payment savings and ignored or understated changes in the borrower’s loan balance. They are payment-myopic, which is a pervasive malady among households who never seem to be able to get out of debt.

The most common approach of my payment-myopic readers was to divide the $17,000 of upfront charges by the $953 of monthly payment savings to derive a "breakeven period" of 18 months. Stay longer than 18 months, they told me, and it is all gravy.

Not so. There is a valid way to calculate a breakeven period, as I will show below, but that isn’t it. The borrower would not have broken even after 18 months because at that point she would owe $35,658 more if she refinanced than if she didn’t. That is a far cry from breakeven.

My preferred way to analyze this type of problem is to estimate the borrower’s wealth if she refinances, compared to what it would be if she didn’t refinance, after an elapsed period equal to the number of years the borrower expects to be in the house. I will assume that period is five years. …CONTINUED

Total payments over five years would be $75,982 if the borrower refinances compared to $133,225 if she doesn’t, a savings of $57,243. However, at the end of the five years, the loan balance if the borrower refinances would be $201,294, a little more than the balance with which she started. This reflects the $17,000 that was added to the balance at the refinancing, and the slow paydown in the early years of a new 30-year loan.

If she didn’t refinance, the balance would be paid down to $114,851, reflecting the rapid paydown on a mortgage that has only 10 years left. The difference in the balances is $86,443, which is $29,200 more than the difference in total payments. Taking account of lost interest and tax savings makes only a small difference in the outcome. Over five years, the refinance is a loser big time.

These numbers were derived from calculator 3a on my Web site. Is there a simple method that doesn’t require a calculator but gives a tolerably accurate answer? There is, and I use it myself when I’m hurried.

A good estimate of the breakeven period is the upfront cost divided by the interest savings. The 0.25 percent reduction in the interest rate is worth $500 a year at the beginning. Dividing the upfront cost of $17,000 by $500 gives a breakeven period of 34 years. This is an underestimate because the interest savings decline over time as the balance is paid down. I ignore the extension of the term from 10 to 30 years because that is neither a cost nor a benefit. On a refinance that works, the period required for the interest-rate savings to cover the upfront cost should be no more than four to five years.

The writer is professor of finance emeritus at the Wharton School of the University of Pennsylvania. Comments and questions can be left at www.mtgprofessor.com.

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