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 (See
Save With a Large Payment at Closing?). 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 deal is worth revisiting.

## An Irresistible Deal For Payment Myopic Borrowers

The borrower in my example had a 6% loan
with a $200,000 balance and 10 years to go. She is offered a 5.75%
**refinance **for 30 years that will reduce her monthly payment from $2220
to $1267. 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 long way from breakeven.

## A Wealth Analysis of the Deal

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 5 years.

Total payments over 5 years would be $$75,982 if the borrower refinances compared to $133,225 if she doesn’t, a saving of $57,243. However, at the end of the 5 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 pay-down 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 pay-down 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 5 years, the refinance is a loser big time.

These numbers were derived from
**refinance 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 Quicker Approach: Relate Interest Saving to Upfront Cost

A good estimate of the breakeven period is the upfront cost divided by the interest savings. The .25% 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 saving declines 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 saving to cover the upfront cost should be no more than 4-5 years.

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