*Editor’s note: This is the first of a two-part series.*

Deciding whether to refinance can be a complicated decision for borrowers, and a lot rides on getting it right. The good news is that many financial calculators designed to help in the decision process are freely available on the Web. The bad news is that most borrowers have great difficulty finding a calculator that will help them, partly because they aren’t sure what their question is, and partly because many of the calculators are badly designed.

To do it right requires three steps. Step 1 is to clarify the question you want answered. Step 2 is to understand how the question ought to be answered. Step 3, discussed next week, is to find the online calculator that will answer your question properly.

**Formulating the question**

Calculators are designed to answer a specific question, and it is important for the borrower to get the question right before looking for the calculator that will answer it. If your question is whether refinancing will reduce your mortgage payment, for example, you don’t need a refinance calculator — a simple mortgage payment calculator will do.

Most borrowers contemplating a refinance want to know whether the financial gain from a lower interest rate more than offsets the refinance costs. Most of the calculators on the Web are directed to this question. Other reasons to refinance, such as raising cash or consolidating debts, receive little attention, as noted next week.

**Comparing refinance and stay-put scenarios**

A refinance decision involves a comparison of net costs under two scenarios, one where the borrower refinances and the other where he retains his current mortgage, over some future period. The period should be the borrower’s best guess as to how long it will be until the house is sold and the mortgage is paid off. For convenience, let’s assume that period is five years.

In both scenarios, the borrower must pay principal and interest monthly for five years, and the balance outstanding at the end of the period. If he refinances, the new monthly payment and/or the balance after five years may be lower than if he stays put, but the borrower must also pay the upfront cost of refinance.

**Measuring net costs**

Economists would compare the two scenarios in terms of the net present value (NPV) of costs, or net future value (NFV), which if done correctly will always yield the same result. With NPV, all costs are valued at the beginning of the period, whereas with NFV, costs are valued at the end. I use NFV because I find that most people find it easier to grasp.

If the NFV is to be accurate, it must account for everything that impacts the cost net of benefits of both scenarios. This includes a) tax savings on interest and points using the borrower’s tax rate, b) mortgage insurance if it is required, c) the interest loss on payments made upfront and monthly using the borrower’s investment rate, d) whether the borrower elects to pay upfront costs in cash or add them to the loan balance, and e) whether and how the borrower plans to make extra payments in both scenarios.

Here is an example of an NFV calculation. Jones took out a $300,000 30-year fixed-rate mortgage at 6 percent five years ago, which now has a balance of $279,163, and is considering refinancing into a 10-year fixed-rate mortgage at 5 percent with refinance costs of one point ($2,792) plus $5,000 in fees. Jones is in the 31 percent tax bracket, earns 2 percent on his investments, and expects to be in his house another five years. Jones pays upfront refinance costs in cash rather than financing them, does not require mortgage insurance, and does not contemplate making extra monthly payments during the five-year period.

Over the five years, monthly payments will total $69,738 more if he refinances, reflecting the short term on the new mortgage. The refinance also involves $7,792 in upfront refinance costs, $2,975 more lost interest, and $7,791 less tax savings than staying put.

However, Jones will pay down his loan balance by $94,154 more if he refinances, resulting in an overall net gain of $6,738. Breakeven, the period over which the gains just balance the losses, is 36 months. The Web version of this article, at www.mtgprofessor.com, will show the complete breakdown.

I had a reason for selecting this particular example. The entire benefit is in the larger balance reduction, which borrowers preoccupied with the monthly payment — a malady I call "payment myopia" — tend to overlook. A properly designed calculator is not vulnerable to payment myopia.

Next week: How well do Web calculators do?

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