“I have $30,000 in cash for a down payment on the $300,000 house I am purchasing. I also have $15,000 of credit card debt at 12 percent that I would love to get rid of. The loan officer says I can roll it into a new $285,000 30-year mortgage at 6 percent. This cuts the rate on my credit card debt in half and makes it deductible. Further, my total monthly payment would be only $1891, compared to $2051 if I didn’t consolidate and took a $270,000 loan. Is there any reason I shouldn’t consolidate?”

Yes, appearances to the contrary notwithstanding, this consolidation will make you poorer.

True, the rate on the mortgage is well below the rate on your credit card debt, and mortgage interest is tax deductible as well. However, if you increase the size of your loan from $270,000 to $285,000, you will increase either the mortgage insurance premium or the interest rate on the purchase mortgage. It takes only a 1/4 percent rate increase on $285,000 to offset the savings from a 6 percent rate reduction (including the shift to deductability) on $15,000 of credit card debt.

Consolidation would also reduce your total monthly payment, but that is mainly because you would be paying down your debt more slowly. If you consolidate, you will owe $260,484 at the end of six years, which is your best guess as to how long you will be in your new house. If you don’t consolidate, you will owe only $246,774.

These numbers and the others cited below are drawn from calculator 1a on my Web site. I used this calculator to determine your total costs over six years if you: a) Don’t consolidate, which means you take the first mortgage for $270,000 and leave the non-mortgage debt as is; b) Consolidate in the first mortgage, which means that you take the first mortgage for $285,000 and pay off the non-mortgage debt; and c) Consolidate in a second mortgage, which means that you take out the first mortgage for $270,000 to buy the house, and afterwards you take a second mortgage for $15,000 to pay off the non-mortgage debt.

Based on what you told me, I entered the terms at which you can borrow under all three options. The $270,000 and the $285,000 first mortgages are both no-cost at 6 percent for 30 years — they differ only in the mortgage insurance premium, which the calculator knows. The $15,000 second mortgage is also no-cost at 10 percent for 15 years. You are in the 25 percent tax bracket and want interest loss to be calculated at 2 percent.

The calculator measures cost as total monthly payments over the six-year period; plus the lost interest on those payments (interest that could have been earned but wasn’t); minus the tax savings on interest, including the interest earnings on tax savings; minus the reduction in debt balances over the six years.

Your costs are $89,904 without consolidation, $92,311 with consolidation into the first mortgage, and $89,523 with consolidation into the second mortgage. While consolidation in the first mortgage rids you of the high payments on the non-mortgage debt and increases your tax savings, these are more than offset by higher mortgage insurance premiums and smaller debt reduction. Consolidation with the 10 percent second mortgage, on the other hand, turns out to be slightly profitable.

In making decisions about consolidation, borrowers make two kinds of mistakes. One is to base the decision on the monthly payment, ignoring what happens to the loan balance. This mistake pervades many financial decisions.

The second mistake is for borrowers to decide in advance that they are going to consolidate, and only price mortgages that allow it. Their focus is the cost difference between the non-mortgage debt and the mortgage that would consolidate that debt. They ignore the fact that if they don’t consolidate, their mortgage would be smaller and therefore less costly.

One benefit of using a calculator is the discipline it imposes. It forces you to consider all the options, and to collect all the data required to assess each option.

Some borrowers are allergic to calculators and need a rule of thumb. Unfortunately, the common one that says “consolidation is profitable if the rate on the first mortgage is below the rate on non-mortgage debt,” is wrong most of the time. Replace it with “consolidation is profitable if the rate on the first mortgage is below the rate on non-mortgage debt, and if the rate or mortgage insurance premium on the first mortgage is no higher with consolidation than without.” This one will be right most of the time.

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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