“I have been shopping online for a 30-year fixed-rate mortgage. All the sites ask you how much you want to put down, and all offer different combinations of interest rate and points. I have cash of only \$15,000 to apply to either down payment or points on my \$500,000 purchase, but obviously I can’t use it for both. Where do I get the biggest bang for my buck?”

Using your cash to pay points lowers the interest rate. (Points are upfront payments expressed as a percent of the loan). Using your cash for down payment reduces the amount you must borrow, and might or might not reduce the rate on the second mortgage if there is one, or reduce the mortgage insurance premium if there isn’t.

Which use of cash generates the lowest cost? There is no general answer to the question; every case is different. To answer the question in individual situations, Chuck Freedenberg and I developed a calculator that shows the total cost of any allocation of cash, over any time period specified by the user.

Cost includes upfront payments and monthly payments, plus the interest lost on those payments at the rate specified by the user. (This is sometimes called an “interest opportunity cost” because it refers to the return you could have earned on the cash used to make upfront or monthly payments.) Deducted from these costs are the tax savings at the user’s tax rate, and the reduction in the loan balances.

To use your case as an illustration, I shopped a 30-year fixed-rate mortgage on www.Amerisave.com, which is one of the sites that offer many rate/point combinations. I assumed you were purchasing a single-family home as your permanent residence, have good credit, can fully document your income and assets, are in the 27 percent tax bracket, and have an interest opportunity cost of 5 percent.

On the day I shopped, using your \$15,000 for down payment would have resulted in a first mortgage of \$400,000 at 7.375 percent and a second mortgage of \$85,000 at 7.75 percent. If instead, the \$15,000 had been used to pay points, the rate on the first mortgage would drop to 6.375 percent, and while the second mortgage rate would remain at 7.75 percent, the amount of the second would increase to \$100,000.

The period you expect to have the mortgages is a critical factor. In general, the longer you have the mortgages, the stronger the case for paying points, since the savings from the lower interest rate accumulate month by month while repayment of the larger balance on the second mortgage is deferred.

I used the calculator to assess your deal over two, five and 10 years. Over two years, paying points was a big loser. Over five years, however, paying points provided modest cost savings, and over 10 years the savings were very large.

I wondered whether the results would be the same for a borrower with \$25,000 to use in the deal, who was otherwise the same. If this borrower used the \$25,000 for down payment, he would pay 7.125 percent on the first mortgage of \$400,000, and 7.25 percent on the second of \$75,000. If he selected the lowest-rate/highest-point combination available, which would leave him with \$5,000 for down payment, his rate on the first mortgage would drop to 6.125 percent, but his rate on the second (now for \$95,000) would increase to 7.75 percent. Paying points would be a loser in this case over two years and over five years, with only moderate savings over 10 years.

The finding that the borrower with less cash does better allocating it to points than the borrower with more cash seems to be counterintuitive. The reason it works that way is that the borrower with less cash is already paying the maximum rate on the second mortgage, while paying points drops the rate on the first mortgage.

I strongly advise borrowers not to rely on any such generalizations, however, and to use the calculator to assess their own individual situation. It accommodates mortgage insurance as well as piggyback second mortgages. Don’t allow yourself to be shoehorned into a deal that may not be in your best interest without checking it out.

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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