Consumers shopping for a mortgage are frequently confronted with having to make a choice between complex alternatives. For example, they can select a fixed-rate mortgage (FRM) on which the rate is fixed at 5 percent for 30 years, or an adjustable-rate mortgage (ARM) on which the rate of 4.375 percent holds only for five years, after which it changes with the market.

On both loans, furthermore, a lower rate is available if the borrower pays points, an upfront charge expressed as a percent of the loan amount. In addition, borrowers have to pay a variety of fixed-dollar fees to lenders, and other fees to third parties such as title agents and appraisers.

To deal with this problem, the federal government in the Truth in Lending Act decreed that lenders had to disclose one number designed to be a comprehensive measure of all costs, which borrowers could rely on in comparing one loan with another. They called it the annual percentage rate, or APR. By law, whenever a lender discloses an interest rate, they must disclose the APR alongside it.

Developing a composite measure of all mortgages costs was a great idea, but APR is the wrong measure. For one thing, very few borrowers understand it. The APR is expressed as a percent, same as the interest rate, except that the APR is somehow a composite of the percentage rate and dollar costs. How they are combined is a mystery to most. The mystery is even deeper on adjustable-rate mortgages because the ARM rate is subject to unknown change in the future.

Few loan officers or mortgage brokers understand it either. Indeed, within most lender firms the only ones who understand how the APR is calculated are the technologists responsible for having it programmed — and sometimes they get it wrong.

A second problem is that, despite its intent, the APR has never been the comprehensive measure of cost it was supposed to be. A comprehensive measure would cover all costs that would not arise on an all-cash transaction, but in practice third-party charges are not covered.

In principle, this is an easy problem to fix, and the Federal Reserve in recent proposals to amend its Truth in Lending regulations has proposed a fix. It has taken them only 30 years.

The third problem is more difficult. Cost depends not only on the characteristics of the mortgage but also on the characteristics of the borrower. A given set of mortgage features may carry different costs to different borrowers, but this is not reflected in the APR.

The most important difference between borrowers is in how long they expect to be in their house. The APR assumes they will be there for the full term of the loan, which very few are. This can lead to bad decisions.

Consider a borrower choosing between two 30-year fixed-rate mortgages, one at 5.125 percent and zero points, the other at 4.25 percent and 4.4 points. The first has an APR of 5.125 percent while the second has an APR of 4.64 percent, suggesting that the lower-rate mortgage is the better deal. But that is only because the APR is calculated on the assumption that the borrower enjoys the lower rate over the full term.

If the borrower expects to be out in five years, the APR on the low-rate mortgage calculated over five years instead of 30 — which I usually call the "interest cost" to distinguish it from the APR — would be 5.31 percent, and the higher-rate mortgage would be the better deal.

Because of the built-in assumption that the borrower will have the loan for the full term, the APR is also useless to borrowers assessing the cost of ARMs. If the borrower expects to be out of the house before the initial rate period is over, an APR calculated over the full term may be misleading.

If the borrower expects to have the mortgage beyond the initial rate period, or isn’t sure, he needs to know how much risk he faces from interest-rate increases after the initial rate period ends. But the APR doesn’t tell him that.

A second difference between borrowers that the APR does not account for is their tax bracket; the APR is a before-tax measure. Because mortgage borrowers can deduct interest payments and points from their taxes, any measure of cost should be after taxes.

A third difference between borrowers that the APR does not account for is their opportunity cost of funds. Because the upfront and monthly payments required by the mortgage could otherwise be invested to yield a return, that return is a cost to the borrower.

For some borrowers who keep all their money in savings accounts, the opportunity cost might be 1.5 percent. For others who run businesses that always require capital, it might be 15 percent. The APR implicitly assumes that the borrower’s opportunity cost is the same as the APR.

An alternative measure of borrower cost is one I call "time horizon cost," or THC. It makes more intuitive sense to borrowers than the APR and is easier to understand. It is comprehensive in its coverage. And it takes account of important differences between borrowers that affect costs: time horizon, tax rates and opportunity costs. The THC is discussed next week.

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


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