As indicated last week, the annual percentage rate (APR) that the law requires mortgage lenders to disclose alongside the interest rate is not a useful measure of cost to the borrower. Expressed as a percent, it makes no intuitive sense to most borrowers, does not yet cover all costs, and does not take account of differences in borrower time horizons, tax rates and opportunity costs. A much more useful measure is the "time horizon cost" (THC) that is described below.

The THC is the total cost of the mortgage in dollars over the period the borrower expects to be in the house. I will illustrate it with the example I used last week of a borrower choosing between a fixed-rate mortgage (FRM) at 5.125 percent and zero points, and another at 4.25 percent and 4.4 points.

As indicated last week, the annual percentage rate (APR) that the law requires mortgage lenders to disclose alongside the interest rate is not a useful measure of cost to the borrower. Expressed as a percent, it makes no intuitive sense to most borrowers, does not yet cover all costs, and does not take account of differences in borrower time horizons, tax rates and opportunity costs. A much more useful measure is the "time horizon cost" (THC) that is described below.

The THC is the total cost of the mortgage in dollars over the period the borrower expects to be in the house. I will illustrate it with the example I used last week of a borrower choosing between a fixed-rate mortgage (FRM) at 5.125 percent and zero points, and another at 4.25 percent and 4.4 points. The loan amount is $100,000 and settlement costs other than points are $1,000 in both cases.

I am going to assume initially that the borrower expects to be in the house four years, is in the 15 percent tax bracket, and has an opportunity cost — the return he can earn on other investments — of 2 percent. The THC for the borrower on the 4.25 percent mortgage consists of the following:

Total monthly payments of principal and interest over four years: $23,613
Lost interest on monthly payments: $803
Points paid upfront: $4,400
Other settlement costs paid upfront: $1,000
Lost interest on points and other settlement costs: $380
Total costs: $30,196

From these costs, we subtract cost offsets:

The borrower’s tax savings on interest: $2,548
The borrower’s tax savings on points: $700
Reduction in loan balance: $7,195
Total offsets: $10,442

Total cost net of offsets: $19,754 …CONTINUED

When we do the same for the 5.125 percent mortgage, the total net cost is $18,768, or $986 less. (Note: The detail is omitted to save space, complete data will be available on my Web site.) The high-rate mortgage with zero points is the better deal.

But the results are sensitive to the specific features of the borrower. If we change the borrower’s time horizon from four years to eight years, the results are reversed, with the low-rate mortgage becoming the better deal because the lower rate extends over a longer period.

If we then raise the borrower’s opportunity cost from 2 percent to 12 percent, keeping everything else the same, the advantage flips back to the 5.125 percent mortgage because of the larger interest loss on the points paid upfront. If finally we raise the borrower’s tax rate to 40 percent, the advantage flips back once more to the 4.25 percent mortgage because of the larger tax savings on the points.

In using the THC, there is no need for borrowers to become enmeshed in the details. So long as they have confidence in the source, many — perhaps most — borrowers will be satisfied with the single bottom line number. Borrowers seeking understanding, however, have access to the detail that will help them understand why the results are what they are. This educational process is not possible with the APR.

It could be particularly useful to borrowers if the Truth in Lending Act is revised to replace APR with THC, which would provide THCs based on prices actually being quoted to them by loan providers. The likelihood of that happening within my lifetime is vanishingly small.

The other way to accomplish this is for a private firm, looking to acquire a competitive advantage, to build THC into its loan origination platform as a way of creating additional value for borrowers. I am quite confident that that will happen during my lifetime.

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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