How Do You Know Which Mortgage Prices Are Lower?
August 3, 2009

Consumers shopping for a mortgage are frequently confronted with having to make a choice between complex alternatives. For example, they can select an FRM on which the rate is fixed at 5% for 30 years, or an ARM on which the rate of 4.375% holds only for 5 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.

Ideally, there should be a single measure that captures all the costs. That is the subject of this article.

Annual Percentage Rate (APR)

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 they called the annual percentage rate, or APR. By law, whenever a lender discloses an interest rate, they must disclose the APR alongside it.

The Comprehension Problem: 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 ARMs 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.

The Comprehensiveness Problem: Despite the 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 only taken them 30 years.

Borrower Differences in Time Horizon: 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 2 30-year fixed-rate mortgages, one at 5.125% and zero points, the other at 4.25% and 4.4 points. The first has an APR of 5.125% while the second has an APR of 4.64%, 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 5 years, the APR on the low rate mortgage calculated over 5 years instead of 30 – which I usually call the “interest cost” to distinguish it from the APR -- would be 5.31%, 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 adjustable–rate mortgages (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.

Borrower Differences in Tax Rate: 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.

Borrower Differences in Opportunity Cost: 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%. For others who run businesses that always require capital, it might be 15%. The APR implicitly assumes that the borrower’s opportunity cost is the same as the APR.

In sum, the APR 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.

Time Horizon Cost (THC)

An alternative measure of borrower cost 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 differences between borrowers in time horizon, tax rates and opportunity costs.

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% and zero points, and another at 4.25% 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 4 years, is in the 15% tax bracket, and has an opportunity cost –the return he can earn on other investments -- of 2%.  The THC for the borrower on the 4.25% mortgage consists of the following:  

Total monthly payments of principal and interest over 4 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  

When we do the same for the 5.125% mortgage, the total net cost is $18,768, or $986 less. 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 4 years to 8 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% to 12%, keeping everything else the same, the advantage flips back to the 5.125% mortgage because of the larger interest loss on the points paid upfront. If finally we raise the borrower’s tax rate to 40%, the advantage flips back once more to the 4.25% 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.

All the numbers referred to above were drawn from calculator 9ci, which was programmed to compare the THCs of different FRMs. Other calculators compare different adjustable rate mortgages (ARMs), and ARMs versus FRMs. Stand-alone calculators like mine, however, require the borrower to enter the relevant prices. This is not nearly as useful to borrowers as receiving THCs based on the prices actually being quoted to them by loan providers.

One way that could happen would be that the Truth in Lending Act is revised to replace APR with THC. The likelihood of that happening within my lifetime is vanishingly small. The other way is that a private firm, looking to acquire a competitive advantage, builds 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. 

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