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

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

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

The

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

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

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