(This is Part 6 of a seven-part series. See Part 1: Mortgage shopping: what you should know before you begin; Part 2: Pros and cons of fixed, adjustable mortgages; Part 3: Three options available on most mortgages; Part 4: How long should you take to pay off your mortgage? Part 5: Investment returns influence real estate down payment and Part 7: Navigating real estate loan locks, docs.)

Borrowers who make down payments of less than 20 percent are charged for the risk they impose on lenders. The charge can take three different forms: private mortgage insurance (PMI), lender-provided mortgage insurance (LPMI), and a higher-rate second or “piggyback” mortgage. Borrowers often have a choice between two and sometimes all three.

With PMI, the borrower pays a premium to a mortgage insurance company selected by the lender. The premium covers the entire loan amount, is not tax deductible, and is in force until terminated. PMI can usually–although not always–be terminated when the loan balance declines to 80 percent of current property value.

With LPMI, the lender purchases insurance from a private mortgage insurance company, and passes the charge on to the borrower in a higher interest rate. The higher rate remains in force until the loan is paid off, but it is tax-deductible.

Under the piggyback arrangement, the borrower takes out two mortgages; a first mortgage for 80 percent of property value, and a second mortgage for the balance of the funds needed. The second mortgage carries a higher rate, and it is tax-deductible.

I frequently receive letters asking me whether LPMI will be less costly than PMI, or whether a piggyback will be less costly than LPMI or PMI. Unfortunately, the answer to these questions can vary from case to case–no general answer is possible.

For example, assume that “Henry” is purchasing a $400,000 house and he can afford to put 3 percent down, which is $12,000. If he finances the purchase with a 30-year fixed-rate mortgage (FRM) of $388,000 at 6 percent and pays for PMI, his annual premium is 0.96 percent of the loan balance, which in the first year amounts to $310.40. Over 10 years, his pre-tax total mortgage cost including all payments and lost interest at 3 percent, less balance reduction, amounts to $284,700. These costs and those cited below are derived from calculator 14b on my Web site.

If Henry takes the same mortgage but purchases LPMI instead of PMI, he avoids the mortgage insurance premium but pays a rate of, say, 6.525 percent instead of 6 percent. His total mortgage cost over 10 years is also $284,700.

If Henry goes the piggyback route, he gets a first mortgage of $320,000 at 6 percent but must pay (say) 8.5 percent on the $68,000 second mortgage. In addition, he has to pay (say) 0.82 points on the first mortgage to cover the added processing expense. You guessed it: his total mortgage cost over 10 years is also $284,700.

Of course, they all came out the same because I juggled the assumptions to make them come out the same, in order to make a point. Since the assumptions are completely plausible, it is clear that any one of the three can have the lowest cost. For example, dropping the LPMI rate below 6.525 percent will lower the cost of that option, and dropping the cost of the piggyback below 8.5 percent will lower the cost of that option.

In a market setting, the different options are likely to be offered by different loan providers, in which case there can also be differences in points and other lender fees. These complicate the issue enormously if you are trying to sort it out in your head, but calculator 14b handles them with no problem.

If I were designing the housing finance system from scratch, it would use LPMI alone. Three options for accomplishing the same objective complicate things unnecessarily. LPMI makes it easy for borrowers to shop, and provides maximum incentive to lenders to negotiate insurance prices with mortgage insurers. But so long as the system we have offers the three options, borrowers need to be able to figure out which option is best for them. None of them are best for everyone.

The writer is Professor of Finance Emeritus at the Wharton School of the University of Pennsylvania. Comments and questions can be left at http://www.mtgprofessor.com.

***

What’s your opinion? Send your Letter to the Editor to opinion@inman.com.

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