One of the risk measures lenders use in underwriting a mortgage is the mortgage's loan to value (LTV) ratio. A mortgage's LTV ratio is a simple calculation made by dividing the amount of the loan by the value of the home. The higher the LTV ratio, the higher the risk profile of the mortgage. Most mortgages with an LTV ratio greater than 80% require private mortgage insurance (PMI) to be paid by the borrower. And PMI is not cheap. Read on to find out whether you can avoid PMI on your mortgage and, if so, if the alternative will pay off.

TUTORIAL: Mortgage Basics

PMI In Depth
Let's take a look at an example.

Let's assume the price of a home is $300,000 and the loan amount is $270,000 (which means the borrower made a $30,000 down payment) and the LTV ratio is 90%. Depending on the type of mortgage, the monthly PMI payment would be between $117 and $150. Adjustable-rate mortgages (ARMs) require higher PMI payments than fixed-rate mortgages. (To learn more about ARMs, see ARMed And Dangerous or Mortgages: Fixed-Rate Versus Adjustable-Rate.)

However, PMI is not necessarily a permanent requirement. Lenders are required to drop PMI when a mortgage's LTV ratio reaches 78% through a combination of principal reduction on the mortgage and home price appreciation. If part of the reduction in the LTV ratio is realized through home price appreciation, a new appraisal, paid for by the borrower, will be required in order to verify the amount of appreciation. (To learn more about PMI, see Six Reasons To Avoid Private Mortgage Insurance and Will You Break Even On Your Home?)

Easy Way Out
An alternative to paying PMI is to use a second mortgage or piggyback loan. In doing so, the borrower takes a first mortgage with an amount equal to 80% of the home value, thereby avoiding PMI, and then takes a second mortgage with an amount equal to the sales price of the home minus the amount of the down payment and the amount of the first mortgage. Using the numbers from the example above, the borrower would take a first mortgage for $240,000, make a $30,000 down payment and get a second mortgage for $30,000. The borrower has eliminated the need to pay PMI because the LTV ratio of the first mortgage is 80%, but the borrower also now has a second mortgage that in most cases will carry a higher interest rate than the first mortgage. There are many types of second mortgages available, but the higher interest rate is still par for the course. Still, the combined payments of the first and second mortgage are usually less than the payments of the first mortgage plus PMI.

The Tradeoff
When it comes to PMI, a borrower who has less than 20% of the sales price or value of a home to put down as a down payment has two basic options:

  1. Use a "stand-alone" first mortgage and pay PMI until the LTV of the mortgage reaches 78%, at which point the PMI can be eliminated.
  2. Use a second mortgage. This will most likely results in lower initial mortgage expenses than paying PMI, but at the same time, a second mortgage carries a higher interest rate than the first mortgage, and can only be eliminated by paying it off or refinancing both the first and the second mortgage into a new stand-alone mortgage, presumably when the LTV reaches 80% or below (so no PMI will be required).

There are also several variables that can play into this decision, including:

  • The tax savings associated with paying PMI verses the tax savings associated with paying interest on a second mortgage. Tax law in the United States allows for the deduction of PMI for specific income levels, such as families that earn less than $100,000.
  • The cost of a new appraisal to eliminate PMI versus the costs of refinancing a first and second mortgage into a single stand-alone mortgage.
  • The risk that interest rates could rise between the time of the initial mortgage decision and the time at which the first and second mortgages would be refinanced.
  • The different rates of principal reduction of the two options.
  • The time value of money. (Explore this point further in Understanding The Time Value Of Money.)

However, the most important variable in the decision is:

  • The expected rate of home price appreciation

For example, if the borrower chooses to use a stand-alone first mortgage and pay PMI versus using a second mortgage to eliminate PMI, how quickly might the home appreciate in value to the point where the LTV is 78% and the PMI can be eliminated? This is the overriding deciding factor. For simplification, and the purposes of this discussion, we're going to ignore the other variable listed above, as price appreciation dominates these.

Appreciation: The Key to Decision-Making
The key to the decision is that once PMI is eliminated from the stand-alone first mortgage, the monthly payment will be less than the combined payments on the first and second mortgages. So we ask the questions: "How long will it be before the PMI can be eliminated?" and "What are the savings associated with each option?"

Below are two examples based on different estimates of the rate of home price appreciation.

Example 1: A Slow Rate of Home Price Appreciation
The tables below compare the monthly payments of a stand-alone, 30-year, fixed-rate mortgage with PMI versus a 30-year fixed-rate first mortgage combined with a 30-year/due-in-15-year second mortgage.

The mortgages have the following characteristics:

Copyright © 2007
Figure 1

In Figure 2, the annual rates of home price appreciation are estimated.

Copyright © 2007
Figure 2

Notice that the $120 PMI payment is dropped from the total monthly payment of the stand-alone first mortgage in month 60, as shown in Figure 3, when the LTV reaches 78% through a combination of principal reduction and home price appreciation.

Copyright © 2007
Figure 3

The table in Figure 4 shows the combined monthly payments of the first and second mortgages. Notice that the monthly payment is constant. The interest rate is a weighted average. The LTV is only that of the first mortgage.

Copyright © 2007
Figure 4

Using the first and second mortgage, $85 dollars can be saved per-month for the first 60 months. This equals a total savings of $5,100. Starting in month 61, the stand-alone first mortgage gains an advantage of $35 per month for the remaining terms of the mortgages. If we divide $5,100 by $35, we get 145. In other words, in this scenario of slow home price appreciation, starting in month 61, it would take another 145 months before the payment advantage of the stand-alone first mortgage without PMI could gain back the initial advantage of the combined first and second mortgages. (This time period would be lengthened if the time value of money were considered.)

Example 2: A Rapid Rate of Home Price Appreciation
The example below is based on the same mortgages as demonstrated above. However, the following home price appreciation estimates are used.

Copyright © 2007
Figure 5

In this example, we only show a single table of monthly payments for the two options (see Figure 6). Notice that PMI is dropped in this case in month 13 because of the rapid home price appreciation, which quickly lowers the LTV to 78%.

Figure 6

With rapid home price appreciation, PMI can be eliminated relatively quickly. The combined mortgages only have a payment advantage of $85 for 12 months. This equals a total savings of $1,020. Starting in month 13, the stand-alone mortgage has a payment advantage of $35. If we divide $1,020 by 35, we can determine that it would take 29 months to make up the initial savings of the combined first and second mortgages. In other words, starting in month 41, the borrower would be financially better off by choosing the stand-alone first mortgage with PMI. (This time period would be lengthened if the time value of money were considered.)

For borrowers who have less than a 20% down payment, the decision of whether to use a first "stand-alone" mortgage and PMI or use a combination of a first and second mortgage is largely a function of how quickly they expect the value of their home to increase. If they choose to pay PMI, it can be eliminated through an appraisal once the LTV reaches 78%. If they choose to use a combination of first and second mortgages, they are likely to have initial payment savings, but the only way to eliminate the second mortgage, which will likely carry a higher interest rate than the first mortgage, is by paying it off or refinancing both the first and the second into a new stand-alone mortgage. A thoughtful analysis should be conducted to analyze your options based on your time horizon.

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