L. Lee Colquitt is an Assistant Professor of Risk and Insurance, Department of Finance, College of Business, 303 Business Building, Auburn University, AL 36849-5245; phone: (334) 844-3010; fax: (334) 844-4016; email: COLQUITT@business.auburn.edu.

V. Carlos Slawson, Jr. is an Assistant Professor of Real Estate, 2164 CEBA, Department of Finance, E. J. Ourso College of Business Administration, Louisiana State University, Baton Rouge, LA 70803; phone: (504) 388-6238; fax: (504) 388-6366; email: fislaw@UNIXl.sncc.lsu.edu

In the past five years, articles have been written which provide an overview of the home purchase and refinancing decision [See Storms (1992) and Walden (1992)]. These articles include a review of such issues as qualifying ratios, points, down-payments, and mortgage terms. Most of the issues discussed in these articles are still relevant today. However, the premium structure for private mortgage insurance (PMI) has changed considerably, and a homeowner's familiarity with this change in PMI can save him or her thousands of dollars. Richard J. Roll, president of the American Homeowners Association (AHA) believes that "well over a million homeowners paying PMI are currently eligible to stop making these payments." [Anonymous, "Homeowners"]

The objective of this article is to explain the purpose and cost of PMI and to provide the homeowner with an understanding of the rates of return that can be achieved by investing in home equity and thereby eliminating unnecessary PMI premiums. This is achieved by, first, explaining the purpose of PMI and how the premium structure of PMI has changed over the last few years, and, second, providing an explanation and examples of the benefits of investing in home equity. Lastly, other issues affecting the home equity investment decision are addressed, such as the illiquidity of home equity and possible changes in the tax law.

**The Purpose of PMI**

Several years ago, lenders typically did not lend more than 80% of the appraised value of the home underlying a mortgage loan due to the dramatic increase in the default risk associated with high loan-to-value mortgages. As a result, many individuals with a down-payment of less than 20% found themselves unable to finance the purchase of a home. [1] However, PMI has made it possible for many of these individuals to become homeowners.

PMI is mortgage guarantee insurance offered by the private insurance market. Lenders typically require PMI on conventional mortgages that have loan-to-value ratios of greater than 80% and are sold on the secondary market. PMI protects the holder of a mortgage from complete loss in the event that a borrower defaults on the mortgage. The mortgage insurer assumes all or part of the default risk in exchange for consideration: a premium. While the lender enjoys the protection of the PMI, it is the borrower who pays the PMI premium. Currently, PMI premiums can be as high as $1,500 per year for a mortgage on a $200,000 home. [2]

**PMI Premiums: Past and Present**

In the past, a significant charge for PMI was made at the beginning of the mortgage. In Storms' 1992 article, he reported that private mortgage insurers were charging 2.2% of the loan amount up-front to pay for private mortgage insurance. However, the premium payment structure for PMI has changed considerably during the last several years. Instead of charging the cost of PMI at closing, these premiums are spread out over the life of the mortgage. This change has made the elimination of future PMI premiums an attractive option for those who have recently financed a home with a down-payment of less than 20%.

Currently, the monthly premium for PMI for the first 20 years of a 30-year mortgage varies with the size of the down-payment. For a mortgage with a loan-to-value ratio of 95% (a down-payment of 5%), a typical monthly PMI premium is 0.78%/12 of the initial mortgage amount. A 90% loan-to-value ratio (a down-payment of 10%) requires a monthly premium of 0.52%/12 of the initial mortgage amount, and a mortgage with a 85% loan-to-value ratio (a down-payment of 15%) requires a monthly premium of 0.32%/12 of the initial mortgage amount. Beyond 20 years, the monthly PMI premium changes to 0.20%/12 of the initial mortgage amount, regardless of the size of the down-payment. In each case, the insurer normally collects an escrow equal to two months' premium at the beginning of the mortgage.

One interesting aspect of PMI is that, when determining the premium to be paid for PMI, the insurer normally does not take into account the true difference in default risk from one mortgagor to another. In most cases, the insured is evaluated simply as being either an acceptable or unacceptable risk. However, beyond being either an acceptable or an unacceptable risk, no consideration is given to the financial stability of the mortgagor. The premium paid for PMI is determined solely by the amount of the mortgage and the size of the down-payment made by the mortgagor. (Its size affects the amount of a potential claim.) Therefore, two insurable mortgagors with equally priced homes and equal down-payments pay the same PMI premium, regardless of the true default risk of one relative to the other. As a result, a mortgagor who is considered a low default risk is subsidizing the PMI premiums of other, higher default risk mortgagors.

**The Value of an Investment in Home Equity**

In evaluating the home equity investment decision, this article explores the effects of PMI on the portfolios of two different groups: (1) those obtaining a mortgage (whether by purchasing a new home or refinancing their current home) and (2) those who already own a home and are currently paying PMI as a part of their monthly mortgage payment. Although PMI is necessary and beneficial to many individuals, we conclude that some individuals purchasing or refinancing probably should avoid paying any PMI premiums. Similarly, many homeowners who initially were required to purchase PMI should terminate the PMI as soon as it is financially feasible. Assuming that an individual has the funds needed to make the minimum down-payment that is required to secure a home mortgage, another premise of our discussion is that he or she has additional cash which can be invested in either home equity or other investments. Such an individual has the option of making the minimum down-payment and investing the remaining cash in other assets or making a larger down-payment.

To determine the attractiveness of one investment option relative to the other, the risk and returns of both options must be estimated. Ignoring the cost of PMI and the home mortgage interest tax deduction, the after-tax return on an additional investment in home equity is simply the mortgage rate of interest. Although returns of other investments may be as attractive as the mortgage rate of interest, the risk of many of these investments may be much greater.

With the current low mortgage rates and recent gains in the stock markets, investing funds outside of the home appears to be a fairly attractive option. In addition, having the extra liquidity of cash invested in stocks or bonds provides further support for this investment strategy. Finally, taking into consideration the home mortgage interest tax deduction, is there any scenario where investing funds in home equity would be the optimal investment strategy? [3]

While the promise of higher investment returns, additional liquidity, and the home mortgage interest tax deduction provide significant motivation for making a minimum down-payment on a home, when PMI premiums are considered, the minimum down-payment strategy becomes much less attractive.

**Avoiding PMI** - Compared to the rates of return that can be achieved on relatively low risk
investments today, the returns on investing in home equity to avoid unnecessary PMI premiums are
considerably higher. Assume, for example, that an individual has a 7.5% fixed, 30-year mortgage
on a $200,000 home with a down-payment of 10%. As seen in Table 1, given that the homeowner
will remain in the home for the life of the mortgage and considering the current full mortgage interest
tax deduction, the pre-tax rate of return needed on cash invested outside of the home is 14.51%
before this option is as financially attractive as investing in home equity. [4] In the event that the
homeowner is expecting to have the mortgage for only seven years [5], the pre-tax rate of return
needed on cash invested outside of the home is 13.88%. Unless liquidity is a significant issue to the
homeowner, investing in home equity is the preferred strategy.

**Table 1****: Down Payment Options with PMI and the Mortgage Tax
Deduction*******

**Assuming a 7.5% fixed, 30-year mortgage on a $200,000 home**

Down-payment percentage | 5% | 10% | 15% | 20% |

Down-payment (initial home equity) | $10,000 | $20,000 | $30,000 | $40,000 |

Monthly house payment | $ 1,329 | $ 1,259 | $ 1,189 | $ 1,119 |

Two months PMI escrow | $ 247 | $ 156 | $ 91 | n/a |

Monthly PMI premium (years 1-20) | $ 124 | $ 78 | $ 45 | n/a |

Monthly PMI premium (years 21-30) | $ 32 | $ 30 | $ 28 | n/a |

Pre-tax rate of return needed on equity outside of the home (in the home for the life of the mortgage) | 14.81% | 14.51% | 15.75% | n/a |

Pre-tax rate of return needed on equity outside of the home (in the home for only seven years) | 14.24% | 13.88% | 14.92% | n/a |

*Assumes a 28% marginal federal tax rate and no state tax

Return to the top of this table.

Go to the spreadsheet calculations in the Appendix

**Terminating PMI** - Given the low interest rates of the past few years, many individuals have
recently purchased a new home or refinanced their existing home. Because PMI premiums are
today paid over the life of the mortgage, rather than in advance, many homeowners with no plans to
refinance still can save thousands of dollars by eliminating future PMI premiums.

In order for PMI premiums to be terminated, two things must occur. First, the homeowner must supply proof of the current value of the home by obtaining an appraisal. Second, the homeowner must reduce the loan-to-value ratio to 80% or below. This reduction might have occurred already as a result of principle being paid over the life of the mortgage, appreciation occurring since the purchase of the home, or a combination of both.

Assume, for example, that a home has appreciated and the loan-to-value ratio has fallen to at least 80%. The only cost required to terminate PMI would be that of an appraisal (normally between $300-$600). If the appraisal showed that the home had appreciated to the point where the loan-to-value ratio fell to 80% or below, then the borrower would simply have to notify the lender of the appraisal results and request that the PMI be terminated.[6]

To determine the attractiveness of this option, the cost of the appraisal is simply compared to the present value of the future PMI premiums that would be eliminated by demonstrating an 80% or lower loan-to-value ratio. Only in cases where the remaining life of the mortgage is expected to be very short--perhaps as short as 3 months on a $200,000 mortgage (.0078/12 x 200,000 x 3 = $390 = the approximate cost of an appraisal--would this option not be beneficial to the borrower. Assuming that the homeowner plans to remain in the house for six months or longer, the rate of return earned on the investment in the appraisal is remarkable.

The home equity investment decision is slightly more complicated when a homeowner's loan-to-value ratio is above the 80% needed to terminate PMI. In this case, the mortgagor must decide whether it is worth the investment in an appraisal and additional home equity in order to have the PMI terminated.

Consider, for example, an individual who assumed an 8%, 30-year fixed mortgage one year ago with a 10% down-payment on a $200,000 home. Also, assume that the home has not appreciated since the purchase. Given one year of mortgage payments, the principle owed on the mortgage would have decreased by approximately $1,504. As seen in Table 2, the cost to terminate future PMI premiums would be the cost of an appraisal (assumed to be $400) and an investment in home equity of $18,496.

**Table 2****: Termination of PMI Subsequent to the Home Purchase*******

**Assuming an 8% fixed, 30-year mortgage on a $200,000 home purchased 1 year ago, no
appreciation and the full mortgage interest tax deduction***

Down-payment percentage | 5% | 10% | 15% |

Down-payment | $10,000 | $20,000 | $30,000 |

Current loan-to-value ratio | 94.21% | 89.25% | 84.29% |

Prepayment needed to achieve 80% loan-to-value ratio | $28,413 | $18,496 | $ 8,580 |

Approximate cost of an appraisal | $400 | $400 | $ 400 |

Pre-tax rate of return needed on equity outside of the home (in the home for 29 or more years) | 11.21% | 10.89% | 11.42% |

Pre-tax rate of return needed on equity outside of the home (in the home for six more years) | 13.67% | 13.31% | 14.1 |

*Assumes a 28% marginal federal tax rate and no state tax

Return to the top of this table.

In this example, the pre-tax rate of return on the additional investment in home equity is 10.89% if the individual remains in the home for the remaining 29 years. [7] In the event that the individual remains in the home for only seven years, the pre-tax rate of return on this investment is 13.31%. Assuming that the home has appreciated, the size of the home equity investment needed to terminate PMI is less and results in an even greater rate of return on the investment in home equity.

**Is Illiquidity Really a Problem?**

One of the arguments for placing money in investments other than the home, such as stocks or mutual funds, is the greater liquidity of these investments. After all, should a homeowner put a considerable amount of money into a home and need access to the money for a short-term emergency, what sources are available? Credit cards are a source of quick cash, but credit card debt and cash advances on these cards are very expensive.

Should a homeowner need additional liquidity after putting a substantial amount of equity into a home, there are two increasingly popular and relatively inexpensive ways to access equity in the home through a home equity loan or a home equity line of credit. A home equity loan is much like a second mortgage, with the borrower receiving a lump sum with a fixed rate of interest and fixed payments on the loan with terms anywhere from 5 to 20 years. Although interest rates vary from bank to bank, they are typically between one and two points above prime. An equity line of credit is a revolving line of credit, with the borrower able to obtain funds as they are needed. Although equity lines are more flexible than equity loans, they typically carry interest rates that are slightly higher than home equity loans. In addition, the rates are variable and are tied to the prime rate. If the prime rate rises, then so does the rate of interest charged on the equity line.

In addition to the relative attractiveness of the interest rates charged on home equity loans and lines of credit, the interest paid on both of these types of credit is tax deductible up to $100,000, regardless of what the money is used to purchase. Therefore, the actual rates of interest paid on these forms of credit are even lower than advertised. Also, the current competitiveness of banks in this market is such that, in many cases, very little or no closing costs are required for either of these options. If closing costs exist, in most cases a substantial portion of these costs is the cost of an appraisal. In the event that an appraisal was recently performed for the purposes of terminating PMI, an additional appraisal is not likely to be necessary. Finally, one note of caution is that, while home equity loans and lines of credit are quite attractive relative to other sources of debt, they are secured by the home itself. A default on either of these sources of debt puts the borrower in jeopardy of losing the home.

**What About the Current Tax Debate?**

The previous discussion assumes the current tax code. In the event that the current debate on a change in tax law leads to some significant changes in the tax code, how might these changes affect the home equity decision? Currently, proposed changes in the marginal tax rates and the mortgage interest tax deduction are the most likely to have an effect on a individual's home equity investment decision.

Today, the popular talk in Washington is to flatten the tax curve, that is, the highest marginal tax rate being reduced. In the event that lawmakers reduce the highest marginal tax rates as a result of a flattening of the tax curve, then the mortgage interest tax deduction will become less valuable to homeowners who are paying taxes in the highest tax bracket. Consequently, the additional tax savings enjoyed by having less equity in a home (and a higher mortgage interest payment) diminish, and the argument for putting more equity in a home and avoiding the costs of PMI strengthens, assuming one has the necessary cash.

In addition to the current debate regarding a change in tax rates, there is also some discussion about disallowing the tax deductibility of mortgage interest, either entirely or for interest on mortgages above a certain size. If lawmakers disallow entirely the deductibility of mortgage interest, the tax advantages of a small down-payment diminish, and the rates of return required on equity invested outside of the home increase. This, too, would reinforce the argument for investing in home equity for the purpose of eliminating unnecessary PMI premiums.

**Conclusions**

While PMI is necessary for those who have few resources to invest in a home, many homeowners have the option of either paying or avoiding PMI premiums. In many cases, a homeowner can realize a significant return on an investment in home equity that is sufficient to eliminate PMI premiums. Also, if the house has appreciated, or if the mortgage has been paid for several years, the cost of an appraisal is often all that is required to eliminate years of future PMI premiums.

We suggest that homeowners first consider investing in home equity (or perhaps just an appraisal) and eliminating PMI premiums as an alternative to investing in other assets. Finally, although the purpose of the examples provided is to demonstrate the returns that are possible with an investment in home equity, every individual's situation is unique. Issues such as mortgage terms, PMI premiums, the individual's financial condition, and his or her preferences towards such things as liquidity and risk must be considered before determining the attractiveness of an additional investment in home equity.

**References **

Anonymous, 1996. "Homeowners Wasting Millions on PMI," *Inman Real Estate News*, June 21.

Return to text.

Canner, Glenn B. and Wayne Passmore, 1994. "Private Mortgage Insurance," *Federal Reserve
Bulletin*, October: 883-899.

Storms, Phillip, 1992. "Guiding Your Client Through the Mortgage Maze," *Journal of Financial
Planning*, April: 87-91. Return to text.

Walden, Michael L., 1992. "The Relative Benefits of Making a Higher Down Payment or Paying
Points For a Lower Interest Rate," *Financial Counseling and Planning*, 3:63-77. Return to text.

**Appendix:**** Spreadsheet Calculations**

The pre-tax rate of return numbers found in Table 1 and Table 2 are generated using a spreadsheet program. First, there was calculated a schedule of cash flows for the loan with a loan-to-value ratio (LV) greater than 80%. For each month, we calculated a row containing 4 columns:

- 1. mortgage payment (principal and interest)
- 2. PMI payment
- 3. Interest deduction
- 4. total monthly outflow (1) + (2) - (3)

Then the same schedule was calculated for an 80% loan (a loan without PMI). Third, a schedule of 'net extra payments' was generated. For each month we calculated a row containing three columns:

- 1. total monthly outflow for higher LV loan
- 2. total monthly outflow for 80% loan
- 3. net extra payments (1) - (2).

Then an internal rate of return (IRR) calculation was performed. IRR is the rate which equates (a) the extra down-payment required to reduce a higher LV loan to an 80% loan with (b) the present value of all the extra payments. Finally, the IRR (after-tax required rate of return) was adjusted for taxes to arrive at the pre-tax IRR. The borrower can then answer the initial loan question: If I forego investing in home equity at origination, what is the pre-tax rate of return needed on investments during the life of the mortgage to justify the extra payments?

For the other calculations in Table 1, the spreadsheet schedule is truncated at seven years, and the larger unpaid mortgage balance of the higher LV loan after the seventh year requires an additional "extra-payment" when compared to the 80% loan. In Table 2, a similar spreadsheet schedule is generated for a one year old mortgage. Adjustments are made for the differences in mortgage balances and the cost of an appraisal.

Return to Table 1.

**Footnotes**

1. Note that FHA loans have been available since the late 1940s for families that qualify. Return to text.

2. This assumes a down-payment of 5% and PMI premiums of .78%/12 of the initial mortgage amount. Return to text.

3. The higher the loan-to-value ratio, the higher the payment and the higher the mortgage interest deduction. We evaluate the offsetting effects of PMI, higher payment, and the mortgage interest deduction using a variety of assumptions. Return to text.

4. A specific explanation for the calculations leading to the results found in Table 1 and Table 2 can be found in the Appendix. Return to text.

5. The average life of a mortgage, as commonly cited by many mortgage lender. Return to text.

6. Typically, the lender requires that the homeowner has lived in the home for at least two years and has made mortgage payments in a timely fashion. If FNMA has purchased the loan, the homeowner might only be required to have lived in the home for one year. Return to text.

7. With the additional equity of $18,496, the term shortens to 21 years, 8 months remaining. However, for comparison purposes, the individual investing in equity today saves the present value of the final 7 years and 4 months of payments (less tax benefits) of the mortgage. Therefore, the analysis is over the remaining 29 years. Return to text..