By John Hatem, Chris Paul, and William H. Wells
John Hatem is associate professor of finance at the College of Business Administration at Georgia Southern University in Statesboro, Georgia.
Chris Paul is a professor of finance at the College of Business Administration at Georgia Southern University.
William H. Wells is associate professor and chair of the Department of Finance, College of Business Administration, at Georgia Southern University.
Abstract
This article extends work that previously appeared in the Journal of Financial Planning," Making the Mortgage Insurance Purchase Decision" (September 2006), which investigated the financial attractiveness of alternative mortgage financing when the buyer does not possess the requisite 20 percent down for a conforming mortgage. But the original analysis was performed before personal mortgage insurance premiums were made tax deductible for qualified individuals by the Tax Relief and Health Care Act of 2006. We recalculate the after-tax marginal interest rate and monthly after-tax payments reported in the original paper with tax-deductible premiums for the three types of personal mortgage insurance included in the original study. These consist of the single-premium, monthly-premium, and FHA alternatives. While the marginal effect is small, due to the assumed 15 percent marginal tax rate, the ordering of the financially preferred alternatives change.
In an article in the Journal of Financial Planning, Eckles, Halek and Wells (September 2006, pp. 66-73) provide guidance on choosing between mortgage alternatives when the buyer lacks the required 20 percent down payment to obtain a conforming mortgage that does not require mortgage insurance. They analyze the relative financial attractiveness of four mortgage alternatives by calculating the monthly after-tax payment and the effective after-tax interest rate. The alternatives considered are (1) an 80/10/10, or piggyback, loan; (2) single-premium personal mortgage insurance (PMI); (3) monthly-premium PMI; and (4) the FHA alternative that requires both a lump-sum and monthly premiums. For comparison they include a traditional 80/20. Note that the after-tax payment for the 80/20 mortgage should not be directly compared with the 10 percent down alternatives as it carries the opportunity cost of the additional 10 percent down payment. In discussing their results, they note (p. 67) that "unlike mortgage interest payments, these insurance premiums are not tax deductible." However, in the Tax Relief and Health Care Act of 2006, Congress made PMI insurance premiums tax deductible for taxpayers with adjusted gross income of less than $100,000 (see p. 7, "Mortgage Insurance Premiums," IRS Publication 936, 2007). Our purpose is to re-examine the relative financial attractiveness of PMI for buyers who can use the deduction allowance.
The Tax Relief and Health Care Act of 2006
The "qualified mortgage insurance deduction" contained in the Tax Relief and Health Care Act of 2006 was initially applied to the 2007 tax year for PMI contracts issued between January 1 and December 31, 2007, but was extended through 2010 by the Mortgage Forgiveness Debt Relief Act of 2007. Obviously, if the deduction is allowed to expire in 2010, the after-tax payment and after-tax effective interest rate will return to the levels reported in the original paper. Consequently, individuals who buy mortgage insurance should consider their expected time horizon for reaching the required loan-to-value (LTV) ratio. The deduction allows the full amount of the mortgage insurance premium for first-time home buyers with an adjusted gross income of less than $100,000 for married couples filing jointly. The deduction is phased out by ten percent for each $1,000 over $100,000 of the taxpayer's adjusted gross income for married couples filing jointly.
Implications for Effective After-Tax Rate and Payments
The tax deductibility of the PMI premium will affect the after-tax payment and effective interest rate for the PMI alternatives while leaving the results for the 80/10/10 piggyback loan unchanged. We recalculate the after-tax payment and the effective after-tax interest rate for the mortgages requiring PMI and compare them with the results for 80/10/10 results. Obviously, loans requiring PMI become more attractive for qualified home buyers. But do the tax savings change the relative attractiveness of the PMI alternatives?
Since the results are proportional we calculate only the results for the $100,000 mortgage with a 15 percent marginal tax rate. For purposes of exposition, our organization differs somewhat from that of the original paper.
Following is a description of the loan types as presented in the original paper:
10/10/80. A 10 percent down payment, 15-year second mortgage of 10 percent of the purchase price, and an 80 percent first mortgage. The interest rate on the second mortgage is assumed to be 2.8 percent over the first mortgage rate.
Single PMI premium-the single premium of 2.10 percent of the primary mortgage amount of $90,000 for 25 percent coverage, paid at closing. This premium is financed and added to the first mortgage, resulting in a total financed amount of $91,890.
Monthly PMI premium-the monthly premium is assumed to be an annual fee of 0.52 percent of the first mortgage amount for 25 percent coverage.
FHA/single and monthly premium-combines a 1.5 percent lump-sum premium at closing and a 0.50 percent annual premium, paid monthly, each of which is based on the original amount of the first mortgage. Note that the FHA changed to risk-based pricing effective July 14, 2008. This means the after-tax savings will have to be calculated on an individual basis. But since the FHA alternative is the higher-cost alternative, it is suggested that home buyers select this option only if the other alternatives are unavailable.
Results
Effective after-tax payment. The original paper demonstrated that the monthly-premium PMI and the FHA exhibit similar patterns as a result of the PMI premium being reduced to zero after the 80 and 78 percent LTV ratio is reached, respectively. This pattern is replicated when the PMI premiums are tax deductible. The only change is the relative positions of the after-tax payment functions in Figures 1 and 2. The PMI alternatives are reduced by 15 percent of the mortgage insurance amount, the marginal tax rate in this example. The reduction in the after-tax payment will always be the marginal tax rate times the insurance premium amount. Note that the relative shift will be greater for higher marginal tax levels. For example, it would result in a reduction of 35 percent for the highest federal marginal income tax bracket. Figure 1 replicates the original results for the monthly after-tax payment, while Figure 2 contains the results for tax-deductible PMI.
Comparison of the results reveals that the monthly-premium (MP) PMI now has a lower after-tax payment than the 80/10/10 from the beginning of the loan's term; this occurred only after the 20 percent equity position was reached in the original results for the mortgage insurance alternatives. Even for the FHA mortgage, the insurance alternative with the highest costs, the initial after-tax monthly payment is almost equal to the 80/10/10 until the 20 percent equity position is attained for the FHA loan, at which time the after-tax payment falls significantly below the after-tax payment for the 80/10/10 until the second mortgage is retired at the end of year 15.
The initial effective after-tax payment for the 80/10/10 mortgage remains unchanged at $508.88, while the initial payment for MP PMI decreased from $511.10 to $505.25, the single-premium (SP) PMI falls from $482.01 to $480.52, and the FHA declines from $516.68 to $509.60. Note that the reduction in the after-tax payment for the PMI alternatives is proportional to the PMI costs, with higher costs resulting in proportional declines in the after-tax payment.
Effective after-tax interest rate. To aid comparison and facilitate discussion, we have reorganized the presentation of results in Table 1. The mortgage alternatives are ordered by their effective after-tax rate. Tax-deductible mortgage interest payments mean that all the effective after-tax rates will be lower than the primary interest rate. The top portion of Table 1 presents the effective after-tax rates when mortgage insurance premiums are non-deductible. As noted in the original article, the SP PMI and the FHA alternative have significantly higher effective after-tax rates as a result of the initial lump-sum premium increasing the amount financed. This causes the FHA mortgage to have a higher effective after-tax rate for the entire mortgage period than any of the alternatives. The SP PMI rate is lower than the MP PMI after approximately five years and almost as low as the 80/20/20 mortgage after 13 years when the 80 percent LTV ratio is attained.
Comparing the mortgage alternatives at a six percent interest rate shows that for the non-conforming mortgage alternatives in Table 1, the 80/10/10 and the single-premium PMI are extremely close, with only a 0.01 percent higher lifetime rate for the SP PMI. The SP PMI and FHA loans are 0.11 percent and 0.24 percent higher, respectively. In the bottom of Table 1, with tax-deductible PMI premiums, the positions of the 80/10/10 and monthly-premium PMI are reversed, with the SP PMI mortgage having a 0.02 percent advantage. Additionally, the interest rate penalty for the MP PMI and the FHA over the 80/10/10 is reduced to 0.07 percent and 0.17 percent, respectively. These results represent a reduction in the effective after-tax interest rate of 0.04 percent and 0.07 percent for the MP PMI and FHA alternatives. Again, the relatively larger reduction in the effective after-tax interest rate results from the higher insurance premiums for the respective alternatives.
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Table 1: Effective After-Tax Rate Under Five Alternative Financing Options
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Primary Mortgage Rate |
80/20 No PMI |
80/10/10 |
SP PMI |
MP PMI |
FHA |
|
|
5.0% |
4.25% |
4.41% |
4.42% |
4.50% |
4.62% |
|
|
5.5% |
4.67% |
4.84% |
4.85% |
4.94% |
5.06% |
|
|
6.0% |
5.10% |
5.27% |
5.28% |
5.38% |
5.51% |
|
|
6.5% |
5.53% |
5.70% |
5.71% |
5.82% |
5.95% |
|
|
7.0% |
5.95% |
6.12% |
6.14% |
6.27% |
6.40% |
|
|
7.5% |
6.37% |
6.55% |
6.57% |
6.71% |
6.84% |
|
|
8.0% |
6.80% |
6.98% |
7.00% |
7.15% |
7.29% |
|
|
8.5% |
7.22% |
7.40% |
7.43% |
7.59% |
7.73% |
|
|
9.0% |
7.65% |
7.83% |
7.86% |
8.03% |
8.17% |
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With Tax-Deductible PMI |
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Primary Mortgage Rate |
80/20 No PMI |
80/10/10 |
SP PMI |
MP PMI |
FHA |
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5.0% |
4.25% |
4.41% |
4.40% |
4.46% |
4.56% |
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|
5.5% |
4.67% |
4.84% |
4.82% |
4.90% |
5.00% |
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6.0% |
5.10% |
5.27% |
5.25% |
5.34% |
5.44% |
|
|
6.5% |
5.53% |
5.70% |
5.68% |
5.78% |
5.89% |
|
|
7.0% |
5.95% |
6.12% |
6.11% |
6.22% |
6.33% |
|
|
7.5% |
6.37% |
6.55% |
6.54% |
6.66% |
6.77% |
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|
8.0% |
6.80% |
6.98% |
6.97% |
7.09% |
7.21% |
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|
8.5% |
7.22% |
7.40% |
7.40% |
7.53% |
7.65% |
|
|
9.0% |
7.65% |
7.83% |
7.83% |
7.97% |
8.09% |
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Figures 3 and 4 present the effective after-tax rate over the life of the loan without and with tax-deductible premiums, respectively. Again, while the changes are relatively small, the effective after-tax rate for both the single-premium and monthly-premium PMI and the FHA alternatives are lower due to the tax-deductible premiums. The SP PMI is almost indistinguishable from the effective after-tax rate for the 80/10/10 in year 10 as opposed to year 14 without tax-deductible premiums.
Conclusion
For individuals unable to pay the required 20 percent down to obtain a traditional mortgage, Eckles, Halek, and Wells offer conclusions for two objectives: (1) the minimization of the effective interest rate and (2) minimizing monthly payments. The piggyback 80/10/10 loan exhibits a lower effective interest rate over the entire life of the loan, while the selection of a PMI mortgage depends on the expected life of the mortgage. The monthly PMI premium has a lower effective interest rate in the near term, up to five years, while the single-premium alternative has a lower effective interest rate for the intermediate period of five to ten years.
When seeking to minimize monthly payments, the pattern is the same with monthly PMI having lower payments in the first 5 to 7 years, single-premium PMI for years 8 through 15, and the piggyback loan for any period longer than 15 years. Note that the time frame results from reaching the 20 percent equity position and paying off the second mortgage, respectively.
Both findings are affected by the tax deductibility of PMI premiums. These results should be applied with consideration of the continued tax deductibility of mortgage insurance premiums. If the deduction is allowed to expire after 2010, the after-tax payment and the effective interest rate will return to approximately the levels calculated in the original paper. Hence, the individuals planning horizon should be considered in applying these results. Note also that these discrete changes occur at the time that the 20 percent equity position results in the dropping of the PMI premium and the satisfaction of the 10 percent second mortgage for the piggyback loan.
References
Dale, Arden. 2008. "Tax Break Aimed at New Mortgages." Wall Street Journal January 16: D9.
Eckles, David L., Martin Halek, and William H. Wells. 2006. "Making the Mortgage Insurance Decision." Journal of Financial Planning 19, 9 (September): 66-73.
