THE EFFECTS OF INCOME TAX RATES AND INTEREST RATES IN CHOOSING BETWEEN 15- AND 30-YEAR MORTGAGES

By David R. Vruwink, PhD, and Dann G. Fisher, CPA, Kansas State University

For most people, the most significant investment decision they will make in their lifetime is the type of home they will purchase. Almost as important is how they will finance that home. A well thought out plan of analyzing their future financial needs when financing that home could have a meaningful impact on their standard of living.

A choice between 15- and 30-year mortgages is what most people normally consider. Those people who select the 30-year mortgage usually like the lower monthly payments and the higher tax deduction for interest on the mortgage. The 15-year mortgage is preferred by those people who want to build equity in their home faster and save tens of thousands of dollars in additional payments of interest. Also, the shorter mortgage offers a means of earning a higher return than a savings account and enforces a savings discipline on the homeowner.

Some homeowners could benefit from an analysis of the advantages and disadvantages of 15- and 30-year mortgages taking into account their personal and financial attributes. Such an analysis will provide insight as to how financing the home would affect their financial status later in life.

The Evaluation Process

The two major financial goals of any homeowner in financing a home should be to either 1) have more money to spend or save or 2) have a greater financial net worth at the end of the financing period. If a homeowner needs to minimize his or her mortgage payment because of their limited ability to make higher mortgage payments, the 30-year mortgage is the easy choice. The decision becomes much more complicated when the major goal of the homeowner is to increase his or her own financial net worth.

To determine whether a 15- or 30-year mortgage is best for increasing net worth, the homeowner must focus on four factors: 1) the net cash difference between the 15- and 30-year mortgage, 2) the hurdle rate or earning rate of return on the net cash difference which the homeowner must exceed to be financially better off with the 30-year mortgage, 3) the investment time horizon of the homeowner, and 4) the homeowner's investment strategy to earn a rate of return that exceeds the simple strategy of building equity through a 15-year mortgage.

Net Cash Difference. Since a 30-year mortgage requires lower monthly payments and produces greater tax savings than the 15-year mortgage, a net cash current saving difference results each year. The amount of the cash difference is significantly affected by both the level of interest rates and the homeowner's expected marginal income tax rate over the relevant 15-year financing period. While the homeowner should be able to predict the interest rates he or she will be able to lock in the near future, the marginal tax rate is more difficult to estimate.

Table 1 indicates that the higher the homeowner's marginal income tax rate, the greater the net cash current saving difference between the 15- and 30-year mortgage regardless of interest rate. This outcome occurs because the 30-year mortgage payment has more interest than a 15-year mortgage payment.

Table 1 reading vertically, indicates that as mortgage rates rise, the net cash difference declines for a particular marginal income tax rate. This outcome occurs because, as rates rise, the amount of interest in the 15-year mortgage payment increases at a faster rate as compared with the 30-year mortgage payment. The tax deductibility of the mortgage interest somewhat offsets this decline. In other words, the net cash difference declines at a slower rate, the higher the marginal income tax rate of the homeowner increase.

Table 1 has two limitations. First it assumes that a homeowner's expected marginal tax rate will be the same throughout the 15-year financing period. If the homeowner expects a future increase or decrease in the marginal income tax rate, then adjustments have to be made to the numbers shown in Table 1.

Second, the table assumes that marginal tax rate of the homeowner will not change under both the 15- and 30-year mortgage. In the later years of the 15-year mortgage, the sizable decline in interest deductions could force the homeowner to use the standard deduction. This event would favor the 30-year mortgage.

Hurdle Rate. After estimating the net cash difference between the 15- and 30-year mortgage, the homeowner must then determine the hurdle rate for alternative investments if he or she selects the 30-year mortgage. Computing the appropriate hurdle rate is complicated because the 30-year mortgage generally demands an interest rate that is about 0.50% higher than the 15-year mortgage due to greater risk and uncertainty with the longer term mortgage.

The higher interest rate means that the net cash difference from having selected the 30-year mortgage must be alternatively invested to earn a higher rate of return than could have been earned by simply paying off faster through the 15-year mortgage. For example, with a $100,000, 30-year mortgage, the homeowner has to earn approximately $500 more on the alternative investments to match the additional financing costs in the first year of the 30-year mortgage. Successive years would have decreasingly smaller amounts because of the declining balance of the 30-year mortgage.

Table 2 reveals that the effects of the additional financing costs can be mitigated if the homeowner's expected marginal income tax bracket is 28% or more. The tax deductibility of the additional interest cost of the 30-year mortgage gives the homeowner in this position a lower hurdle rate and an incentive to select the 30-year mortgage. During periods of low mortgage rates, a homeowner in an upper income tax bracket should have less difficulty in finding alternative investments that exceed the 15-year hurdle rate.

Time Horizon

A third factor in choosing between a 15- and 30-year mortgage is the investment time horizon of the homeowner. For example, assuming a 31% marginal tax rate and a $100,000 mortgage, a homeowner selecting a 9%, 30-year mortgage vs. a 8.5%, 15-year mortgage would have $46,964 in net cash difference (Table 3, column 7) over a 15-year period to invest and a hurdle rate of slightly less than 8% (Table 3, column 9). If the homeowner is able to earn 10% (the long-term rate of return for equities) on the net cash difference, then, the homeowner will have $13,067 more in net worth at the end of 15 years (Table 3, column 10).

A time horizon of 15 years does allow a reasonable assumption that the homeowner will be able to earn 10% on the net cash difference. However, the homeowner is assuming more risk and the expected return is not guaranteed when compared to building equity through a 15-year mortgage. Some homeowners may decide the increased risk is not worth the additional $13,000, especially if the homeowner is nearing retirement.

A more persuasive case for the 30-year mortgage can be made if the homeowner's time horizon is 30 years or more. At the end of 15 years, the homeowner who has selected the 30-year mortgage will have $92,395 in investments and $20,668 paid on the mortgage (Table 3, column 10) compared to the homeowner who selected and paid off the $100,000, 15-year mortgage. If the homeowner with the 30-year mortgage is able to continue to earn 10% over the next 15 years then, he or she will have $129,756 more in net worth (Table 4, column 10) than someone who paid off his or her mortgage early and then started investing the mortgage payments in equities.

Thus, a homeowner with a long time horizon and a willingness to assume some risk will likely have a much higher net worth than someone who selects the less risky option of the 15-year mortgage. The probability of that happening, however, will depend greatly on the homeowner's investment strategy.

Investment Strategy

To greatly improve the likelihood that the rate of return on alternative investments will exceed the hurdle rate, a homeowner should first take advantage of any tax-sheltered retirement plans [401(k), Keogh, SEP, or IRA] that allow pretax dollars to be used in funding his or her investments and also shelter investment income from income taxes. Next, a homeowner should search for investment vehicles that use after-tax dollars but shelter or reduce taxable investment income. A final investment strategy is to ignore taxes and seek the highest rates of return.

Pretax Dollars. By taking advantage of any tax-sheltered retirement plans, a homeowner will be able to contribute pretax dollars for investment. Following this strategy, a homeowner can contribute more funds than his or her net cash difference from the 30-year mortgage because funds that would have been used to pay income taxes can now be used to make additional contributions to his or her investment fund. The amount of additional funds available for such investment is dependent on the homeowner's marginal income tax rate.

The second step in this investment strategy is to search for mutual funds that have good long-term records of above-average rates of return. The homeowner will also need to select different types of mutual funds (growth, index, emerging markets, small stocks, etc.) so that the risk of losing capital is minimized through diversity. The homeowner should have a policy of reviewing the performance of the selected mutual funds every two or three years and removing underperformers to improve returns.

Reducing Taxable Investment Income. If a homeowner is already utilizing all tax-sheltered retirement plans that use pretax dollars, then the next best investment strategy is to find investment vehicles that shelter or minimize taxable investment income. Deferring taxes on investment income will likely increase the rate of return on the investment (assuming a high marginal tax rate for a homeowner) and the likelihood of the homeowner surpassing his or her hurdle rate. The income taxes must eventually be paid, but the compounding of the investment funds at a higher rate of return for 15 years should prove quite beneficial.

A homeowner should consider several possibilities. The purchase of annuities can defer taxes on investment income until retirement. The annual administrative costs of a deferred annuity, however, usually exceed one percent, and additional costs may be imposed if the homeowner tries to switch to other annuities. A second alternative is the use of index funds or other mutual funds with low turnover to minimize the amount of taxable investment income. The fund holder would pay taxes mostly on the dividends. The funds also have very low operating costs and often outperform more actively managed funds.

As a third choice, the homeowner may establish a college fund in his or her child's name. A child can have $600 of unearned income before paying any taxes. The next $600 of unearned income is taxed at the child's tax bracket. Unfortunately, once the unearned income exceeds $1,200, it becomes taxed at the parent's marginal income tax rate until the age of 14. The kiddie tax no longer applies after age 14 and additional asset transfers can be considered.

Maximizing Investment Income. A third investment strategy is to ignore the tax consequences of a particular investment and focus on mutual funds, direct ownership of stocks, or other investments that will produce the highest rates of return. Such a strategy means that the homeowner is willing to assume greater risk, but has a higher level of investment expertise and a time commitment to follow his or her investment portfolio. If successful, such a strategy can add tens of thousands of dollars to the homeowner with an additional one percent increase in rate of return. *

15-year 30-year Marginal Tax Rate

Mortgage Mortgage

Rate Rate 0% 15% 28% 31% 36% 39.6% 50%

6.0% 6.5% $38,160 $43,323 $47,798 $48,830 $50,551 $51,790 $55,370

8.0 8.5 33,660 40,319 46,090 47,421 49,641 51,239 55,856

10.0 10.5 28,800 36,876 43,874 45,490 48,182 50,120 55,718

12.0 12.5 23,940 33,358 41,250 43,404 46,543 48,803 55,333

15-year 30-year Marginal Tax Rate

Mortgage Mortgage

Rate Rate 0% 15% 28% 31% 36% 39.6% 50%

6.0% 6.5% 8.63% 7.23% 6.06% 5.79% 5.34% 4.97% 4.13%

8.0 8.5 11.13 9.30 7.77 7.43 6.86 6.45 5.29

10.0 10.5 13.77 11.47 9.56 9.13 8.42 7.92 6.48

12.0 12.5 16.61 13.78 11.45 10.94 10.08 9.47 7.74

Editor:
Milton Miller, CPA
Consultant

Contributing Editors:
Andrew B. Blackman, CFP, CPA/PFS
Shapiro & Lobel LLP

David Kahn, CPA
Goldstein, Golub, Kessler &
Company, P.C.

NOVEMBER 1995 / THE CPA JOURNAL

15-YEAR MORTGAGE 30-YEAR MORTGAGE Future Value of Cash Differences Invested at

(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)

After-Tax Net Cash After-Tax Net Cash Cash

Year Principal Interest Cost Principal Interest Cost Difference 6% IF 8% IF 10% IF

1 $3,449.20 $5,773.70 $9,222.90 $683.16 $6,190.87 $6,874.03 $2,348.86 $5,310.55 $6,899.06 $8,918.64

2 3,754.08 5,563.33 9,317.41 747.25 6,146.65 6,893.90 2,423.51 5,169.18 6,591.03 8,365.96

3 4,085.90 5,334.37 9,420.28 817.35 6,098.28 6,915.63 2,504.65 5,039.85 6,307.13 7,859.58

4 4,447.06 5,085.17 9,532.24 894.02 6,045.38 6,939.40 2,592.84 4,921.98 6,045.56 7,397.36

5 Thru 11 44,312.24 26,500.10 70,812.34 9,102.64 40,354.97 49,457.61 21,394.73 32,010.76 36,554.62 41,704.25

12 8,756.94 2,111.36 10,868.30 1,831.78 5,398.33 7,230.10 3,638.19 4,333.16 4,583.07 4,842.44

13 9,530.97 1,577.28 11,108.25 2,003.61 5,279.76 7,283.37 3,824.88 4,297.63 4,461.34 4,628.10

14 10,373.43 995.98 11,369.41 2,191.56 5,150.08 7,341.64 4,027.77 4,269.44 4,349.99 4,430.55

15 11,290.18 363.42 11,653.60 2,397.15 5,008.22 7,405.37 4,248.23 4,248.23 4,248.23 4,248.23

TOTAL $100,000.00 $20,668.52 $46,963.66

Equity from alternative investment $69,600.78 $80,040.03 $92,395.11

Equity from 30-year mortgage 20,668.52 20,668.52 20,668.52

Wealth increase‹30-year mortgage $90,269.31 $100,708.56 $113,063.63

Equity from 15-year mortgage 100,000.00 100,000.00 100,000.00

Net difference in wealth ($9,730.69) $708.56 $13,063.63

Annual payment for 15-year mortgage is $11,816.88. Annual payment for 30-year mortgage is $9,655.44. (3)=(1)+(2) (6)=(4)+(5) (7)=(3)-(6)

15-Year Mortgage 30-Year Mortgage

(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)

Future amt. of investment from 15-year mortgage option 375,451.70

Net increase in wealth from 30-year mortgage option $129,756.72

(2) and (4)--annual payment for 15-year mortgage Annual payment for 30-Year mortgage is $9,655.44 (7) = (5) + (6) (8)=(4)-(7)

Year

1-15

16

17

18-26

27

28

29

30

TOTAL

NOVEMBER 1995 / THE CPA JOURNAL