15-Year Versus 30-Year Mortgage: Which Is the Better Option? by Delbert C. Goff, Ph.D., and Don R. Cox, Ph.D.

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1 15-Year Versus 30-Year Mortgage: Which Is the Better Option? by Delbert C. Goff, Ph.D., and Don R. Cox, Ph.D. Over the past several years, many home buyers have opted for a 15-year mortgage rather than a 30-year mortgage, based on the belief that the earlier you pay off your home, the better off you are financially. The 15-year mortgages typically offer a lower interest rate, and the lower rate coupled with the shorter borrowing period saves home owners thousands of dollars in interest over the life of the mortgage. The major negative aspect of the 15-year mortgage is the higher monthly payment; however, it appears that many home owners view the 15-year mortgage as the most desirable alternative if they can afford the higher payment. These home owners, however, may not be adequately considering the opportunity costs of the investment in their home. Individuals should not attempt to analyze the mortgage decision in isolation from their overall personal financial plan. Instead they should consider the mortgage decision along with their plans for long-term investing, insurance needs, tax planning and so forth. If the only way home buyers can afford the higher 15-year mortgage payment is by delaying long-term investments or by limiting the funds they commit to a long-term investment plan, they may be better off in the long run by taking the 30-year mortgage with the lower payment and investing the difference. The purpose of this paper is to demonstrate that for investors with access to taxdeferred investment plans such as a 401(k) or a 403(b), the 30-year mortgage is clearly the best financial choice for many home buyers. This study will provide financial planners with additional information that will help them advise clients who are considering the purchase of a home or refinancing a home. In addition, this study will help financial planners demonstrate to many home buyers/investors how they can begin a taxdeferred investment plan while buying a home. This information may enable financial planners to convince many younger home buyers that they can and should begin saving for retirement early and that they do not have to wait to start saving. Several articles have focused on the potential advantages of a 30-year mortgage over a 15-year mortgage (such as Vruwink and Fisher [1995], Marshall [1989], and McCartney [1989]). While these articles note some benefits of the 30-year mortgage over the 15-year mortgage, from a financial perspective their arguments are not totally convincing. For example, Marshall (1989) and McCartney [1989] indicate that the 15-year mortgage is less costly than the 30-year mortgage. Then, to make the case for using a 30-year mortgage, both authors rely on other factors such as the flexibility afforded by the lower payment on the 30-year mortgage. Vruwink and Fisher [1995] indicate that the 30-year mortgage option is beneficial to many home buyers. In addition, they indicate that the existence of a tax-deferred investment vehicle may make the 30-year mortgage even more attractive; however, they do not support this claim with empirical analysis. 1

2 This study demonstrates that many home buyers with the financial ability to pay the higher 15-year mortgage payment would be much better off taking the lower 30-year payment and investing the difference in a tax-deferred investment plan. The benefits of the 30-year mortgage are the greatest for home buyers in high tax brackets buying relatively expensive homes. For example, a home buyer in the 33-percent tax bracket (combined federal and state) taking on a $150,000 mortgage could have a retirement investment account value of over $1.17 million after 30 years if he or she were to follow the strategy suggested in this paper. This account value is approximately $379,000 more than the home buyer would have if he or she waited until after paying off the 15-year mortgage to begin making contributions to a tax-deferred investment plan. This study is especially interesting in light of the results of Dhillon, Shilling and Sirmans [1990] indicating that wealthy borrowers are more likely to take 15-year mortgages than are low-wealth borrowers. That is, it appears that the individuals who may benefit the most from the 30-year mortgage are more likely to take the 15-year mortgage, indicating that many wealthy borrowers need counseling on this issue. Methodology The methodology is designed to analyze the trade-off between the financial benefits of paying off a mortgage relatively early using a 15-year mortgage and then saving for an additional 15 years, with the financial benefits of paying the smaller 30-year mortgage payment and making annual contributions to a tax-deferred investment plan. The base case used in this analysis is as follows: 1. Mortgage amount of $150, Combined federal and state income tax rate of 33 percent 3. A 15-year mortgage interest rate of 7.5 percent 4. A 30-year mortgage interest rate of eight percent 5. A ten percent rate of return on the tax-deferred investment plan. Since the spread between mortgage rates and the investment rate of return is critical to this analysis, it may be useful to offer a couple of comments related to our assumptions. We assume that money placed in the tax-deferred investment account will be invested in equity investments. The ten percent return assumed in our base case reflects the approximate historical return of the U.S. stock market. Because we assume that there will be equity investing in the tax-deferred investment account with both the 15-year mortgage and the 30-year mortgage (the difference is with regard to the timing of these investments), this assumption does not alter the risky ness of the two alternatives. Since we are viewing this decision as a part of the home owner s total financial plan, and we assume that most individuals need some exposure in equity investments, we believe this is a reasonable and appropriate set of assumptions. Clearly, if an individual is so risk averse that they will not consider anything beyond a "risk-free" investment, the benefits described in this article generally will not be applicable. 2

3 To account for the tax savings from the mortgage interest deduction, the annual after-tax payments are used. An amortization schedule is constructed on a monthly basis and the relevant variables are summed across the months to find the total annual payment, total interest paid during a year and the total principal repaid during the year. The annual aftertax payment is calculated as follows: Annual After-tax Payment = I (1 t) + PR where I is the total interest paid during a year, t is the tax rate, and PR is the principal repaid during a year. For example, the monthly payment for the 15-year mortgage is $1, For the first year, the total annual payment is $16,686, the total interest paid is $11,059 and the total principal repaid is $5,627. Therefore the annual after-tax payment is Annual After-tax Payment = $11,059 (1 0.33) + $5,627 = $13,037 The annual after-tax payment for the 30-year mortgage is calculated in a similar manner yielding an after-tax payment of $9,263 for the first year of the 30-year mortgage. The difference in the payments is calculated by subtracting the annual after-tax payment for the 30-year mortgage from the annual after-tax payment for the 15-year mortgage. An underlying assumption of the methodology is that a home buyer has the financial resources to pay the higher 15-year mortgage payment. Therefore, even if the 30-year mortgage is selected, the home buyer will be able to put an amount equal to the difference in the mortgage payments into a tax-deferred investment plan. Primary Methodology Difference The primary way in which this study differs from earlier studies is in the assumption that home buyers will be able to invest the difference in the payments in a tax-deferred investment plan such as a 401(k) or a 403(b). Since funds placed in a tax-deferred investment plan reduce the investor s current taxable income, the investor s taxes decline. For example, an investor in the 28-percent tax bracket putting $100 into a tax-deferred investment plan will reduce his or her after-tax income by $72 because the $100 tax deduction will result in a tax-savings of $28. Likewise, if the investor can afford to do without $100 in after-tax income, he or she could place $ into a tax-deferred investment plan. This will result in a tax savings of $38.89 ($ ); therefore, the investor s after-tax cash outflow will be $100. The advantage of the tax-deferred investment plan will make a 30-year mortgage more attractive than a 15-year mortgage for many home buyers. By investing the difference between the 15-year mortgage payment and the 30-year mortgage payment in a tax deferred investment plan, home buyers may be able to save a considerable amount of money over time. For example, in the example given above, the after-tax payments for the 15-year and 30-year mortgages are $13,037 and $9,263, respectively. If a home 3

4 buyer can afford the larger payment but opts for the 30-year mortgage, he or she will have $3,774 of after-tax cash available to invest. If the money is invested in a taxdeferred investment plan, the home buyer could invest $5,633 pre-tax into the account. With a 33 percent marginal tax rate, the investor s tax savings would be $1,858, yielding an after-tax cash flow of $3,774. It is assumed that, after paying off the mortgage, the home buyer with the 15-year mortgage will invest an amount equal to the annual mortgage payment in a tax-deferred investment plan. For the base case, the home owner will have $16,686 a year available after paying off the mortgage. Therefore, the home owner could invest $24,905 a year in a tax-deferred investment plan and have an after-tax cash outflow of $16,686. This assumption allows for a comparison of the home buyer s wealth under both mortgage options over a 30-year period. Therefore, the argument is considered that many home buyers prefer the 15-year mortgage because after they pay off their home they will use their mortgage payments to make large contributions to a retirement savings plan. Note that many home buyers may not be eligible for a tax-deferred investment plan contribution as large as $24,905 a year. In that case, the home buyers could put the maximum amount possible in a tax-deferred plan and put the additional after-tax funds into a mutual fund or other investment vehicle. The effect of this action will be to lower the total amount saved each year under the 15-year mortgage option and will make the 30- year mortgage option more attractive. Comparing the 15-Year and 30-Year Mortgages Over Time Table 1 provides a comparison of the 15-year and 30-year mortgages and demonstrates the benefits of investing in a tax-deferred investment plan. Under the "Total Annual Payments" heading are the annual pre-tax and after-tax payments for the 15-year and 30- year mortgages. As discussed above, the annual payments are the sum of the monthly payments during each year. Note that after year 15 of the 15-year mortgage, the payments continue. The continuation of the payments is based on the assumption that after the home is paid for, the home buyer will use the after-tax payment to make contributions to a tax-deferred investment plan. The next column provides the after-tax difference in the mortgage payments. This difference is the additional after-tax cash flow available to a home buyer who selects the 30-year mortgage rather than the 15-year mortgage. Note that since the interest payment decreases over time, thus reducing the interest tax deduction, the after-tax payment increases each year. Since the principal is repaid at a faster rate with the 15-year mortgage than with the 30-year mortgage, the difference in the payments increases over the life of the 15-year mortgage. The next four columns give the tax-deferred saving balances under each mortgage option. With the 15-year mortgage, there are no deposits in the investment plan for the first 15 years (because the home buyer s cash flow is going to pay the mortgage payments). After year 15 when the home is paid for, it is assumed that the after-tax payment is available to invest in a tax-deferred investment plan. The account value is calculated by finding the future value of the account each year, assuming an investment rate of return of ten percent. 4

5 Table 1: Annual Mortgage Payments and Tax-Deferred Investment Account Balances with 15-year Mortgage and 30-Year Mortgage 5

6 The calculation of the deposits given under the "Savings with 30-Year Mortgage" headings is described in the previous section (after-tax payment difference divided by one, minus the tax rate). The account value is the future value of the account at the end of each year. Note that with the 15-year mortgage option, the home buyer will have saved $791,288 by the end of the 30-year period. With the 30-year mortgage option, however, the home buyer will have saved $1,170,239. The final three columns in Table 1 allow for a direct comparison of the advantages of the 15-year mortgage and the advantages of the 30-year mortgage on an annual basis. The "Difference in Mortgage Balances (15-30)" is the principal balance remaining on the 15- year mortgage minus the principal balance remaining on the 30-year mortgage. Note that after year 15, the difference in the balances is equal to the balance remaining on the 30- year mortgage. The difference in the balances shows an advantage of the 15-year mortgage over the 30-year mortgage. The "Difference in Savings Account Values" column demonstrates the benefits of the 30- year mortgage that is, the savings accumulated under the 30-year mortgage option minus the savings accumulated under the 15-year mortgage option. This difference demonstrates the savings advantage of going with the 30-year mortgage option. To determine which mortgage option is best for an individual home buyer, he or she would need to compare the benefit of having the home paid for after 15 years with the potential retirement savings available under the 30-year option. With over $1 million available for retirement under the 30-year option, the analysis clearly favors taking the lower payments of a 30-year mortgage and investing in a tax-deferred investment plan. Selling Early An assumption used in this analysis is that the home buyer is going to keep the home for at least 30 years. For many home buyers, this assumption may not be valid, and it may be argued that the advantages of the 30-year mortgage may not occur to these home buyers. There are two responses to this argument. First, the primary purpose of this analysis is to demonstrate a method that many home buyers can use to help build a substantial nest egg for retirement. Second, even if a home buyer does not hold the home for 30 years, he or she may still be better off with the 30-year mortgage, albeit with a smaller net advantage over the 15-year mortgage. To determine which mortgage option would be most favorable for a home buyer, the difference in mortgage balances should be compared with the difference in the investment account balances. However, keep in mind that since the principal on a mortgage is paid with after-tax dollars, the difference in mortgage balances represents after-tax dollars owed. The investment account is tax-deferred and the difference in investment account values represents pre-tax dollars. Therefore, a direct comparison of the difference in mortgage balances and the difference in savings account balances would be misleading. 6

7 To provide for a more meaningful comparison, the final column of Table 1 gives the net advantage (disadvantage) to the 30-year mortgage option. These values are calculated by taking the difference in savings account values on an after-tax basis and then subtracting the difference in mortgage balances from this after-tax value. By taking the after-tax difference in savings account values, this column provides a direct comparison of the impact on a home buyer s wealth. The after-tax difference in savings accounts is calculated as follows: After-tax Difference in Savings Account Values = Difference in Savings Account Values (1 t) Using the values from Table 1 for the first year: After-tax Difference in Savings Account Values = $5,633 (1.33) = $3,774 The net advantage to the 30-year mortgage for the first year is calculated as follows: $3,774 $4,374 = ($600) Note that after six years, the 30-year mortgage provides a clear advantage over the 15- year mortgage. This comparison does not imply that a home buyer could take the 30-year mortgage option and after a few years sell the home, cash in the retirement plan and use the proceeds to purchase another home. Rather, this comparison implies that, even after considering taxes, a home buyer may be able to amass more equity or wealth with the 30- year mortgage than with the 15-year mortgage. The purpose of this analysis is to demonstrate how a 30-year mortgage may enable home buyers to make considerable contributions to their retirement accounts; it is not intended as a short-term strategy for saving money to buy another home. Not For Everyone The strategy discussed in this paper clearly is not for everyone. For this strategy to work to its fullest, the home buyer must have the ability to make the higher 15-year mortgage payments and have the willpower to invest the difference between the 15-year payment and the 30-year payment in a tax-deferred investment plan. Further, the individual should be willing to invest in some asset (such as stocks) that has an expected return above the mortgage rate. Finally, the strategy will provide the largest benefits to home buyers in the highest tax brackets, purchasing relatively expensive homes and holding them for the long-term. Table 2 presents the results of a sensitivity analysis that shows the advantage of the 30- year mortgage option, assuming various mortgage amounts and various tax rates different from the base case. The values in this table are calculated by subtracting the ending value of the investment account for the 15-year mortgage option from the ending value for the 30-year mortgage option. Using the base case of a $150,000 mortgage and a 33-percent marginal tax bracket, the advantage to the 30-year mortgage is $378,951 (from Table 1: $1,170, ,288 = 378,951). Table 2 demonstrates that the advantages are the greatest for large mortgages and for home buyers in the highest tax brackets. 7

8 Table 2: Sensitivity Analysis of the Impact of the Marginal Tax Rate and the Mortgage Amount on the Advantage of a 30-Year Mortgage. Marginal Tax Rate $75,000 $100,000 $125,000 $150,000 $175,000 $200,000 $225,000 15% $81,370 $108,494 $135,617 $162,741 $189,864 $216,988 $244,111 28% 154, , , , , , ,073 33% 189, , , , , , ,427 36% 213, , , , ,945 69, ,216 39% 239, , , , , , ,065 44% 289, , , , , , ,255 The values in the body of the table represent the difference in savings account balances for the 30-year option minus the 15-year option under various tax rates and mortgage amounts (assumes a 30-year analysis period). For example, over a 30-year period a home buyer in the 28-percent tax bracket with a $100,000 mortgage could accumulate $203,366 more in an investment account if he or she chose the 30-year mortgage option rather than the 15-year mortgage option. Conditions Favorable for the 30-Year Mortgage Option With any comparison of 15-year and 30-year mortgages, the level of mortgage interest rates and the spread between the 15-year and 30-year mortgage rates are important factors. Holding other factors constant, the higher the mortgage rates, the more favorable the 15-year mortgage. In addition, the larger the spread between the 15-year and 30-year rates, the more favorable the 15-year mortgage. The 15-year mortgage becomes more favorable because with high mortgage rates or a large spread, the interest saved with the 15-year mortgage offsets the investment opportunities with the 30-year mortgage. Table 3 presents the results of a sensitivity analysis examining the impact of mortgage rates and spreads on the investment plan proposed in this paper. This table shows the advantage of the 30-year mortgage option for various 15-year mortgage rates and various spreads between the 15-year and 30-year mortgage rates using the base case (mortgage of $150,000 and tax rate of 33 percent). For any given spread, an increase in the 15-year mortgage rate will result in a decrease in the advantage to the 30-year mortgage option. Likewise, for any given 15-year rate, an increase in the spread also results in a decrease in the advantage of the 30-year mortgage option. This analysis demonstrates that the 30- year mortgage option is the most favorable in a low interest rate environment or when the spread between 15-year mortgage rates and 30-year mortgage rates is relatively narrow. Over the past several years, the spread between 15-year and 30-year mortgage rates has been declining. During the early 1990s, the spread was approximately 1.0 percent, but currently the spread is approximately 0.3 percent. Therefore, the current interest rate environment is very conducive to the 30-year mortgage option. 8

9 Table 3: Advantage of a 30-Year Mortgage under Various Mortgage Rate Scenarios 15 Year Rate (30-15) 6% 7% 8% 9% 10% 11% 12% 0.10% $541, $484, $423, $357, $289, $218, $146, % $524, , , , , , , % $506, , , , , , , % $489, , , , , ,448 80, % $471, , , , , ,981 58, % $453, , , , , ,462 36, % $436, , , , ,242 89,889 14, % $418, , , , ,174 68,264 7, % $400, , , , ,046 46,588 29, % $381, , , , ,859 24,862 52, % $363, , , ,677 79,615 3,086 74, % $345, , , ,982 58,315 18,738 96, % $326, , , ,223 36,958 40, , % $308, , ,349 92,401 15,546 62, , % $289, , ,132 71,515 5,921 84, ,623 Values in the body of the table represent the difference in savings account balances for the 30-year option minus 15-year option under various 15-year mortgage rates and various spread between the 30-year mortgage rates and the 15-year mortgage rates (assumes a 30-year analysis period). The final factor examined is the rate of return on investment which represents an opportunity cost for taking the 15-year mortgage option. If the expected rate of return on investment is low, then the 15-year mortgage may be the most favorable. Table 4 demonstrates the impact of changes in the rate of return on investment on the advantage to the 30-year mortgage option. This table shows that for various mortgage amounts, the higher the rate of return on investment, the greater the advantage of the 30-year mortgage option. For home buyers who can earn eight percent or more on their investments, the 30-year mortgage option appears attractive. Home buyers/investors should keep in mind that in order to earn a high return, they will have to take on riskier investments such as stocks. Therefore, it is important to bear in mind that the 30-year mortgage option calls for a long-term investment strategy. If over a 30-year period investors can earn a return equal to the average long-term rate of return on the stock market, the 30-year mortgage option appears to be the most favorable. Home buyers who are extremely conservative or who are not willing to invest in riskier investments (such as common stocks) probably will favor the 15-year mortgage option. 9

10 Table 4: Advantage of a 30-year Mortgage with Various Mortgage Amounts and Rates of Return on the Tax-deferred Investment Plan. Return on Mortgage Amount Investment $75,000 $100,000 $125,000 $150,000 $175,000 $200,000 $225,000 5% $23,058 30,743 38,429 46,115 53,801 61,487 69,173 6% $ ,013 1,140 7% $31,239 41,652 52,065 62,447 72,890 83,303 93,716 8% $1,401 95, , , , , ,203 9% $123, , , , , , ,574 10% $189, , , , , , ,427 11% $273, , , , , , ,349 12% $380, , , , ,721 1,014,539 1,141,356 Values in the body of the table represent the difference in savings account balances for the 30- year option minus 15-year option under various rates of return on the tax-deferred investment plan and various mortgage amounts (assumes a 30-year analysis period). Risk Considerations Some would argue that since the mortgage payments on the 15-year mortgage are essentially risk-free investments, the analysis should only consider risk-free investment opportunities for the tax-deferred investment plan. However, if you consider the mortgage decision as part of a complete financial plan and not as an isolated decision, there does not appear to be a reason to only consider risk-free investments. The 30-year mortgage option will enable many home buyers to begin investing for retirement at an earlier age than if they took on the 15-year mortgage. Therefore, with the 30-year mortgage, the home buyer will have a much longer investment horizon than with the 15-year mortgage. This longer investment horizon is favorable for riskier investments because the investor/home buyer has more time to ride out fluctuations in the market. Another important risk-related consideration in the mortgage decision is the impact of the mortgage on the home buyer s cash flow. If the home buyer selects a 15-year mortgage, he or she is obligated to a higher mortgage payment than if the 30-year mortgage is selected. The higher payment could present a problem if the home buyer has cash-flow problems. The lower payments with the 30-year mortgage gives the home buyer more flexibility. If a home buyer used the strategy of taking the lower 30-year mortgage payment and investing in a tax-deferred investment plan, he or she would have a lower cash flow requirement because the payments are lower and would have the ability to stop making the deposits into the investment plan. Therefore, the home buyer would have more cash available than with the 15-year mortgage. With the 15-year mortgage, the home buyer could refinance and lower his or her payments. However, it will be quicker, easier and less costly to stop making the contributions to the investment plan under the 30-year option than it will be to refinance the mortgage under the 15-year option. In addition, it is not highly desirable to have to refinance a mortgage due to cash-flow problems. Given the additional flexibility of the 30-year mortgage, the home buyer s risk may be significantly lower with the 30-year mortgage than with the 15-year mortgage. 10

11 Summary and Conclusion This paper demonstrates that many home buyers may benefit greatly from taking a 30- year mortgage rather than a 15-year mortgage. By investing the difference between the 30-year mortgage payment and the 15-year mortgage payments in a tax-deferred investment plan, the home buyer may be able to build a sizable retirement investment account balance. The 30-year mortgage is most favorable for home buyers in high tax brackets purchasing relatively expensive homes. In addition, the 30-year mortgage option is preferred when mortgage rates are relatively low and the spread between 15-year and 30-year rates is relatively small. References 1. Paul S. Marshall, "Help Buyers Make the Right Mortgage Wish," Real Estate Today, January 1989, pp Lucinda L. McCartney, "15- Vs. 30-Year Mortgages," Consumers Digest, July/August 1989, pp Upinder S. Dhillon, James D. Shilling and Clemon F. Sirmans, "The Mortgage Maturity Decision: The Choice Between 15-Year and 30-Year FRMs," Southern Economic Journal, April 1990, pp David R. Vruwink and Dann G. Fisher, "The Effects of Income Tax Rates and Interest Rates in Choosing Between 15- and 30-Year Mortgages," The CPA Journal, November 1995, pp Delbert C. Goff, Ph.D., is an associate professor of finance at Appalachian State University in Boone, North Carolina, where he teaches undergraduate and graduate courses in financial management. He has taught several executive seminars and workshops on financial management and business valuation techniques. Don R. Cox, Ph.D., is an assistant professor of finance at Appalachian State University, where he teaches courses in investments, international finance and financial management. His research interests are in the areas of investment management and stock market efficiency. 11

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