## Comparing 15-year and 30-year Mortgages

Question One: A person is considering taking out a \$180,000 mortgage and must choose between a 15-year FRM and a 30-year FRM.   The interest rate on the 15-year mortgage is 2.90 while the interest rate on the 30-year mortgage is 3.40.

What are the monthly payments on the two loans?

What are the total interest payments on the two loans over the life of the loan?

What is the after-tax cost of the interest payments on the two loans?

What is the tax savings from the tax deductibility of mortgage interest?

What is remaining loan balance after 15 years for the two loans?

Answer: The monthly mortgage payment calculation is directly calculated from the PMT function in Excel.  The variables inputted into the PMT function are the interest rate, the term and the loan balance.

The lifetime interest cost is calculated two ways.   The first way involves noting that the difference between total payments and the repaid loan balance is equal to interest payments. (180* \$1234-\$180,000) =\$42,193.

The second way involves calculating cumulative interest payments directly from the CUMIPMT function in Excel. Put Rate=0.029/12, NPER=180, PV=\$180,000 STARTPERIOD=1, ENDPERIOD=180, and Type=0 into CUMIPMT and get \$42,193.)

The after tax cost of interest payments is (1-MTR) x INTEREST.

The tax savings from interest payments is MTR x INTEREST

The mortgage balance after 15 years is obtained directly from the FV function in Excel. Note FV (RATE=0.029/12,NPER=180, PMT=-1234,PV-180000) is equal to \$0. This is a good way to check your work since the balance on a 15-year mortgage held for 15 years must be \$0.

The complete answers are laid out in the table below.

 A Comparison of 15-year and 30-year FRM 15-year FRM 30-year FRM Notes Rate 0.029 0.034 Assumption Period 180 360 Assumption Loan \$180,000 \$180,000 Assumption Payment -\$1,234 -\$798 Calculation From Payment Function Interest Cost Calculation One \$42,193 \$107,376 Calculation: Total Payments – Loan Balance Interest Cost Calculation Two \$42,193 \$107,376 Calculation From CUMIPT Function Marginal Tax Rate 0.3 0.3 Assumption After Tax Interest Cost \$29,535 \$75,163 Calculation: (1-mtr)*Interest Cost Tax Savings from Mortgage Deductibility \$12,658.05 \$32,212.75 Tax Savings from Mortgage Deduction Mortgage Balance After Fifteen Years \$0 -\$112,435 Calculation: From FV Function Total Mortgage Payments Over 15 Years -\$222,193 -\$143,688 Calculation 180*MONTHLY MORTGAGE PAYMENT

Discussion of Comparison of 15-year and 30-Year FRM:

• Over a 15-year period the homeowner with the 30-year FRM has accumulated \$112,435 less house equity than the homeowner with the 15-year FRM.
• Over the 15-year period, the homeowner with the 15-year mortgage has paid over \$78,000 more in mortgage payments than the homeowner with the 30-year mortgage. However, the owner with the 30-year mortgage is not done yet.
• The additional tax savings from the use of the 30-year FRM is around \$20,000.

Authors Note:   People interested in what will happen to the Affordable Care Act under Trump should go to my health care blog on the topic.

Here is a post on Senator Paul’s health care plan.

http://healthcarememos.blogspot.com/2017/01/senator-rand-pauls-health-care-plan.html

My own outline of potential modifications to the ACA will be presented shortly.

## Increases in Undergraduate Debt 2003/2004 to 2011/2012

The statistics presented in this post document the dramatic increase in student debt between 2004 and 2012.

Increases in Undergraduate Debt 2003/2004 to 2011/2012

My holiday visit with in-laws included less discussion of politics this year for obvious reasons but I did have a brief discussion on student debt with one relative.   His view of the issue is that since his generation paid for their college no additional cost subsidies are needed. My concern is that the recent increases in costs are having substantial adverse impacts on the current cohort of students.

I am planning several more posts on college costs and their economic and impacts.   This post looks at the trend growth of student debt between the 2003/2004 and the 2011/2012 academic years.

The Data: The source of data for this study is the NSPAS database. I was able to access the data from the NCES Power Statistics Portal.

https://nces.ed.gov/datalab/index.aspx

My variable of interest in this post is cumulative amount borrowed in the undergraduate years by people receiving a bachelor’s degree at four-year institutions.   I have presented separate tables for private and public four-year institutions.

Three statistics are presented – Average debt for borrowers, the percent of students who borrowed, and the percent of students who borrowed more than \$25,000.

The data does not include information on borrowing by parents through the PLUS program.

Statistical Results:

The statistics describing change in cumulative student debt are presented in the table below.

 Cumulative Under Graduate Student Debt at Four-Year Institutions 2004 to 2012 Bachelors Degree Four-Year Public 2003/2004 2011/2012 Diff. % Diff. Average Debt for Borrowers \$11,958 \$18,845 \$6,887 57.6% % of Students who Borrowed 56.6 63.5 6.9 12.1% % of Students with debt greater than \$25,000 5.3 16.9 11.6 218.7% Bachelors Degree Four-Year Private 2003/2004 2011/2012 Difference % Diff Average Debt for Borrowers 14,536 22,962 \$8,426 58.0% % of Students who Borrowed 66.9 69.1 2.2 3.3% % of Students with debt greater than \$25,000 9.6 22.9 13.3 138.0% Both Public and Private Four-Year Programs Average Debt for Borrowers 12,876 20,163 \$7,287 56.6% % of Students who Borrowed 60.8 65.2 4.4 7.2% % of Students with debt greater than \$25,000 6.8 18.7 11.9 176.4%

Summary of Statistical Results:

The growth of cumulative student debt among people receiving a bachelor’s degree from a four-year institution was tremendous during this brief eight-year period.

Total debt incurred by student borrowers receiving a bachelor’s degree rose by around 57% over this eight year period.

The proportion of undergraduate bachelor degree students incurring debt rose by 6.9 percentage points at public institutions and 2.2 percentage points at private institutions.

The proportion of undergraduate bachelor degree students incurring more than \$25,000 in debt went from 5.3% to 16.9 percent for students at public schools and from 9.6 percent to 22.9 percent for students at private institutions.

Other Student Debt Trends:   There are other student debt trends that need to be be addressed including  — the expansion of PLUS loans to parents, increased  use of private debt, changes in debt incurred by graduate students, changes in the number of students with excessive levels of student debt:

Economic Financial and Social Implications:

Economic issues related to the increase in student debt include – (1) A decision by many young people to live with parents and delays in starting a family, (2) a decision to delay home purchases, (3) the choice between a 30-year and 15-year mortgage, and (4) a decision to delay placing funds in a 401(k) plan.

Many older financial experts do not agree with the decision by many in the current generation to delay home purchases and delay saving for retirement.

My view is that the older generation is not in fully touch with the economic realities facing many in the millennial generation from the explosion in student debt occurring over a mere eight years.

## Retire Mortgage Debt or Accumulate in Your 401(k) Plan?

Increasingly, many Americans nearing the end of their work life find they have a large mortgage and must choose between paying off the mortgage or contributing more funds to their 401(k) plan. A large number of financial advisors advise their clients to increase 401(k) contributions rather than pay off their mortgage.

http://www.forbes.com/sites/nancyanderson/2014/01/03/7-reasons-not-to-pay-off-your-mortgage-before-you-retire/

http://www.kiplinger.com/article/real-estate/T040-C000-S002-should-you-pay-off-your-mortgage-before-you-retire.html

http://www.washingtonpost.com/news/get-there/wp/2015/03/26/the-case-for-not-paying-off-your-mortgage-by-retirement/

http://www.schwab.com/public/schwab/nn/articles/Should-You-Pay-Off-Your-Mortgage-Early-Before-You-Retire

http://www.principal.com/planningcenter/retirementplanning/nearingretirement/retirementnews/mortgagequestion.htm

My view is that it is essential for people nearing retirement to eliminate their mortgage debt even if this goal requires some reduction in 401(k) contributions.   I have two reasons for this view.   First, as noted and explained in the previous section 401(k) plans are not capable of mitigating the impact of market down turns at the end of a career or during retirement.   Intuitively, a person with no debt is much better able to withstand market downturns than a person with a mortgage.   The Wall Street analysts always say don’t sell on a panic the market will come back.   Well retirees with a large mortgage often have no choice but to sell.

Second, the financial risk considerations interact with another factor, the tax treatment of 401(k) plans. During working years mortgage interest and 401(k) contributions reduce income tax burdens.   During retirement a person with a large mortgage payment and most financial assets inside a 401(k) plan will pay more in tax than a person without a mortgage.

All disbursements from a 401(k) plan are fully taxed at the ordinary income tax rate.   A person with no mortgage disburses enough to cover discretionary expenses and taxes   A person with a mortgage must disburse enough to cover discretionary expenses, the mortgage and taxes.

The disbursement to cover the mortgage leads to additional taxes because all disbursement from the 401(k) plan is taxed. MOREOVER, THE DISBURSEMENT ON FUNDS USED TO COVER THE TAX ON THE 401(K) DISBURSEMENT IS ALSO TAXED.

Part of Social Security is taxed for people with income over a certain threshold. A quick way to find out if part of Social Security benefit is taxable is to compare your income to the threshold for your filing status — \$25,000 for filing status single and \$32,000 for filing status married.

http://www.irs.gov/uac/Newsroom/Are-Your-Social-Security-Benefits-Taxable

Higher disbursements from the 401(k) plan can increase your adjusted gross income beyond the threshold and increase the amount of the Social Security benefit subject to tax.   Of course any 401(k) disbursement used to pay the income tax is also taxed.

So let’s take a household with all financial assets in their 401(k) plan with a \$30,000 annual mortgage.   This monthly mortgage is \$2,500, not huge.   Let’s assume that the person has to pay around \$1,000 more in tax on Social Security benefits because of the additional disbursement to pay down the mortgage. A first order approximation of the amount of additional tax needed because of the additional \$31,000 disbursement is \$31,000 x the marginal tax rate for the taxpayer.   For most filers the marginal tax rate would be around 25 percent in 2014.

So the taxpayer with the mortgage and the additional tax burden because of the additional 401(k) disbursement will probably disburse \$39,000 more per year from their 401(k) plan.

This analysis puts a whole new wrinkle on the question how much money does one have to save in their 401(k) to have a secure retirement.   The answer is much more if you have not paid off your mortgage.

Note that the disbursement to cover the unpaid mortgage must occur whether the market falls or rises.

Many people who choose to add to their 401(k) plan rather than pay off their mortgage prior to retirement are going to have sell their home and downsize. Downsizing may make sense but most people don’t want to downsize until they are fairly old.

Some people who end up selling their home may choose to rent rather than buy a new home.   The main risk of choosing to rent throughout retirement is that home prices and rents may rise.   This exacerbates longevity risk.

Downsizing should be a choice not an outcome from a failed financial plan or worse the result of financial advisors putting their interests over your interests

Concluding thoughts on mortgage debt in retirement: An increasing number of households are retiring prior to their mortgage being entirely paid off. Surprisingly, the existence of a mortgage in retirement is often consistent with a financial plan developed by a financial planner.   Many financial analysts and planners advise their clients to increase savings in their 401(k) plan rather than retire their mortgage.

These financial planners are not being upfront with their clients.   Retirees with mortgage debt and all or most financial assets in a 401(k) plan are at the whim of the market and have a substantial tax obligation.   The advice that put people in this position is in my view a form of malpractice.

Appendix to Essay on Mortgage Debt and 401(k) Assets in Retirement

The issue of whether to pay off a mortgage or contribute to a 401(k) plan for an older worker is related to the issue of mortgage choice, especially for older homebuyers.   The following question addresses the interaction between mortgage choice and 401(k) investment strategy for an older worker.

Question:   A 50 year-old person is buying a house and must choose between a 15-year mortgage and a 30-year mortgage.   The mortgage choice will impact how much money the person can contribute to his or her 401(k) plan.

The person makes \$80,000 per year. The initial mortgage balance is \$400,000.   The person’s 401(k) balance at age 50 is \$200,000. The 30-year FRM rate is 3.9 percent and the 15-year FRM rate is 3.1 percent.

Discuss the advantages and disadvantages of two strategies (1) taking the 30-year FRM and investing 15% of salary in the 401(k) plan and (2) taking the 15-year FRM and investing 5% of salary in the 401(k) plan.

Analysis:

Let’s start with a reiteration of mortgage choice issues a subject previously broached in essay four.

Observations and Thoughts on Mortgage Choice Issues:

• The monthly payment on the 30-year FRM is nearly \$900 less than the monthly payment on the 15-year FRM. The higher mortgage payment on the 15-year FRM will all else equal require the person who chooses the 15-year FRM to make a smaller 401(k) contribution than the person who chooses the 30-year FRM.
• After 15 years the 15-year FRM is completely paid off.   The remaining loan balance on the 15-year FRM is around \$257,000.
• Note that gains from the quicker pay down on the 15-year mortgage are not dependent on market fluctuations.   The gain from debt reduction occurs regardless of whether the market is up or down and regardless of when bear or bull makers occur.
 Analysis of 15-Year Versus 30-Year FRM 30-Year 15-Year Mortgage Interest Rate 0.039 0.031 Mortgage Term 360 180 Initial Loan Balance 400000 400000 Payment -\$1,886 -\$2,781 Loan Balance after 15 years \$256,799 \$0.00

Observations and Thoughts on Two 401(k) Contribution Strategies:

As noted in essay eight, the final 401(k) balance after 15 years depends on both the rate of return of the market and the sequence of the returns in the market.   Outcomes are presented for two market scenarios.   The first involves 7% returns for the entire 15-year period.   The second involves 7% returns for 10 years followed by -4% returns for 5 years.

• The difference in the final 401(k) balances (high contribution minus low contribution) under the 15-year bull market scenario is around \$211,000.
• The difference in the final 401(k) balance (high contribution minus low contribution) under the 10-year bull and 5-year bear scenario is around \$131,000
 Analysis of Different 401(K) Contribution Strategies 5% Contribution Rate 15% Contribution Rate Difference 7.0% Return for 15 Years \$675,442 \$886,752 \$211,309 7.0% Return for 10 years followed by -4.0% return for 5 years \$394,339 \$525,090 \$130,751

The initial balance in the 401(k) plan for both scenarios is \$200,000.

• The 30-year mortgage/high 401(k) contribution strategy results in major tax savings during working years compare to the 15-year mortgage/low 401(k) strategy.   All mortgage interest is tax deductible and the 401(k) contribution is not taxed.
• The 15-year mortgage/low 401(k) contribution strategy results in major tax savings during retirement compared to the 30-year mortgage/high 401(k) strategy.   The previous example in this section demonstrated exposures for the person with mortgage debt in retirement when the person is dependent on 401(k) disbursements.   Remember all disbursements from a conventional 401(k) plan including disbursement used to pay the mortgage and disbursements used to pay taxes are fully taxed at ordinary income rates.   By contrast, the money gained from paying off the mortgage and most capital gains on owner-occupied real estate is not taxed.
• Financial risks associated with a bull market persist through retirement as long as the saver allocates 401(k) assets into equity.

## Review of Retirement Heist

Review of Retirement Heist:  How Companies Plunder and Profit from the Nest Eggs of American Workers

Ellen Schulz describes the different ways companies have reduced worker’s pension benefits in order to increase profits, manipulate earnings, cut costs, or fund pension benefits for top managers instead of workers.

http://www.amazon.com/Retirement-Heist-Companies-Plunder-American/dp/B00AK3WCZ8

Some highlights:

Chapter two describes how companies cut or froze benefits in the traditional defined benefit plan without antagonizing workers or creating bad publicity for the firm.   The replacement of a generous defined benefit plan with a new less generous plan is generally introduced in a way where changes are not transparent to workers.   Phillip Strella a lawyer with Mercer consulting advised the industry to “Pick your words carefully.  The law doesn’t require you say, “We’re significantly lowering your benefit,” “

Chapter three discusses how pension reductions allow companies to report greater earnings to shareholders. Management has a strong incentive to report good and stable earnings because their compensation is often tied to the stock price of the firm.  Pensions are often cut to increase earnings when the company suffers losses from its core business activities.  One of the main problems is that actuaries have great latitude in the assumptions used to price health and retirement benefits hence; official accounting standards allow management to reduce or increase the value of pension and health benefits in order to report whatever income figure it needs to report.

The drop in pension and health benefits and the increase in health premiums have significant impacts on workers, retirees and their families.  The most difficult situations revolve around the loss of health benefits because Medicare does not begin coverage until age 65.  According to a Department of Labor Review cited by Schulz by the late 1990s around two-thirds of retired workers with employer sponsored health coverage were dropping coverage when costs of the health plan rose.  The departure of individuals from employer sponsored health plans resulted in adverse selection or a “death spiral” because sicker workers and families tended to maintain coverage while healthier workers tended to exit.  One of the more important aspects of the still not fully implemented and tested Affordable Care Act was to fix this problem by mandating that all people be covered and by establishing age-rated premiums that will be unaffected by health status.

Schulz’s book includes a lot of personal stories.  Some of the anecdotes involved overpayments to workers that companies tried to reclaim.  Often companies that acquire other firms and their pension obligations look for past overpayments to retirees in order to claw the overpayments back.  This can create large problems for households who created a budget based on their anticipated and previously receive pension.

Chapter 11 discusses denial of benefits with a focus on disability claims in two industries -– energy and football.  The discussion of how the NFL aggressively denies claims to injured players was especially revealing.  It demonstrates that even in a small high-profile industry with a strong union the system is rigged against workers.

The pension system based on company-run defined benefit plans is experiencing a slow death.  The 401(k) has become the dominant pension vehicle for current workers.  There are a lot of problems with 401(k) plans including inadequate contributions by workers and a high degree of investment risk.  Schulz’s disturbing book vividly reminds us that there are also problems with traditional defined-benefit pension.

## Understanding the four percent rule

Question:   Is the 4.0% rule an appropriate guideline for determining the amount of savings a retiree should spend each year?

Background on the 4.0% rule:  Under the four percent rule (as I understand it ) the retiree’s expenditure in her first year of retirement is four percent of wealth in certain accounts.  It is more difficult to apply the 4.0% rule to total household wealth because house equity, a major component of wealth is not liquid.  (The application of the 4.0% rule to total wealth including house equity would at some point require the sale of the home.)

Whether strict adherence to the 4.0% rule leads to a smooth, stable, and sustainable consumption pattern for the household depends on asset returns, inflation, and the timing of inflation and asset returns.  A sharp decrease in returns at  the beginning of retirement could lead to a relatively quick depletion of assets.  A sharp increase in returns at the beginning of retirement could allow retirees to spend more than allowed or provide a bequest to heirs.

The 4.0% rule may result in retirees too quickly depleting their resources in the current financial environment where the risk free return is lower than inflation.

http://financememos.com/2013/02/15/chasing-yield-by-investing-in-long-term-bonds/

Illustrating the 4.0% rule:  We consider four scenarios — (1) 2.00% returns and 3.0% inflation all years, (2) 4.0% returns and 3.0% inflation rate for all years, (3) a -20% return the first year followed by 2.0% returns and 3.0% inflation, and (4) -20% return the first year followed by 4.0% return and 3.0% inflation.

We calculate the number of years it would take for the retiree to deplete all assets under the four scenarios.  Results presented in Table Four indicate that years until depletion range from 19 years for scenario three to 30 years for scenario two.

 Adequacy of resource for 4% rule under four scenarios Shock Return Inflation Rate Year Balance goes to \$0 None 2.00% 3.00% 23 None 4.00% 3.00% 30 -20% first year 2.00% 3.00% 19 -20% first year 4.00% 3.00% 23

I suspect that these calculations understate the financial risk associated with adherence to the 4.0% rule.   Some analysts suggest that investors who use the 4.0% rule should maintain a larger portion of their portfolio in equites.  I disagree.  The worse case scenario for the 4.0% rule involving poor stock returns in a period of inflation actually occurred during the 1970s.

 Initial Balance \$100,000 Disb. Rate 4.00% Rate of return Inflation rate Real Value of initial balance Beginning of year balance Disbursement End of year balance 1 2.00% 3.00% \$100,000 \$100,000 \$4,000 \$98,000 2 2.00% 3.00% \$103,000 \$98,000 \$4,120 \$95,840 3 2.00% 3.00% \$106,090 \$95,840 \$4,244 \$93,513 4 2.00% 3.00% \$109,273 \$93,513 \$4,371 \$91,013 5 2.00% 3.00% \$112,551 \$91,013 \$4,502 \$88,331 6 2.00% 3.00% \$115,927 \$88,331 \$4,637 \$85,460 7 2.00% 3.00% \$119,405 \$85,460 \$4,776 \$82,393 8 2.00% 3.00% \$122,987 \$82,393 \$4,919 \$79,122 9 2.00% 3.00% \$126,677 \$79,122 \$5,067 \$75,637 10 2.00% 3.00% \$130,477 \$75,637 \$5,219 \$71,931 11 2.00% 3.00% \$134,392 \$71,931 \$5,376 \$67,994 12 2.00% 3.00% \$138,423 \$67,994 \$5,537 \$63,817 13 2.00% 3.00% \$142,576 \$63,817 \$5,703 \$59,390 14 2.00% 3.00% \$146,853 \$59,390 \$5,874 \$54,703 15 2.00% 3.00% \$151,259 \$54,703 \$6,050 \$49,747 16 2.00% 3.00% \$155,797 \$49,747 \$6,232 \$44,510 17 2.00% 3.00% \$160,471 \$44,510 \$6,419 \$38,982 18 2.00% 3.00% \$165,285 \$38,982 \$6,611 \$33,150 19 2.00% 3.00% \$170,243 \$33,150 \$6,810 \$27,003 20 2.00% 3.00% \$175,351 \$27,003 \$7,014 \$20,529 21 2.00% 3.00% \$180,611 \$20,529 \$7,224 \$13,715 22 2.00% 3.00% \$186,029 \$13,715 \$7,441 \$6,548 23 2.00% 3.00% \$191,610 \$6,548 \$7,664 -\$985 24 2.00% 3.00% \$197,359 -\$985 \$7,894 -\$8,899 25 2.00% 3.00% \$203,279 -\$8,899 \$8,131 -\$17,208 26 2.00% 3.00% \$209,378 -\$17,208 \$8,375 -\$25,927 27 2.00% 3.00% \$215,659 -\$25,927 \$8,626 -\$35,072 28 2.00% 3.00% \$222,129 -\$35,072 \$8,885 -\$44,659 29 2.00% 3.00% \$228,793 -\$44,659 \$9,152 -\$54,704 30 2.00% 3.00% \$235,657 -\$54,704 \$9,426 -\$65,224