## Buy or Rent a House?

Realtor groups have created a number of on-line calculators that attempt to provide an objective view of the advantages of buying a home versus renting a home.  The link to one such calculator is presented below.

First, I describe the calculator.   Then I critique it.

Description of Calculator:

The simple version of the buy/rent calculator at www.realtor.com allows one to put in an address and get financial estimates for renting or buying.  The more advanced and interesting version allows a consumer to select assumptions on costs of buying and cost of renting.

The key assumptions on the cost of buying involve home price, down payment mortgage term, buying costs, selling costs, house appreciation, real estate taxes and miscellaneous homeowner fees.

The most important renting costs include the initial rent and the yearly appreciation in rent.

Other key assumptions include the exemption of  \$500,000 on capital gains in housing, an investment return, and an inflation rate.

Based on the inputted assumptions the model provides an estimate of the amount of time that it takes for buying a home to be cheaper than renting a home.

The model at www.realtor.com assumes that buying costs are 4.0 percent of the purchase price and selling closing costs are 6.0 percent of the final sales price.   Due to transaction costs associated with home purchases, renting will be less expensive than buying for people who stay in a house for a short period of time.   The output of the model is the number of years it takes for buying to be less

Comments on the calculator at www.realtor.com

Comment One:  Often realtors and bankers persuade young homebuyers to use available cash for a down payment rather than immediately retire consumer or student debt.  The model does not have an option to explicitly consider the impact of credit card debt or student debt on the buy versus rent outcome.   The model does require input on the assumption of investment returns.   One way to model the impact of keeping debt is to increase the investment return assumption so that it equals cost of credit cards and student loans.   It would be useful if the model allowed for separate assumptions on investment return and the cost of existing debt.

Comment Two:   I modified one example to consider the breakeven point of a transaction with a 15-year FRM at current interest rates.   I found that buying was preferable to renting after a 6-year period for the 15-year FRM compared to 8 years for the 30-year FRM.   Essay Four provides more information on mortgage choice and lifetime savings.

Comment Three:   The model cannot be easily modified to allow for interest rate uncertainty associated with adjustable rate mortgages.

Comment Four: The model requires an assumption of average annual growth in house appreciation over the entire period and does not consider issues related to the uncertainty of future house appreciation.  House prices do not appreciate in a steady or reliable fashion.   The realtor’s model would have severely overestimated the value of buying a home during the 2004 to 2009 time period and would have underestimate returns from purchasing in 2011 or 2012.  The argument that housing prices would continue to rise was made quite strenuously in 2007 and was used to motivate unrealistic price appreciation assumptions in the breakeven analysis.

The house price appreciation assumption is usually based on what the analyst expects will occur.   An alternative approach would involve basing this parameter on the certainty equivalent.   A certainty equivalent is the guaranteed return that someone would accept rather than take a risk on a higher but uncertain return.

Comment Five. Many people are forced to move because of a new job or divorce.   The rent versus buy calculator does not allow for economic costs associate with moving when house prices fall and house equity turns negative.   Nor does the buy versus rent calculator consider economic costs associated with negative equity that make it difficult for a home buyer to refinance should interest rates fall.

The more relevant question not answerable from this calculator is it better for a person to buy now or reduce debt and buy in a couple of years.

Comment Six:  Often realtors will expect home sellers to put additional investments into the property prior to selling the home.  (Most recently in many neighborhoods realtors are pushing home sellers to install granite kitchen tops.)   The model does not include an option to consider likely upgrade costs.  It may be able to correct for this problem by reducing the price appreciation assumption in the model.  However, the need for upgrades appears to differ widely across properties.

Comment Seven:: The buy-sell calculator can also be used to evaluate mortgage properties financed with FHA loans.   The FHA loan program is geared for relatively small mortgages.  The program has a loan limit that varies across counties and can change over time.   The FHA loan program allows for down payments as low as 3.5% FHA loan costs include mandatory mortgage insurance premiums, part of which is paid up front.  Due to the insurance premiums the cost of the FHA loan is often one percent point higher than the cost of conventional loans.  Most often, the number of years it takes for a home buyer to break even on an FHA loan program will be substantially higher than the number of years it takes to break even on a transaction financed with a conventional loan.   Not surprisingly, the use of real estate break- even calculators is usually illustrated with conventional loan examples rather than FHA loan examples.

Comment Eight: The assumption regarding the rate of appreciation of rents has a major impact on the buy versus rent decision.    A larger percent of people are choosing to rent rather than buy consequently more rents are continuing to rise often at a rate that exceeds the increase in the value of the home.   In some markets it may be legitimate to assume a higher increase in rents than home prices.  This alternative assumption might persuade more people to buy rather than rent.

Comment Nine:  Realtors often argue that a house purchase should occur now rather than later because macroeconomic conditions are about to change.   Over the last three or four years realtors have argued that people should buy because the FED is about to raise interest rates.  An increase in interest rates induced by Fed policy would increase the cost of interest on a home but might also lower house prices.

The Fed will eventually raise interest rates but even Nobel Prize winning economists are confused about when this will happen.  Potential homebuyers should not rely upon the interest rate forecasts of realtors when determining whether or not or buy or rent a home.

Concluding thoughts on the Limitations of Buy Versus Debt Calculators:  My comments suggest that for a wide variety of reasons buy versus debt calculators often overstate the case for buying rather than renting a home.    The approach relies on subjective assumptions on a wide variety of economic variables.   Assumptions on the most crucial variable – the future growth of housing prices have been grossly inaccurate in the past.

The one factor that favors buying over renting in the current environment is that stock prices are currently at historic highs and long term interest rates are at historic lows.   I suspect that based on the current market conditions returns on real estate will outpace returns on financial assets in the near future.  Hence an assumption of a low future return on financial assets might be justified at this time.

The buy versus rent calculator does not accurately measure the benefits of delaying a home purchase until consumer debt and student loans are substantially reduced or eliminated.   Nor does the model allow for active consideration of costs, which might be incurred if a young worker with little initial house equity is forced to sell a home in order to take advantage of a new job opportunity.  Usually younger households will be much better off by delaying the home purchase and using all available funds to retire student loans and consumer debt.

## How much house can a student borrower qualify for?

How much house can a student borrower qualify for?

This answer depends on the maturity of the student loan.

Situation:

Consider a person with a \$100,000 student debt.

• The person can either pay the debt back over a 10-year period or a 20-year period.
• The student loan is this person’s only consumer debt.
•  The person earns \$80,000 per year.
• The student loan interest rate is 7.0 percent.
• The mortgage interest rate is 4.0 percent.
• The mortgage term is 30 years.

Questions:

• How much mortgage can the person qualify for if the person keeps the student loan at 10 years?
• How much mortgage can the person qualify for if the person changes the student loan term to 20 years?
• What is the increased cost of the student loan payments involved by switching from a 10-year to 20-year student loan?

Answer:   I developed a spreadsheet that calculates the maximum allowable mortgage this person can qualify for.

In order to qualify for a mortgage two conditions must hold.

• Monthly mortgage payments must be less than 28% of income.
• Monthly mortgage and consumer loan payments must be less than 38% of income.

The procedure used to calculate the allowable mortgage is as follows:

• First, I calculate the maximum allowable mortgage payment based on zero consumer debt.   This value is 28 percent of monthly income.
• Second, I calculate the maximum allowable mortgage payment consistent with mortgage payments and consumer debt payments equal to 38 percent of income.   This is done by backing out the student loan and allocating the rest to mortgage debt.
• Third, I insert mortgage interest rate, term and payment info into the PV functions to get the mortgage amount
• Fourth, The allowable mortgage is the minimum of the mortgage totals consistent with the two constraints.

The calculations for the two situations presented in this problem are presented in the table below

 Mortgage Qualification Example for Borrower with Student Debt row # Student Loan Information Note 1 Student loan Amount \$100,000 \$100,000 Assumption 2 Interest Rate 0.07 0.07 Assumption 3 Number of Payments 120 240 Assumption 4 Student Loan Payment \$1,161 \$775 From  PMT Function Mortgage Information 5 Rate 0.035 0.035 6 Term 360 360 Income Assumption 7 Income \$80,000 \$80,000 Assumption 8 Constraint One:  Maximum monthly mortgage payment consistent with this income assumption \$1,867 \$1,867 28% of monthly income 9 Constraint Two:  Maximum monthly consumer and mortgage payments consistent with income \$2,533 \$2,533 38% of monthly income 10 Maximum mortgage consistent with constraint one. \$415,697 \$415,697 pv of mortgage rate number of periods, and pmt where mortgage rate and payments are assumptions baed on the market and product chosen and payment is max allowable given   income 11 Allowable mortgage payment consistent with constraint two given required student debt \$1,372 \$1,758 Row 9 minus Row 7 12 Max mortgage consistent with borrowing contraint two. \$305,593 \$391,505 Use PV function with rate and term set by market and product and payment the amount of mortgage payment after required consumer payments 13 Allowable mortgage debt \$305,593 \$391,505 Minimum of Row 10 and Row 12

An increase in the term of the student loan from 10 to 20 years increases the size of a mortgage a household can qualify for from \$305,000 to \$391,000.

Getting the extra mortgage is not cheap.  The increased student loan term causes total student loan payments to go from \$139.000 to \$186,000.

Concluding thoughts:  Most people who have \$100,000 in student debt will have to refinance the student loan if they are going to buy a house.

## Student debt and qualifying for a mortgage

Student debt and qualifying for a mortgage

Excel Topics:  PMT function and Spreadsheet design

Question:  A person graduates from college and graduate school with \$100,000 in student debt.   The interest rate on a 10-year student loan is 5% per year.   The person wants to buy a house that costs \$300,000 with a 90% LTV loan. The home mortgage interest rate is 4.5% on a 30 year FRM.

Assume that in order to qualify for the house the person must meet two conditions.

Constraint One:  The ratio of mortgage interest to income must be less than 0.28.

Constraint Two: The ratio of total interest (mortgage and non-mortgage) interest must be less than 0.38.

How much income does this person need to qualify for a loan on this house?

Why might student debt have a smaller impact on the purchase of a \$700,000 home than the purchase of a \$300,000 home.

Analysis:   The analysis for the \$300,000 home is laid out in the table below.

 Mortgage Qualification Example for Borrower with Student Debt Note Student loan Amount \$100,000 \$0 Assumption Interest Rate 0.05 0.05 Assumption Number of Payments 120 120 Assumption Student Loan Payment \$1,061 \$0 From  PMT Function House Amount \$300,000 \$300,000 Assumption LTV 0.9 0.9 Assumption Loan Amount \$270,000 \$270,000 LTV * House Amount Intrerest Rate 0.045 0.045 Assumption Number of Payments 360 360 Assumption Mortgage Payment \$1,368 \$1,368 From PMT Function Total Loan Payments \$2,429 \$1,368 Sum Payments Monthly Income Constraint One \$4,886 \$4,886 Student Loan Payment divided by 0.28 Monthly Income Constraint Two \$6,391 \$3,600 Mortgate Payment Divided by 0.38 Required Monthly Income \$6,391 \$4,886 Max of income over both constraints Required Annual Income \$76,696 \$58,631 12* Max Income

Observations Pertaining to the \$300,000 home for a person with and without student loans

A person with no student debt could qualify for this mortgage with an annual income of \$58,630.

The person with the student debt needs an annual income of \$71,585.

The impact of student debt on purchases of a larger home:   The allowable mortgage is determined by two constraints one involving mortgage debt only and the other involving the sum of mortgage and consumer debt.   When the mortgage debt is very large, constraint one (the mortgage debt constraint) will be the binding constraint.

Continue reading Student debt and qualifying for a mortgage

## A House Equity and Mortgage Payoff Spreadsheet

A House Equity and Mortgage Payoff Spreadsheet:

Question:   A person buys a house and plans to either sell and move or pay off the mortgage in twelve years.

The person is considering taking out a 15-year or a 30-year fixed rate mortgage.

The assumptions on the home purchase, house equity growth, the cost of selling and moving, and the cost of funds for the payoff of the mortgage are presented in the table below.

Table One: Assumptions for 30-year vs 15-year FRM Comparison:

 Label 30-year FRM 15-year FRM Purchase Price of House \$500,000 \$500,000 Down payment percentage 0.9 0.9 Initial Loan Balance \$450,000 \$450,000 Mortgage Term 30 15 House appreciation rate 3.0% 3.0% Mortgage Interest Rate 4.0% 3.3% Years person owns house 12.00 12.00 Cost of selling and moving to a new home as % of house value 9.0% 9.0% Tax Rate on Disbursements from 401(K) Plan 30.0% 30.0%

Create a spreadsheet that provides estimates of house equity after the sale and move or mortgage payoff amounts after twelve years when the house buyer uses a 30-year FRM and when the house buyer uses a 15-year FRM

Base your mortgage payoff calculation on the assumption that the source of funds for the mortgage payoff are fully taxed funds from a 401(k) plan.

http://wp.me/a2WYXD-4i

Results:

The results for the comparison of the 15-year and 30-year FRM for the assumptions presented in table one are presented in Table 2.

Table Two: Results for the 30-year vs 15-year FRM Comparison:

 30-year FRM 15-year FRM House Equity after Selling and Moving Costs \$318,303 \$540,109 Forecasted Mortgage Payoff Amount -\$472,025 -\$155,160

Observations on the 30-year vs 15-year FRM comparison:

The person taking out the 15-year FRM mortgage has around \$222,000 more in house equity at the end of the 12-year holding period.

The mortgage payoff calculation when funds are disbursed from a 401(k) plan includes tax on the disbursements.   Inclusive of the tax bill, the mortgage payoff amount is \$317,000 higher for the buyer who uses the 30-year FRM than for the buyer who uses the 15-year FRM.

Other Applications for the House Equity or Mortgage Payoff Spreadsheet:

Modify the mortgage payoff calculation to allow for a situation where funds for the mortgage payoff are obtained from three sources – (1) a savings account, (2) sales of common stock, and (3) disbursements from a 401(k) plan.   Treat tax rates as an endogenous variable in the new model.

Compare results for both mortgage types under the 90% LTV assumption to results under an 80% LTV assumption.

Run the model on 15-year and 30-year FRMs for holding periods ranging from 1 to 15 years.   How does the advantage of the 15-year FRM vary with holding period?

Authors Note:   This problem was discussed further in the post below.

Essay Nine: Retire Mortgage Debt or Accumulate in Your 401(k) Plan:

https://financememos.com/2015/10/09/essay-nine-retire-mortgage-debt-or-accumulate-in-your-401k-plan/

Essay nine points out that many financial advisors stress accumulation of wealth in 401(k) plans rather than mortgage balance reductions even when their clients are nearing retirement.  The major banks employing the same financial advisors issue mortgages and sponsor 401(k) plans.   As a result, the interests of the financial advisors and the interests of their clients are not automatically aligned.

This approach can backfire when stock markets underperform nearing retirement.

During working years. the tax code favors people with large mortgages and people who are contributing to their 401(k) plan.  However, after retirement the person who must disburse funds from a 401(k) plan often has a hefty tax bill.

Interestingly, most financial analysts advise their clients to add more to their 401(k) plan rather than pay off their mortgage.  More discussion of this problem can be found below.

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 0.039 0.031 Term 360 180 Loan Balance 400000 400000 Payment -\$1,886 -\$2,781 Future Value \$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.