Buy or Rent a House?

14 Oct

  Discussing Buy Versus Rent Calculators

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 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 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


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.


Two Ways to Calculate a Portfolio PE Ratio

14 Oct

Two Ways to Calculate a Portfolio PE Ratio 

Question:  The table below contains data on the market cap and the earnings for four high-tech firms.

Market Cap and Earnings for Four Tech Firms
Market Cap

($ B)


($ B)

AAPL 892.16 46.65
MSFT 585.37 21.2
AMZN 475.37 1.92
TWTR 13.11 -0.44797


In this post, I am asking you to use two methods to calculate the PE ratio of this four-stock portfolio and to confirm that both methods provide the same answer.

Method One:

Calculate the PE ratio of this portfolio by taking the sum of the market cap numbers for the four stocks and dividing by the sum of the earnings of the four stocks.

Method Two:

Calculate the ratio of (market cap minus earnings) divided by market cap for the four stocks.

Calculate a weighted average of the values (MC-E)/MC for the four stocks with the ratio weighted by MC.  Give the name to this weighted average the letter f.

Calculate 1/(1-f).

Show that the PE ratio from method one is identical to 1/(1-f).


The straight forward way to calculate the PE ratio by taking the ratio of the sum of the market caps to the sum of the earnings is presented below.

Portfolio PE Ratio – Method One
Market Cap

($ B)


($ B)

AAPL 892.16 46.65
MSFT 585.37 21.2
AMZN 475.37 1.92
TWTR 13.11 -0.44797
Total 1966.0 69.3 28.4


This four-firm portfolio has a PE ratio of 28.4.

The PE ration calculation for method two  is presented below.


Portfolio PE Ratio — Method Two
Market Cap Earnings (MC-E)/MC Weight
AAPL 892.16 46.65 0.9477 0.4538
MSFT 585.37 21.2 0.9638 0.2977
AMZN 475.37 1.92 0.9960 0.2418
TWTR 13.11 -0.44797 1.0342 0.0067
1966.01 1.0000
f 0.9647
1/(1-f) 28.4


The second method for calculating a PE ratio gives the same result as a the first – 28.4.

Implications:   The PE ratio of a portfolio can be expressed as function of the weighted average of the ratio of the difference between market cap and earnings of the firm to market cap of the firm.    This is a very useful result.

PE ratios of firms are frequently not useful.

First, the PE ratio can become very large when earnings are very small. This means it is misleading to look at a weighted average of PE ratios because one firm can have a a very large impact. In our current example, the PE ratio of Amazon is 248 and the weighted average PE ratio for the four stocks is  77.

Second, PE ratios have no economic meaning when earnings are negative.

The PE ratio of a firm with negative earnings would reduce the weighted average of PE ratios in a portfolio.  By contrast, (MC-E)/MC will be larger than 1 if E is less than 0.

A firm with slightly negative earnings would have a negative PE ratio with a larger absolute value than a firm with very large losses.  This ranking of firms is incorrect because larger losses should be associated with lower relative valuations.   By contrast, (MC-E)/MC will always rise when E falls.

By contrast, the ratio of the difference between market cap and earnings over market cap is inversely related to the valuation of a firm.   When earnings are negative this ratio is greater than one.   When earnings are zero the ratio equals one.   When earnings are very small the ratio approaches one and is not an outlier.  The ratio of the difference between the market cap and earnings to market cap is intuitively defined for all earnings and not impacted by outliers.

In my next post, I will show that statistical tests based on samples of the ratio of the difference between the market cap and earnings to market cap are more useful than statistical tests based on PE ratios.


Measuring Returns for Different Investment-Consumption Patterns

14 Oct

Measuring Returns for Different Investment-Consumption Patterns

Question:   An investment advisor tells his client to invest $1,000 per month in VFIAX (Vanguard S&P fund) for five years.   The person will then live off the proceeds in this fund for 36 consecutive months.

Calculate the return on assets from this investment/consumption plan for two different start dates – January 1, 2002 and January 1, 2003.

What is the NPV of investment returns from this investment strategy/ consumption plan on the same start dates?

What should investors who are planning to save for five years and spend for three years learn from this example?

Mutual funds and ETFs tend to advertise holding period returns based on specific purchase dates and specific sale dates.   These returns are based on the price of securities on two dates only.   What does the example presented here tell you about the usefulness of two-period return statistics reported by mutual funds?

Methodological Note:  The shares purchased each month are $1,000/PVFIAX where PVFIAX is the price of the ETF.   I sum over 60 months to get the total shares purchased, which I will denote TSHARES. The formula for cash inflow for the 36 months are (1/36)*TSHARE*PVFIAX.

The cash inflow/outflow column and the date column are inputted into the XIRR function in Excel to give the IRR of the inflows/outflows on these particular dates. The XNPV function gives net present value of the cash flows.


The value of VFIAX reached its pre financial crisis high in 10/2007 and reached its crisis trough in 02/2009.   Hindsight is 20/20 but it appears as though diversification prior to the downturn would have been beneficial.

What follows are return calculations for the two scenarios.

Results are in the table below.

Returns for Two Investment/Consumption Scenarios
Invest Period Consumption Period IRR NPV
2002/2006 2007/2009 12.04 $15,766
2003/2007 2008/2010 2.98*e-9 $801


  • The person who stopped saving in December 2006 did fairly well despite the financial crisis.The IRR for this investor was 12.04 %.   The NPV of the investments was $15,766.   (NPV calculation assumes a5 percent cost of capital.) 
  • The person who stopped investing in December 2007 realized a return only slightly higher than 0 percent.The NPV of this person’s investment was around $800.

Discussion of Investment Strategy:

In my view, a 100 percent VFIAX strategy is unwise for an investor with this type of investment and consumption period.

How to fix this problem is a more difficult question.  It is important to note that the strategy of putting 100 percent of funds in VFIA for an investor with a start date of January 1 2009 or January 1, 2010 did quite well.

529 plans offer life-cycle funds that drift towards a more conservative investment as the person nears the date where he must spend money.   Lifecycle funds would have done reasonably well for both of the scenarios considered here.  However, the life-cycle approach creates miserable results when the market does poorly in the first few years of the investment period and then rebounds.

My view on how to solve this problem is evolving.  A 60/40 (stock/bond) portfolio would have done well in these time periods but I don’t believe that it will work in the next crash.  Interest rates are now very low and I expect in the next crisis bonds and stocks will crash together.   Perhaps allocating some resources into an inflation-indexed bond fund would help balance returns during the next crisis.

The trend in investment is toward investment in passively managed funds like the ones offered by Vanguard.    This is at best a partial solution.   Investors need help in allocating money across several passively managed funds.  This includes advice on initial allocations and reallocation over time.

I believe there is a need for an actively managed fund that invests exclusively in passively managed funds and reallocated assets across funds as market conditions change.

Note on traditional holding period statistics:  The value of VFIAX in January 2002 was 17.9.  In December of 2010 the value of VFIAX was 39.5.   The return for this 7.9 year  holding period was at 10.5%.

Holding Period Calculation
Jan-03 17.9
Dec-10 39.5
Holding Period in Years 7.92
ROR 10.5%

However a person who started investing in January 2003 and started spending in January 2008 earned squat!   

The mutual funds can legally and honestly report great eight-year or ten-year holding return but their clients aren’t doing particularly well.

Such a surprise!   

Expected Profit and Risk with Random Transaction Dates

13 Oct

Profit and risk when there are four random purchase dates and four random sale dates

Question:   In 2013 a person buys QQQ the high tech ETF) on one of four randomly selected dates determined by when the broker arranges a meeting.   I

The person who bought the QQQ shares in 2014 got fired in 2015.   As soon as the person was fired he realized he needed cash so he called his broker and said “SELL QQQ” The firing is a random event independent of the market and out of control of the person, which occurred on one of four dates.

The four potential purchase and four potential sales dates for the QQQ transactions are presented below.

Information on Potential Purchases and Sales of QQQ
Potential Purchase Date Purchase Price QQQ Quantity purchased $25,000/Price Potential Sale Date Sale Price
20-May-14 88.0 284.1 5-Jan-15 101.4
7-Jul-14 95.1 262.9 8-Aug-15 110.5
7-Aug-14 94.2 265.4 24-Aug-15 98.5
10-Sep-14 100.1 249.8 5-Nov-15 114.7

The person spends $25,000 on the purchase of QQQ in 2014 and sells all shares in 2015.

Assume no dividends are paid.

What are all possible profit outcomes from the purchase and sale of the QQQ securities?

What is the expected profit?

What is the variance of profit?

Analysis:  The number of share purchased is $25,000 divided by the purchase price; hence the purchase price determines the number of shares purchased.

Tabulation of Number of Shares Purchased
Potential Purchase Date Purchase Price QQQ Number of shares purchased
20-May-14 88.0 284.1
7-Jul-14 95.1 262.9
7-Aug-14 94.2 265.4
10-Sep-14 100.1 249.8

Revenue received after the sale is price at time of sale times the number of shares owned.

Profit after the sale is revenue minus the $25,000 initial investment.

There are four possible purchase dates and four possible sale dates.   The purchase and sale dates are independent so there are a total of 16 possible equally likely combinations of sale and purchase dates.   The probability of each purchase/sale combination is 0.0625 (0.25*0.25).

The profit calculation for the 16 purchase-sale combinations is presented in the table below.

Potential Profit Calculation for Four Purchase Dates and Four Sale Dates
Comb # Probability Purchase Date Sale Date Number of Shares Owned Sale Price Profit
1 0.0625 20-May-14 5-Jan-15 284.1 101.4 $3,807
2 0.0625 20-May-14 8-Aug-15 284.1 100.5 $3,552
3 0.0625 20-May-14 24-Aug-15 284.1 98.5 $2,984
4 0.0625 20-May-14 5-Nov-15 284.1 114.7 $7,586
5 0.0625 7-Jul-14 5-Jan-15 262.9 101.4 $1,656
6 0.0625 7-Jul-14 8-Aug-15 262.9 100.5 $1,420
7 0.0625 7-Jul-14 24-Aug-15 262.9 98.5 $894
8 0.0625 7-Jul-14 5-Nov-15 262.9 114.7 $5,152
9 0.0625 7-Aug-14 5-Jan-15 265.4 101.4 $1,911
10 0.0625 7-Aug-14 8-Aug-15 265.4 100.5 $1,672
11 0.0625 7-Aug-14 24-Aug-15 265.4 98.5 $1,141
12 0.0625 7-Aug-14 5-Nov-15 265.4 114.7 $5,441
13 0.0625 10-Sep-14 5-Jan-15 249.8 101.4 $325
14 0.0625 10-Sep-14 8-Aug-15 249.8 100.5 $100
15 0.0625 10-Sep-14 24-Aug-15 249.8 98.5 -$400
16 0.0625 10-Sep-14 5-Nov-15 249.8 114.7 $3,646
Min -$400
Max $7,586
Range $7,986

The minimum profit is -$400.   The maximum profit is $7,985.

The expected profit is obtained by taking the dot product or the sumproduct of the probability vector with the profit vector.   The variance was obtained from the computational formula.

Var (Profit) = E(profit2) – E(Profit)2

For a discussion of these calculations see the previous post.

The expected value and variance or profit from the purchase of QQQ on one of four dates in 2014 and the sale of QQQ on one of four dates in 2015 are presented below.

Expected Profit and Variance of Profit Calculations
E(PROFIT) 2555.4
E(PROFIT2) 11036765.0
E(PROFIT2)-E(PROFIT)2 4506556.2
E(PROFIT-E(PROFIT))2 4506556.2

Financial Discussion:

The purchaser of QQQ or any stock that buys randomly and is forced to sell because of random events unrelated to the market bears substantial risk compared to an investor with enough liquid assets who will not need to sell in an emergency.   Investors would be wise to consider the level of the market and their ability to hold through downturns prior to selling.  The experts say that stock market returns beat returns on other securities over the long haul.  But this investor was only able to hold for a year.

Outcomes could have been worse.   The broker put the investor in QQQ a relatively diversified ETF that focuses on tech stocks.  Had the broker put his client in one particular stock (say IBM) and the investor was forced to sell he would have realized a large loss.

A note on the difference between geometric and arithmetic averages

13 Oct

Question:  The table below has price data and daily return data for Vanguard fund VB.   Calculate the arithmetic and geometric averages of the daily return data.   Show that the geometric average accurately reflects the relationship between the initial and final stock price and the arithmetic average does not accurately explain this relationship.

Daily Price and Returns For Vanguard 

Fund VB

Date Adjusted Close Daily Return
7/1/16 115.480674
7/5/16 113.99773 0.987158509
7/6/16 114.744179 1.006547929
7/7/16 114.913373 1.001474532
7/8/16 117.202487 1.019920345
7/11/16 118.128084 1.007897418
7/12/16 119.451781 1.011205608
7/13/16 119.10344 0.997083836
7/14/16 119.262686 1.001337039
7/15/16 119.402023 1.00116832
7/18/16 119.63093 1.001917112
7/19/16 119.202965 0.996422622
7/20/16 119.959369 1.006345513
7/21/16 119.481646 0.996017627
7/22/16 120.297763 1.00683048
7/25/16 120.019083 0.997683415
7/26/16 120.616248 1.004975584
7/27/16 120.347522 0.997772058
7/28/16 120.536625 1.001571308
7/29/16 120.894921 1.002972507
8/1/16 120.735675 0.998682773
8/2/16 119.12335 0.986645828

Analysis:   The table below presents calculation of the two averages and the count of return days.  The product of the initial value of the ETF, the pertinent average and the count of return days is the estimate of the final value.   Estimates of final ETF value are calculated for both the arithmetic average and the geometric average and these estimates are compared to the actual value of the stock on the final day in the period.

Understanding The Difference Between Arithmetic Mean and Geometric Mean Returns
Statistic Value Note
Arithmetic Average of Daily Stock Change Ratio 1.001506208 Average function
Geometric Average of Daily Stock Change Ratio 1.001479966 Geomean function
Count of Return Days 21 Count Function
Estimate of final value based on arithmetic average 119.1889153 Initial Value x Arithmetic Return Average x Count Days
Estimate of final value based on geometric average 119.12335 Initial Value X Geometric Return Average x Count Days
Ending Value 119.12335 Copy from data table

There is another way to show that the daily return should be modeled with the geometric mean rather than arithmetic mean.  The average daily return of the stock is (FV/IV)(1/n) – 1 where FV is final value and IV is initial value and n is the number of market days in the period, which for this problem is 21.

Using this formula we find the daily average holding period return is 0.001479966.  Note that 1 minus the geometric mean of the daily stock price ratio is also 0.001479966.

The geometric mean gives us the correct holding period return.

How much house can a student borrower qualify for?

13 Oct

How much house can a student borrower qualify for?

This answer depends on the maturity of the student loan.


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.


  • 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 

13 Oct

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
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.

Download the student debt and mortgage qualification spreadsheet by clicking below:
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