Wednesday, September 18, 2019

Modeling House Equity Growth Over Multiple House Purchases


Abstract:   This post shows how to model house equity accumulation over a lifetime for different mortgage choices.   We consider a person who purchases two homes over 25 years, staying in the first home for 10 years and the second home for 15 years.  Two mortgage scenarios are considered.  The first scenario involves two 30-year mortgages.   The second scenario involves two 15-year mortgages.

Question:   How does the choice between a 30-year and 15-year mortgage impact house equity and lifetime debt payments for multiple house purchases?

The Specific Problem:   Our example involves a person purchasing two houses over twenty-five years.   The buyer stays in the first house for 10 years and the second house for 15 years.  

The first house costs $250,000 with the buyer taking out a 90 percent LTV loan.  

The second house costs $500,000 with the buyer placing all funds from the sale of the first house as a down payment on the second house.   The house appreciates at an average annual rate of 1 percent per year.   The seller of the first house pays a 6 percent commission.

The home buyer considers two financing options.   The first financing option involves two 30-year fixed rate mortgage at 3.8 percent.  The second option involves two 15-year fixed rate mortgages at 3.3 percent.   Typically, the interest rate on a 30-year FRM is higher than the interest rate on a 15-year FRM; although, rate levels and the differential between 30-year and 15-year mortgage rates can vary.  The interest rates used in this example are similar to rates currently available in the market.

How do the financing options impact monthly debt payments, lifetime debt payments and accumulated house equity?   

Analysis:


The lifetime debt payment calculations and the accumulated mortgage calculations for the two financing scenarios are presented in the table below.

Two Lifetime House Financing Scenarios

Scenario One
Two 30-year
FRM
Scenario Two
Two 15-year 
FRM
House One Purchase Price
$250,000
$250,000
LTV
0.9
0.9
Loan House One
$225,000
$225,000
Interest Rate First House
0.038
0.033
Term
30
15
Payment
($1,048)
($1,586)
Years in House
10
10
Total House Payments for first House
($125,808)
($190,377)
Appreciation Rate for First Home
0.01
0.01
Value of First Home on Sale Date
$276,156
$276,156
Mortgage Balance on Sale Date
($176,056)
($87,640)
Sale Commission
0.06
0.06
House Equity from the Sale of First House
$83,530
$171,947
Down Payment of Second Home
$83,530
$171,947
Value of Second Home
$500,000
$500,000
Mortgage on Second Home
$416,470
$328,053
Interest Rate on. Second Home
0.038
0.033
Term (Years)
30
15
Payment
($1,941)
($2,313)
Years in Home
15
15
Total Payments for Second Home
($349,303)
($416,360)
Total Payment on Both Homes
($475,112)
($606,737)
Appreciation Rate for Second Home
0.01
0.01
Value of Second Home at end of period
$580,484
$580,484
Mortgage Balance on Second Home at end of period
($265,939)
$0


Major Differences Between the Two Financing Scenarios:


·      The person who uses two 15-year FRM has a $0 mortgage balance at the end of 25 years after staying in his second home for 15 years.   The person employing two 30-year fixed rate mortgages has 15 years of mortgage payments remaining and an outstanding mortgage balance of nearly $266,000.  

·      The person using the two-15-year FRM paid around $132,000 more in mortgage payments over the 25-year period.  However, the person using 30-year mortgages must either sell the home or continue making payments.   The mortgage is not scheduled to be repaid for 15 more years.

·      The monthly payments on the two 15-year loans are higher than the monthly payments on the two 30-year loans.  The differential is 34 percent for the first home purchase compared to 16 percent for the second home purchase.   The smaller differential in monthly mortgage payments occurs because of the larger accumulation of equity and the larger down payment stemming from the use of the 15-year mortgage.


Comment on Pros and Cons for the Two Financial Scenarios:


Pros associated with use of two 15-year FRM:

·      The advantage of using the two 15-year FRMs is that a home is completely paid for after 25 years.  The person using this strategy can now increase his savings in financial assets if still employed.  The person does not have to disburse funds from a 401(k) plan to pay down a mortgage during retirement.

Cons Associated with use of two 15-year FRMs:

·      The person using two 15-year FRMs makes larger mortgage payments and will probably have to reduce investments in liquid assets to make the larger mortgage payments.


Pros of use of 30-year FRMs:

·      The lower mortgage payments allow this homebuyer to make larger investments in financial assets.

Cons of use of 30-year FRMS:

·      The person after 25 years still has a large mortgage payment.  This reduce future savings in financial assets if the person is still working

·      Additional payments from 401(k) plans to pay down the mortgage are fully taxed as ordinary income. Hence, the person who retires with a 401(k) balance because of the use of 30-year FRMs will have larger tax obligations.  

Caveats on this Analysis  The potential gain from different mortgage arrangements depends on holding periods for each home, the number of homes purchased during a lifetime, and interest rates.  We look at two different mortgage arrangement for only one scenario.   Results presented for different assumptions on house purchases and interest rates will differ from the results presented here.

Final Question:   Is it better to increase house equity and totally eliminate mortgage debt or should one stay in 30-year mortgages and increase investment in financial assets?  This question is not addressed in this post.  The breakeven point for holding debt must account for taxes when assets are invested in a conventional 401(k) plan because all disbursements from 401(k) plans are taxed as ordinary income.  The desire to avoid financial risk would also favor the mortgage elimination option.  

Certainly, if you are planning to stay in your home after you retire you are exposed to a lot of financial risk if you keep a large mortgage and a large share of your financial assets are equity tied up in a 401(k) plan.  The topic presented here is related to the issue of to what extent investors should prioritize 401(k) saving over other financial priorities.  Go here for a discussion of this topic.

Six Reasons 401(k) plans should not be your top priority





  




Tuesday, September 17, 2019

The path of stock returns and financial risk for 401(k) investors


The path of stock returns and financial risk for 401(k) investors

This post compares terminal wealth in a 401(k) plan for two stock return scenarios.   The average return for the two scenarios are identical.  One scenario has a bad year at the beginning of the holding period.   The other scenario has a bad return at the end of the holding period.

This problem is solved using basic math in an Excel spreadsheet.

Question:   Consider a 401(K) plan with a $300,000 balance ten years prior to retirement. The person contributes $10,000 every year to her 401(k) plan.  For simplicity of calculation assume the entire annual $10,000 contribution goes into the account at the beginning of the year.

Calculate wealth at retirement for two financial scenarios.   Scenario one involves a negative 20 percent return in the first year followed by positive 8 percent returns in the following nine years.   Scenario two involves positive 8 percent returns for the first nine years followed by a negative 20 percent return in the year leading up to retirement.

What is the average stock market return during the 10-year period?

What is 401(k) wealth at retirement for both scenarios?

Financial advisors often recommend holding stock in 401(k) plans over long time horizons because stocks tend to have higher returns than other financial assets.  Financial advisors also recommend starting 401(k) savings early because wealth accumulation is enhanced by compounding of returns.

What does the result presented here suggest about the risks associated with 401(k) investing?

Analysis:   The holding period return can be measured by the geometric mean of (1+r) minus 1.   The calculation is laid out in the table below.


Scenario One
Scenario Two
1
0.8
1.08
2
1.08
1.08
3
1.08
1.08
4
1.08
1.08
5
1.08
1.08
6
1.08
1.08
7
1.08
1.08
8
1.08
1.08
9
1.08
1.08
10
1.08
0.8
Geomean minus one
4.81%
4.81%

The wealth for each period is beginning balance multiplied by (1+r).   The calculation for wealth at retirement for scenario one where the bad stock return year is the first year of the last ten years prior to retirement is laid out in the table below.


Wealth Calculation Scenario One
Time
401(k) Balance
Contribution made at beginning of year
r for
 scenario one
0
$300,000
$10,000
1
$248,000
$10,000
-0.2
2
$278,640
$10,000
0.08
3
$311,731
$10,000
0.08
4
$347,470
$10,000
0.08
5
$386,067
$10,000
0.08
6
$427,753
$10,000
0.08
7
$472,773
$10,000
0.08
8
$521,395
$10,000
0.08
9
$573,906
$10,000
0.08
10
$630,619
0.08


The wealth calculation for scenario two where the bad stock return is the year prior to retirement is laid out in the following table.


Wealth Calculation Scenario Two
Time
401(k) Balance
Contribution made at beginning of year
r for
scenario two
0
$300,000
$10,000
1
$334,800
$10,000
0.08
2
$372,384
$10,000
0.08
3
$412,975
$10,000
0.08
4
$456,813
$10,000
0.08
5
$504,158
$10,000
0.08
6
$555,290
$10,000
0.08
7
$610,514
$10,000
0.08
8
$670,155
$10,000
0.08
9
$734,567
$10,000
0.08
10
$595,654
-0.2


Comments:

Wealth in scenario one where you get the bad year over sooner rather than later is around $35,000 higher than in scenario two where the bad return year is the last year prior to retirement.  The difference is 5.87 percent of wealth at the end of scenario two.

The reason for the lower end of period wealth in the second scenario is the market downturn impacts a larger value of assets.

This example understates financial path risk because stock downturns can and do last more than one year.  

Financial advisors generally favor taking advantage of higher returns on stocks and compounding by starting 401(k) investments as soon as a worker enters the workforce.  The calculations supporting this recommendation do not account for financial return path risk shown in this post.  Often workers will be better off by immediately eliminating student debt rather than increase exposure to the market.