Tuesday, June 11, 2019

Mobility and lifetime house equity.

This post utilizes a housing equity calculator to estimate the impact of a move from one house to another on lifetime house equity.   

Question   In this problem all houses are purchased with 15-year FRMs at an interest rate of 5.0%.  Also, all houses appreciate in value at a rate of 1.0% per year.    These assumptions can of course be altered in a spreadsheet.

At the beginning of a 15-year period two people purchase a $300,000 house.   One person stays in the same house for all 15 years.   The other person buys a new house identical in value to the one he is currently living in after 7 years.

The sales commission on the first house is 6.0%.   In addition, closing costs on the new house are equal to 4.0% of the house price.

The second person lives in his second house for eight more years.

How much equity do the two people have after 15 years?




Answer:    The house equity calculation for the first homebuyer involves only one home.   The two-home house equity calculator used in the previous problem needs to be modified to include costs associated with sale of first home and purchase of the second home.

The results presented in the table below demonstrate the high cost of moving when all financing is done with 15-year mortgages.   The person who stays in the same house for 15 years has equity of $348,291.    The person who moves to an identical house after 7 years has house equity of $215,036.    The difference in house equity is $133,255.  

Note most of the difference in equity is due to the reduction in the payoff of the mortgage.  Only around 25% of the loss in house equity is due to the sales commission on the first house and the closing costs on the second house.  Nearly ¾ of the loss in house equity is due to a reduction in the pay off the mortgage.  (Mortgages pay off more rapidly near the end of their life.   Since Person B sells his first house he does not enter the rapid payoff period for his mortgage during the 15-year period.)




The Potential Loss of House Equity From Moving
Person A Lives in One Home for 15 Years
Person B Lives in One Home for 7 Years and One Home for 8 Years
Assumption
Price of First House
$300,000
$300,000
Assumption
Mortgage LTV First House
0.90
0.90
Assumption
Mortgage $ First House
$270,000
$270,000
Assumption
Mortgage Term Years First House
15
15
Assumption
Mortgage Interest Rate
0.05
0.05
Calculation
Mortgage Payment First House
-$2,135
-$2,135.14
Assumption
Holding Period First Home
15
7
Calculation
Mortgage At End of First Period Holding Period
$0
-$168,653.73
Assumption
Annual Appreciation First House
0.01
0.01
Calculation
House Price At End of Holding Period First House
$348,291
$321,641
Assumption
Sales Commission on Old House and Closing Costs on New House
0.10
Calculation
Loss of Equity due to Commission and Closing Costs
32,164.06
Calculation
Available Equity First House
$120,823
Assumption
Fraction Used for Down payment First House
1
Calculation
Down payment Second House
$120,823
Assumption
Price Second House
$321,641
Calculation
Mortgage Second Home
$200,818
Assumption
Mortgage Term Second Home
15
Assumption
Mortgage Interest Rate Second Home
0.05
Calculation
Mortgage Payment Second Home
-$1,588.06
Assumption
Holding Period Second Home
8
Calculation
Mortgage at End of Second Period Holding Period
-$112,357.98
Assumption
Annual Appreciation Second House
0.01
Calculation
House Price at End of Holding Period Second House
$348,291
Assumption
Sales Commission
0.06
Calculation
House Equity After 15 Years
$348,291
$215,036



The loss in equity is smaller but still considerable when 30-year mortgages are used instead of 15-year mortgages.   This is so because equity accumulation under 30-year mortgage is very slow until the final years of the mortgage.

The decrease in the tax deduction of the mortgage interest for the person who entirely pays off their mortgage will offset part of the equity difference but the offset is relatively small.


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