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 15year 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 15year 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
twohome 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 15year 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 15year 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
30year mortgages are used instead of 15year mortgages. This is so because equity accumulation under
30year 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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