Question Ten: One person graduates college with no debt
and immediately purchases a home for $200,000 with a 30year FRM. The LTV is 90%. The interest rate is 5.0%
The second person graduates college with a lot of student
debt and chooses to wait five years before buying an identical house. The second person also gets a 30year FRM
with an interest rate of 5.0% and a LTV of 90%.
The price of both houses increases 2.0% per year for a
15year period. What is the house equity
for the two people after 15 years?
Answer: The delay in the house purchase will reduce
ultimate house equity for three reasons.
First, the person who delays purchasing a home will pay more for the
house if house prices increase overtime.
Second, the person will hold the house for fewer years and therefore
have a smaller gain. Third, the smaller
holding period reduces the amount of the mortgage, which is repaid.
The person who waits five years to purchase a house pays
nearly $21,000 more for the house than the person who immediately purchases the
house. The price of the house after five years is $200,000(1.02)^{5} This increases monthly payments by around
$100.
The holding period for the person who waits five years to
purchase the house is 5 years shorter than the holding period for the person
who immediately purchases after graduation. The shorter holding period reduces the
amount by which the mortgage is paid down. The difference in the balance of the
mortgage 15 years after graduation is around $40,000 even though the difference
in the mortgage balance at origination is only around $19,000.
The difference in equity build up would be even larger if
both people used a 15year mortgage. The
person who bought at graduation would have amassed house equity of
$269,174. The person who delays purchase
for five years would have amassed equity of $185,895. In this case, the difference in the mortgage
balance 15 years after graduation is over $80,000.
There are likely other indirect costs to student debt
including higher credit rates associated with a poor credit rating and delayed
or reduced contributions to 401(k) plans.
The Impact of House
Purchase Delays on House Equity Accumulation


Person 1 Buys House
Immediately After Graduation

Person 2 Buys House 5
Years After Graduation


Purchase Price of House

$200,000

$220,816

LTV

0.9

0.9

Initial Mortgage

$180,000

$198,735

Interest Rate on Mortgage

0.05

0.05

Term of Mortgage

360

360

Payment of Mortgage

$966.28

$1,066.85

Holding Period of
Mortgage and House

180

120

Mortgage Balance 15 years
after Graduation

$122,191

$161,655

House Price 15 Years After
Graduation

$269,174

$269,174

House Equity After 15
Years

$146,983

$107,519

The Impact of House
Purchase Delays on House Equity Accumulation
(Analysis based on
15year FRMs)


Person 1 Buys House
Immediately After Graduation

Person 2 Buys House 5
Years After Graduation


Purchase Price of House

$200,000

$220,816

LTV

0.9

0.9

Initial Mortgage

$180,000

$198,735

Interest Rate on Mortgage

0.05

0.05

Term of Mortgage

180

180

Payment of Mortgage

$1,423.43

$1,571.58

Holding Period of
Mortgage and House

180

120

Mortgage Balance 15 years
after Graduation

$0

$83,279

House Price 15 Years
After Graduation

$269,174

$269,174

House Equity After 15
Years

$269,174

$185,895

Other financial math problems can be found here.
This comment has been removed by the author.
ReplyDeleteVipul Plaza
ReplyDeleteGreat point and excellent illustration but getting a recent college grad to take on what he or she perceives as 'massive debt" is a hard sell.
ReplyDelete