Tuesday, November 17, 2015

Question Ten: Impact of House Purchase Delays on Ultimate Wealth

Question Ten:  One person graduates college with no debt and immediately purchases a home for $200,000 with a 30-year 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 30-year 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 15-year 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 15-year 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 15-year 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.



3 comments:

  1. This comment has been removed by the author.

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  2. Great 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.

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