6. THE BUILDING OF NEW HOUSES Suppose a family is trying to decide whether to bu

Question

6. THE BUILDING OF NEW HOUSES
Suppose a family is trying to decide whether to build a new
house. They fi nd a lot that costs $120,000 and learn that
building the house will cost $180,000. They have $40,000
saved to make a down payment.
a. Ignoring various other costs (legal fees, taxes, and the
like), what is the size of mortgage required for this family
to purchase this house?

b. Use a search engine to fi nd a mortgage calculator and
retrieve the monthly payment for this mortgage when
the mortgage interest rate is 4% and the period of amortization
(the length of time to repay the entire mortgage)
is 25 years.
Use a search engine to fi nd a mortgage calculator
and retrieve the monthly payment for this mortgage
when the mortgage interest rate is 6% and the period
of amortization (the length of time to repay the entire
mortgage) is 25 years.
Explain the effect of interest rates on the decision to
purchase the house.

c. Suppose the family expects they will have to move in
fi ve years. They will sell this house and pay off the
remaining mortgage. They have two expectations about
the price of houses: when they are pessimistic they believe
that house prices will fall by 1% each year for the
next fi ve years; when they are optimistic they believe
that house prices will rise by 3% for the next fi ve years.
How much more money will they have in fi ve years
if the optimistic projection is correct? How does their
belief about house price affect their decision to build
the house?

Explanation / Answer

a) Total size of the mortgage required for this family to purchase this house is ($120,000 + $180,000 - $40,000) = $260,000.

b) If interest rate is 4% with mortgage amount of 260,000 for 25 years then monthly payment for this mortgage will be $1372 and for 6 percent interest the monthly payment for the mortgage amount will be $1675.

In case of higher interest the family needs to pay a higher amount as mortgage and this higher interest will create negative impact on purchase of the house. Because in higher interest rate the family needs to pay more amount as mortgage. This higher interest rate has adverse effect on purchase of house.

Now if we assume and start with initial house price i.e $300,000, then if house price will fall by 1 percent in each year i.e when they are pessimistic then the value of the house after 5 years will be 300,000(1+0.01)^-5 = $300,000(1.01)^-5 = $285,439.70 = $285,440 (Approx).

Now if they are optimistic about the price of the house and if house price increases by 3 percent in each year for 5 years then after 5 years the price of the house will be 300,000(1+0.03)^5 = $300,000*(1.03)^5 = $347,782.22 = $347,782 (approx).

So, when they are optimistic i.e their optimistic projection becomes correct then they will get the price $347,782. In this case they will have $47,782 more in their hand.

The belief about house price has an effect on decision to build the house. If projection becomes pessimistic then they will go for to build the house and if their projection is pessimistic then they will not go for to build the house.

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