2. (20 points) A couple plans to purchase a home for $320,000. Property taxes are expected to be $1,200 per year while insurance premiums are estimated to be $1400 per year. Annual repair and maintenance are estimated at $1,950. An alternative is to rent a house of about the same size for $2,150 per month [approximate using $25,800 per year]. If an 8.0% return before-taxes is the couple's minimum rate of return, what must the resale value be 10 years from today for the cost of ownership to equal the cost of renting

$371,200

Explanation:

For the computation of annual price escalation first we need to follow some steps which are shown below:-

Future value of payment if the property purchased is

= Property taxes + Insurance premium + Annual repair and maintenance

= $1,200 + $1,400 + $1,950

= $4,550

Future value = (1 + K)^n

= (1 + 0.08)^10

= 2.158924997

or

= 2.16

Future value of annuity factor = (1 + K)^n -1 ÷ K

= ((1 + 0.08)^10 - 1) ÷ 0.08

= 1.158924997

÷ 0.08

= 14.487

Future value of the cost of property = Purchase amount of a home × Future value

= $320,000 × 2.16

= $691,200

Future value of recurring cost = Future value of payment if property purchased × Future value of annuity factor

= $4,550 × 14.487

= $65,915.85

Total value of payment = Future value of the cost of property + Future value of recurring cost

= $691,200

+ $65,915.85

= $75,7115.85

Future value of the payment in property taken on rent

The Total value of the payment in 10 year when the property taken on rent = Amount using per year × Future value of annuity factor

= $25,800 × 14.487

= $373,764.6

The amount incurred in both the methods will be the same if the property can be sold = Total value of payment - Total value of the payment in 10 year when the property was taken on rent

= $75,7115.85  - $373,764.6 0

= 383351.25

finally,

The annual price escalation = Future value of the cost of the property - Purchase amount of home

= $691,200  - $320,000

= $371,200