3-5 A couple plans to purchase a home for $250,000. Property taxes are expected

Question

3-5 A couple plans to purchase a home for $250,000. Property taxes are expected to be $1,900 per year while insurance premiums are estimated to be $700 per year. Annual repair and maintenance is estimated at $1,400. An alternative is to rent a house of about the same size for $1,500 per month (approximate using $18,000 per year) payments. 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 equivalent cost of renting? Finally, given the break-evern year 10 sale value just asked for, what is the corresponding annual price escalation or de-escalation in the house over the 10 years?

Explanation / Answer

A.First we calculate the future value of the anuual expenses for the purchase of the house

Total annual expenses are = 1900+700+1400 = 4000

The future value of these annual expenses(annuity) = FV(rate,nper,pmt) in excel = FV(0.08,10,4000) = 57,946.25

The future value of the monthly payments of $1500 for 10 years (120 months) at 8% annual interest or (8/12% monthly rate ) is: =FV(rate,nper,pmt) =FV(0.08/12,120,1500) = 274,419.05

Since the cost of ownerhip and renting are equal, let us assume "X' to be resale value after 10 years

X +  57,946.25 =274,419.05

X = 216,472.80

The resale value after 10 years must be $216,472.80

B. Now since the price after 10 years is lower than the price today, there is a de-escalation

Total de-escalation over 10 years = 250,000 - 216,472.80 = 33,527.20

Annual de-escalation = 33,527.20/10 = $3,372.72

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