Question

You are considering an option to rent or to purchase a single-family house. You can rent it for

$1,500 per month. If you rent the property, the current owner will be responsible for

maintenance, property insurance and taxes. Your second option is to purchase the property for

$125,000. You have enough money for a 20% down payment, and would need to finance the

other 80% with a fixed-rate mortgage at a four percent interest rate. Assume that the mortgage

would fully amortize over thirty years. You can prepay the mortgage at any time without a

penalty.

Assume that the property will appreciate at four percent per year, and that the owner would

plan to increase the rent at a rate of three percent per year during the next five years. Assume

that maintenance is $3,000 per year. Property insurance runs $1,000 per year. Both

maintenance and insurance are anticipated to increase at a rate of four percent per year during

the next five years.

If you purchase the house, you plan to stay in it for at least four years, but because of the

possibility of your job moving you to another city, you want to analyze how long you must

stay in the house to make purchasing a better option than renting. If you do purchase the

property and sell it, you will incur a seven percent sales charge.

In regard to taxes, property taxes are about four percent of the home value, which is re-

assessed each year. You are in the 28% marginal income tax bracket.

a) If you would like to earn an eight percent rate of return on your invested equity, would it

be better to rent or to buy the property, if your investment horizon is four years?

b) What would be your expected rate of return if you lived in the house for only three years?

c) If you expected to live in the house for five years, what would be the level of rent to

begin now that would make you indifferent between renting and purchasing the property?

Answer 1

	Year	0	1	2	3	4	5	6
	Rent	18000	18540	19096.2	19669.09	20259.16	20866.93	21492.94
	Property Buying
	investment	25000
	property	125000	130000	135200	140608	146232.3	152081.6	158164.9
	property tax	5000	5200	5408	5624.32	5849.293	6083.265	6326.595
	interest	4000	4000	4000	4000	4000	4000	4000
	Maintenane	3000	3120	3244.8	3374.592	3509.576	3649.959	3795.957
	total outflow	37000	12320	12652.8	12998.91	13358.87	13733.22
	selling
	sales charge	8750	9100	9464	9842.56	10236.26	10645.71	11071.54
a)	rent paid =	95564.44
	investment maid in property=	88330.58
	at 8% investment earned
	assuming that the investment will be of 25000 and it will give return of 8% compunded anually
	therefore, using formula A = P(1 + r/n)nt, amount will be 34,012.22
	so clearly, compared to buying, the outflow is more in buying then renting
	when buying	88330.58
	when renting	61552.22
	so renting makes more point here.
b)	assuming that I will be buying the house and selling it at the end of three years
	total outflow = expenses till 3 year+sales charges			84814.2
	selling amount			140608
	so rate of return per year			0.132268	13.22 percent
c)
	total amount incurred till 5 years when buying option is choosen
	is	102063.8
	rent to be paid
	Year	0	1	2	3	4	5	sum
	expected cash flow	15778	16251.34	16738.88	17241.05	17758.28	18291.03	102058.6
	so rent to be paid	15778