Question

                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                          Case Study: Rent vs Own

You are considering an option to purchase or rent a single residential property. You can rent it for $4,000 per month and the owner would be responsible for maintenance, property insurance, and property taxes.

Alternatively, you can purchase this property for $300,000 and finance it with an 80% mortgage at 7% interest, 25 year - fixed. The loan can be prepaid at any time with no penalty.

You have done research in the market and found that properties have historically appreciated at an annual rate of 4% per year. Rents on similar properties have also increased at the same rate. Maintenance and insurance are currently $2,500 each per year and they have been increasing at a rate of 4% per year. Property taxes have generally been about 3% of the property value each year.   

If you purchase, the plan is to occupy the property for at least four years. Selling costs would be 7% in the year of sale.

Based on this information you must decide:

• In order to earn a 10% internal rate of return, should you buy the property or rent it for a four-year period of ownership?

Answer 1

		CASH FLOW FOR RENT OPTION:
		Rent expense in Year 1=4000*12	$48,000
		Rent expense in Year 2	$49,920	(48000*1.04)
		Rent expense in Year 3	$51,917	(49920*1.04)
		Rent expense in Year 4	$53,993	(51917*1.04)
		CASH FLOW FOR PURCHASE OPTION
		Maintenance and Insurance Year1	$5,000	(2500+2500)
		Maintenance and Insurance Year2	$5,200	(5000*1.04)
		Maintenance and Insurance Year3	$5,408	(5200*1.04)
		Maintenance and Insurance Year4	$5,624	(5408*1.04)
			A		B=3%*A
			Property Value		Property Taxes
		End of Year 1	$312,000	(300000*1.04)	$9,360
		End of Year 2	$324,480	(312000*1.04)	$9,734
		End of Year 3	$337,459	(300000*1.04)	$10,124
		End of Year 4	$350,958	(300000*1.04)	$10,529
	Rate	Mortgage interest rate	7%
	Nper	Number of years of mortgage	25
	Pv	Loan amount =80%*300000	$240,000
	PMT	Annual Mortgage Payment	$20,595	(Using PMT function of excel with Rate 7%,Nper=25,Pv=-240000)
		Initial Cash outflow =20%*300000	$60,000
		Terminal Cash Flow:
		Loan Balance =Present Value of future mortgage payments at end of year4
	Nper	Number of mortgage payments at end of year4(25-4)	21
	Rate	Mortgage interest rate	7%
	Pmt	Annual Mortgage Payment	$20,595
	PV	Loan Balance	$223,153	(Using PV function of excel with Rate 7%,Nper=21,Pmt=-20595)
		Property Value at end of year4	$350,958
		Selling Cost =7%*350958	$24,567
		Cash inflow from sale=350958-24567	$326,391
		Cash Outflow for payment of Loan Balance	$223,153
		Net Terminal Cash Flow=326391-223153	$103,238
		Present Value of Cash Flow=(Cash Flow)/((1+i)^N)
		i=discount rate =10%=0.1
		N=Year of Cash Flow
	N	Year	0	1	2	3	4
	I	Initial Cash Flow for Purchase Option	-$60,000
	a	Annual Mortgage Payent		($20,595)	($20,595)	($20,595)	($20,595)
	b	Maintenance and Insurance		($5,000)	($5,200)	($5,408)	($5,624)
	c	Property taxes		-$9,360	-$9,734	-$10,124	-$10,529
	d=a+b+c	Total annual cash flow		($34,955)	($35,529)	($36,126)	($36,748)
	e	Annual cash flow for rent option		($48,000)	($49,920)	($51,917)	($53,993)
	F=d-e	Annual Savings for Purchase Option		$13,045	$14,391	$15,790	$17,246
	T	Terminal Cash Flow for Purchase Option					$103,238
	CF=I+F+T	Net Cash Flow	-$60,000	$13,045	$14,391	$15,790	$120,484	SUM
	PV=CF/(1.1^N)	Present Value of net cash flow	-$60,000	$11,860	$11,893	$11,864	$82,292	$57,909
	NPV=Sum of PV	Net Present Value	$57,909
		DECISION:
		Select Purchase Option
		NPV is positive