Question

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

The decision will be based on which of the contract provides higher NPV.

for the rent agreement we have

Initial rent/month	4000
appreciation rate	4%
Discount Rate	10%
Year	1	2	3	4	Formula used
Rent	4000	4160	4326.4	4499.456	rent= 4000*1.04^(yr-1)
PV of rent each year	($45,498.03)	($47,317.96)	($49,210.67)	($51,179.10)	PV= rent*(1-(1+i/12)^-12)/(1-(1+i/12))
NPV of rent	($152,396.32)	=NPV(B3,B7:E7)			NPV= sum(pv*(1+i)^-yr)

For Mortgage:

Since the question is not clear, I'm making certain assumptions

1. Mortgage is paid by equal annual installments

2. By 80% mortgage it means 80% loan to value ratio where 20% is down payment.

Purchase price	300000
Mortgage loan	240000
Down Payment	60000
Rate	7%
Term	25	years
Yearly Installment	($20,594.52)
Year	0	1	2	3	4	Formula used
Property Value		300000	312000	324480	337459.2
CashFlows
Down Payment	-60000
Installments		($20,594.52)	($20,594.52)	($20,594.52)	($20,594.52)
Maintenance and Insurance		-2500	-2600	-2704	-2812.16	2500*1.04^(yr-1)
Property Tax @3%		-9000	-9360	-9734.4	-10123.776	3% of property value
Selling Value					337459.2
Selling Cost@ 7%					-23622.144	7% of property value
Loan Repayment Amount= PV(future installments)					($223,152.53)	PV of all future installments
Net Cashflow each year	-60000	-32094.5241	-32554.5241	-33032.9241	57154.06673	sum(all Cash flows)
PV	-60000	($29,176.84)	($26,904.57)	($24,818.12)	$39,037.00	CF*discounting factor
NPV	-101862.5337					sum(PVs)

Since NPV of Mortgage is lesser,  Mortgage is the ideal option