Question

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?

Please show work in excel!

Answer 1

We should buy the property since NPV of cash outflows under owning the property are less by $63,536 than renting.

Workings 1 Cost of Property Year Value $ 3,00,000.00 $ 3,12,000.00 $ 3,24,480.00 $ 3,37,459.20 $3,50,957.57 2 Property Tax (normally on value of property as on first day of the year) Year 2 3 . Value $ 3,00,000.00 $ 3,12,000.00 $ 3,24,480.00 $ 3,37,459.20 Tax $ 9,000.00 $ 9,360.00 $ 9,734.40 $ 10,123.78 2,40,000.00 20,594.52 3 Interest on Loan Loan $ Equal Annual Repayments $ Year Loan Balance $ EMI $ Interest $ Principal $ 2,40,000.00 $ 2,36,205.48 $ 2,32,145.34 $2,27,800.98 20,594.52 $ 20,594.52 $ 20,594.52 $ 20,594.52 16,800.00 $ 16,534.38 $ 16,250.17 $ 15,946.07 3,794.52 $ 4,060.14 $ 4,344.35 $ 4,648.46 4 Charges on Sale of property at the end of year 4 (assuming sold at market value) Value $ 3,37,459.20 Charges $ 23,622.14 Net Sale Proceeds $ 3,13,837.06 Purchase Value $ 3,00,000.00 5 Profit on Sale 13,837.06

Discount Rate 10% 4 Rent Year Rent Per Month Rent Per Year $ 4,000.00 $ 4,160.00 $ 4,326.40 $ 4,499.46 $ 48,000.00 $ 49,920.00 $51,916.80 $53,993.47 (1+r)^n 1.10 1.21 1.33 1.46 Net Present Value Present Value $43,636.36 $41,256.20 $39,005.86 $36,878.27 $1,60,776.69 Own Year Interest Difference $63,536.05 Tax Maintenance Sales Charges Profit on Sale Net Cash Outflow $ 16,800.00 $ 16,534.38 $ 16,250.17 $15,946.07 $ 9,000.00 $ 9,360.00 $ 9,734.40 $10,123.78 $ 2,500.00 $ 2,600.00 $ 2,704.00 $ 2,812.16 23622.144 -13837.056 $ 28,300.00 $ 28,494.38 $ 28,688.57 $ 38,667.09 (1+r)^n 1.10 1.21 1.33 1.46 Net Present Value Present Value $25,727.27 $23,549.08 $ 21,554.15 $ 26,410.14 $ 97,240.64