Mark and Alicia have found a small bungalow they believe they can afford to buy.

Question

Mark and Alicia have found a small bungalow they believe they can afford to buy. Ms. Anne Vendor is prepared to sell this house for $250,000. Mark and Alicia find they can obtain a $200,000 mortgage with monthly payments computed at a rate of j2 = 7%, amortized over 25 years. The mortgage has a five year term; early prepayment results in a penalty of 3 months interest on the amount prepaid. On closing day (purchase of the house), they have to come up with the down payment, plus additional closing costs (legal fees etc.) equal to 2% of the purchase price. Monthly costs are expected to be $200 for property taxes, $150 for utilities, $60 for property insurance and an estimated $110 for repairs and maintenance.

Alternatively, Mark and Alicia discover that Anne is willing to rent them the house for $1600 per month for five years. If they rent, their monthly costs for utilities would remain the same, insurance costs would drop to $15 a month and Anne would be responsible for maintenance, repairs and property taxes.

Mark and Alicia plan to move into a larger home in five years. Consequently they wish to compare the costs of renting versus owning over this five year period. They project that the bungalow will sell for $300,000 at the end of five years, less selling costs of 7% including commissions and legal fees.

a)         Which tenure option is more affordable based on just the monthly cash outlay?

b)         Compute the present value of the total cost of ownership for five years, using a discount (interest) rate of j2 = 6%. (This is the rate of return they could earn on savings.) The down payment and closing costs are initial (time zero) costs, Mark and Alicia have monthly costs as listed above and they have the benefit of the cash they receive from selling the house in five years (after repaying the loan).

c)         Use the same discount rate as b) to compute the present value of the total monthly costs of renting. Based on this analysis, which option, renting or buying, has a lower PV cost?

d)         Which implicit assumptions in the analysis critically affect your answers to b) and c)?

Explanation / Answer

a) Based on mothly cash outlay Option 1 Option 2 Monthly costs: 520 Monthly cost                         165 Hence Option 2 is better b) Cost at t=0 Down Payment          50,000 Closing Cost            5,000 Mortgage       200,000 Yearly Interest          14,000 PV of 5 yr interest          58,973 PV of 5 yr monthly cost          26,285 Bungalow value at year 5 Selling price*93%       279,000 PV of bungalow       208,485 Total Cost       131,773 c) Yearly Cost in renting Yearly rent +Yerly extra cost (1600+165)*12          21,180 Pv of 5 yr cost of renting          89,218 Hence Renting has lower PV d) Assumtion: Rent and all the monthly cost will remain constant in 5years. Ans there will not be any inflation effect.

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