One of most common and significant financial decisions people make is whether to buy or to rent a home. In Melbourne, a family-sized home in a suburb within 20km of the CBD costs roughly $1 million and requires maintenance costs of about $7000 per year, growing by 3% per annum. By comparison, the annual rent for a similar home is approximately $36,000. To purchase, a buyer generally pays a 20% down payment on the purchase price, as well as a stamp duty (tax) of 5.5% payable to the state government. Loans are currently available at about 3.5% interest per annum per on 30-year loans.

Suppose we are making a decision between buying or renting a house. For simplicity, well make the following assumptions:

Buying Option

1. The house price is $1 million. And, the house requires maintenance costs of about $7000 per year, growing by 3% per annum.

2. The buyer needs to pay cash for the down payment (20% of purchase price) and stamp duty (5.5% of purchase price) and borrows the remaining 80% of the purchase price at 3.5% interest per annum per on 30-year loans today.

3. The buyer will sell the house in 9 years. The house is the buyers main residence, so capital gain or loss on the sale of the house will be disregarded. (They dont pay tax on any capital gain, and they can't use any capital loss to reduce their assessable income.)

Renting Option

1. The annual rent for a similar home is $36,000 this year. There is no down payment to be made for rental option. Other than the down payment and stamp duty, all cash flows occur lump-sum at the end of the year. This means that a) well estimate loan repayments assuming 30 annual payments are made, the first starting in one year; and b) the first years maintenance or rent will similarly be due in one year. (i.e., the first rent payment is $36,000 one year from now.)

Well evaluate the following scenarios:

Scenario 1 Both house prices and rents grow at 3% per annum After 4 years, the interest rate increases to 4% per annum

Scenario 2 Both house prices and rents grow at 2% per annum After 4 years, the interest rate increases to 4.5% per annum

Scenario 3 House prices grow at 1% per annum Rents decline by 1% per annum After 4 years, the interest rate decreases to 3% per annum

2. For each scenario,

a) [3 mark] What is the balance on the home loan in 9 years, after the 9 th mortgage payment has been made? [Hint: Perhaps the simplest way to solve this is to use Excel to calculate the year-byyear balance, where Balance(t+1) = Balance(t) + Balance(t) * InterestRate(t) - Repayment(t+1)]

b) [2 marks] What is the year-by-year difference in net cash flows for renting versus buying, assuming that in year 9 the house is sold and the remaining loan balance is repaid?

3. [2 marks] Suppose that any cash not spent on housing costs can be invested at an 6% aftertax return in the stock market. Given your answers to 2(b) above, what is the estimated difference in net wealth for renting versus buying in each of the scenarios? [Hint: For each scenario,