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Assignment 1
Financial Management FNCE90060
Semester 1, 2024
This assignment is due by 8 pm Friday 12 April 2024 via the Assignment 1 submission link
on the LMS. Late assignments will have marks deducted. The system will only accept PDF
documents. You should type up your answers in a program like Word, then output/print to
PDF. If your computer is not set up to make PDFs, search the web for CutePDF, which allows
you to create them from any program.
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answers will be penalised. You will not, however, be evaluated on visual presentation. A
simple, typed document will be good enough.
Answers without (mathematical) justification will not receive any credit. In particular, you
should indicate clearly in your PDF how you calculated your answers.
Overview
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 $9000 per year, growing by 3%
per annum. By comparison, the annual rent for a similar home is approximately $48,000.
To purchase, a buyer generally pays a 20% down payment on the purchase price, as well as a
stamp duty (tax) of 6% payable to the state government. Loans are currently available at about
6% interest per annum per on 30-year loans.
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Suppose we are making a decision between buying or renting a house.
For simplicity, we’ll make the following assumptions:
 Buying Option
1. The house price is $1 million. And, the house requires maintenance costs of about
$9000 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 (6% of purchase price) and borrows the remaining 80% of the purchase
price at 6% interest per annum per on 30-year loans today.
3. The buyer will sell the house in 9 years. The house is the buyer’s main residence,
so capital gain or loss on the sale of the house will be disregarded. (They don’t 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 $48,000 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) we’ll estimate loan repayments assuming 30 annual payments
are made, the first starting in one year; and b) the first year’s maintenance or rent will
similarly be due in one year. (i.e., the first rent payment is $48,000 one year from now.)
We’ll evaluate the following scenarios:
Scenario 1
 House prices grow at 3% per annum
 Rents grow at 2% per annum
 After 4 years, the interest rate increases to 7% per annum
Scenario 2
 House prices grow at 2% per annum
 Rents grow at 3% per annum
 After 4 years, the interest rate decreases to 5% per annum
Scenario 3
 House prices grow at 6% per annum
 Rents grow at 1% per annum
 After 4 years, the interest rate decreases to 3% per annum
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Questions
1. [1 mark] How much is the first mortgage payment? [Hint: The first mortgage payment solves
for C in the equation: = C ∙
, where r is the loan rate (interest rate), and N is
the number of payment periods.]
2. For each scenario,
a) [3 mark] What is the balance on the home loan in 9 years, after the 9th mortgage
payment has been made?
[Hint: Perhaps the simplest way to solve this is to use Excel to calculate the year-by-
year 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 8% after-
tax 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, calculate the NFV (net future value) of the difference in cash flows in 2(b) using r =
8%.]
4. [2 mark] Supposing you view each scenario as equally likely (i.e., you assign equal
probability to each of the three possibilities (i.e., 1/3) occurring in the future), which would
you recommend: buying or renting? Why?
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Comments and Hints
1. In all 3 scenarios, the home loan rate is fixed for the first four years, then it changes and is
fixed at the new rate for the remaining years.
2. Regarding the timing of the interest rate change: If, for example, you deposit $100 at year 3,
you will have $106.00 at year 4. If the interest rate then rises to 7%, one year later you will
have $106.00 * 1.07 = $113.42 at year 5.
3. The loan is only for 80% of the house value that you borrow. Maintenance is paid out of
pocket in cash annually.
4. When the house is sold, the remaining loan balance must be repaid.
5. For Question 3, the idea is to work out how much better or worse you would be by renting
in terms of your net wealth at year 9.1 You can do this by solving for the NFV of the annual
difference in cash flows for renting versus buying.
6. You can think of housing costs as all the (negative) cash flows that are related to housing.
For example, housing costs are either rent (if you rent) or the down payment, stamp duty,
maintenance, mortgage payments etc (if you buy).
1 Net wealth at year 9 is equivalent to the Net Future Value of the cash flows associated with buying or renting
the house.
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