Research School of Finance Actuarial Studies & Statistics
ANU College of Business and Economics
Australian National University
Canberra ACT 2601
https://www.rsfas.anu.edu.au/
STAT2032 ASSIGNMENT 2 COVER SHEET
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STAT2032 Assignment 2
Instructions to Students
1. This assignment has 1 question and is worth 20 marks.
2. This is an individual assignment worth 20% of your final grade.
3. You may submit your completed assignment in the provided Excel workbook.
4. Ensure you have shown sufficient working and calculation in your solution.
Formulas should be entered for all calculations. Hardcoded answers and
intermediate answers will not earn any credit.
5. Complete and include the signed assignment cover sheet in your workbook. You may
insert a new sheet and copy paste the completed cover sheet as a screenshot/picture in
this sheet.
6. Name your assignment with your student ID only – that is, ‘uXXXXXX’ (with the X’s
corresponding to your student ID exactly). Then submit your assignment via the
designated link on the Wattle course page.
7. Assignment must be submitted by 9 pm on Friday 3 May. Late submission without prior
approval for extension will be given 0 mark.
Question 1 (20 marks)
Sam is considering purchasing an investment property at either location A or location B which
will be fully funded by bank mortgage (i.e. loan) at a fixed effective interest rate of 6% per
annum. The investment property will be placed on the market for short-term rental immediately
after purchase for 30 years before resale.
The total annual rental income is equal to the product of the number of days rented per year
and the average rental price per night each year. Sam expects that the average nightly rental
price each year will grow with inflation according to an inflation index. The average rental
price is $110 per night at both locations for the past year. The number of days rented each year
depends on the location and the inflation in that year. The relationship between inflation and
the number of days rented at each location is expected to follow the table below:
Annual inflation Number of days rented in a year
Location A Location B
< 2.8% 330 332 ≥ 2.8% and < 4.3% 250 250 ≥ 4.3% 180 230
The property price now is $500,000 at location A and $600,000 at location B. Capital gain over
30 years (i.e. percentage growth in property price) is expected to be 97% for location A and
190% for location B.
The projected inflation index for the next 30 years is provided in column G of the tab “main”
in the Excel workbook named “STAT2032_Assignment_2.xlsx”. You are expected to
complete your assignment in this workbook.
a) Go to tab “main” of workbook “STAT6046_Assignment_2.xlsx”, calculate the annual
inflation rate and average price per night each year in columns H and I. Next, calculate
number of days rented and rental income each year in columns J:K for location A and
columns L:M for location B. For convenience of calculation, the annual rental income is
treated as to be collected at the end of each year. (3 marks)
b) For both locations, calculate the respective discounted payback period of each investment.
Then, calculate the respective resulting accumulated profit at the end of 30 years, assuming
that the rental income collected at the end of each year will be used to pay off the mortgage
first. Sam plans to deposit any excess cash inflows into a savings account that will provide
a real reinvestment rate of $1.2% per annum. Report your final answers in range B14:C15.
Show you working clearly in the tab “main” where applicable. You are free to decide how
you want to present your working/ intermediate answers. (5 marks)
c) For both locations, calculate the respective yield of each investment, assuming a real
reinvestment rate of $1.2% per annum. Report your final answers in range B16:C16. Show
you working clearly in the tab “main” where applicable. (3 marks)
d) For both locations, calculate the respective net present value of each investment assuming
an effective risk discount rate of $8.65% per annum. Report your final answers in range
B17:C17. Show you working clearly in the tab “main” where applicable. (3 marks)
e) Based on all the metrics calculated in part b) to d), discuss how prioritization over each of
the three driving factors, namely risk aversion, dollar profit maximisation and percentage
return maximisation, would affect Sam’s choice of investment at either location A or B.
Type your answer in range A31:C200 of the tab “main”. (6 marks)
End of Assignment