The idea, step by step
Build the return calculation
Net profit is all receipts minus all costs. A simple return on investment is . State the denominator: for a share purchase, the actual initial cost includes the stated purchase brokerage.
A loss gives a negative return. A large dollar profit can still be a small percentage return when the initial investment is large. Compare both the amount and its reference cost.
Consider the time period
An ROI is tied to its investment period. A 15% return over five years is not a 15% annual rate. For one starting payment and one final receipt, the equivalent compound annual rate is .
That annualisation does not automatically handle extra payments at intermediate dates. In that case the timing of each cash flow must be modelled rather than compressed into a single ratio.
A common trap
Divide profit by the final amount.
Instead: ROI normally compares profit with the initial cost, not final receipts.
See the thinking
Worked example
An investment costs AUD 1700 including fees. Sale proceeds plus dividends total AUD 1848. Find ROI.
- Profit=1848−1700=148.
- ROI=148/1700×100%=8.71%.
Worked example
A single AUD 4000 investment returns AUD 4840 after 2 years. Find total ROI and equivalent annual rate.
- Total ROI=(4840−4000)/4000=0.21.
- Annual rate=(4840/4000)^(1/2)−1=0.10.
Check your understanding
Cost AUD 800; net receipts AUD 760. Find ROI.
Show answer
−5%
Profit=−40;−40/800=−0.05.
Your turn
6 questions · 12 marks · Work at your own pace.
Read the questions online
- Cost AUD 2500; total receipts AUD 2775. Find ROI.2 marks
- Cost AUD 1200; net receipts AUD 1110. Find ROI.2 marks
- An investment earns AUD 480 profit at an ROI of 12%. Find its initial cost.2 marks
- Compare AUD 200 profit on AUD 1000 with AUD 300 profit on AUD 2000.2 marks
- A single investment grows by 33.1% over 3 years. Find its equivalent annual rate.2 marks
- A report says ROI was 8%. What extra timing information is needed before calling it 8% per year?2 marks
Read the worked solutions
Equivalent correct methods earn the corresponding marks. Include units where asked.
- Cost AUD 2500; total receipts AUD 2775. Find ROI.2 marks
Profit=275;275/2500=0.11.
11% - Cost AUD 1200; net receipts AUD 1110. Find ROI.2 marks
Profit=−90;−90/1200=−0.075.
−7.5% - An investment earns AUD 480 profit at an ROI of 12%. Find its initial cost.2 marks
P=480/0.12=4000.
AUD 4,000.00 - Compare AUD 200 profit on AUD 1000 with AUD 300 profit on AUD 2000.2 marks
200/1000=0.20.
300/2000=0.15.
20% versus 15%; first has the larger percentage return. - A single investment grows by 33.1% over 3 years. Find its equivalent annual rate.2 marks
1.331^(1/3)−1=0.10.
10% - A report says ROI was 8%. What extra timing information is needed before calling it 8% per year?2 marks
A totalperiod ROI does not by itself specify an annual rate.
The investment period and any intermediate cash-flow dates.
Curriculum reference & lesson scope
SACE Board of South Australia
Stage 1 General Mathematics: investing and borrowing. Supplied educational models cover interest, investment comparisons, shares and credit; they are not recommendations of real products or statements of personal tax liability.
Official curriculum source ↗