Return on investment | Year 11

01 / LEARN

Understand the idea.

Build the return calculation

Return on investment compares net profit with the initial amount committed. Find all net receipts, subtract the initial cost to obtain profit, then divide by that initial cost. Include purchase fees in the starting cost when the scenario says they are part of the outlay.

A loss produces a negative return. The denominator matters: the same dollar profit represents a smaller percentage gain on a larger investment. State the investment period as well, because a percentage without its duration gives an incomplete comparison.

Consider the time period

A total return over several years is not automatically an annual rate. For a single starting payment and a single final receipt, choose an annual compound factor that reproduces the same overall growth: $1 + r = {(\frac{F V}{P V})}^{1 / t}$ .

This annualisation assumes there are no intermediate cash flows to time separately. Extra deposits, partial withdrawals or dividends paid and used earlier cannot generally be handled by one final-to-initial ratio. Keep the supplied cash-flow model explicit rather than inventing a common holding period.

02 / WORKED EXAMPLES

See the method in action.

EXAMPLE 01

Worked example

An investment costs AUD 1700 including fees. Sale proceeds plus dividends total AUD 1848. Find ROI.

Worked solution

1
Find the net profit.
$Π = 1848 - 1700 = AUD 148$
Net receipts exceed the complete initial outlay, including fees, by AUD 148.
2
Compare profit with the initial cost.
$ROI = \frac{148}{1700} \times 100 %$
The starting investment is the reference amount for ROI.
3
Evaluate the percentage return.
$ROI \approx 8.71 %$
Round the percentage only after calculating the full ratio.

Answer

8.71%

EXAMPLE 02

Worked example

A single AUD 4000 investment returns AUD 4840 after 2 years. Find total ROI and equivalent annual rate.

Worked solution

1
Calculate the total profit and total ROI.
$\begin{aligned} Π & = 4840 - 4000 = 840 \\ ROI & = \frac{840}{4000} \times 100 % = 21 % \end{aligned}$
The 21% gain describes the entire two-year investment period.
2
Set up an equivalent annual compound rate.
$4000 {(1 + r)}^{2} = 4840$
The same annual factor must act twice to reproduce the supplied final amount.
3
Take the positive growth-factor root.
$1 + r = \sqrt{\frac{4840}{4000}} = \sqrt{1.21} = 1.10$
A positive investment growth factor uses the positive square root.
4
State the annualised rate separately.
$r = 1.10 - 1 = 0.10 = 10 % per year$
Ten percent compounded for two years gives 21% total growth, rather than 20%.

Answer

21% total;10% annualised

03 / YOUR TURN

Try it yourself.

Check your understanding

Cost AUD 800; net receipts AUD 760. Find ROI.

Show answer & reasoning

−5%

The loss is $760 - 800 = - 40 (AUD)$ . Therefore $ROI = \frac{- 40}{800} \times 100 % = - 5 %$ ; the negative sign records a loss relative to the initial cost.

Keep practising

6 worksheet questions · 12 marks

Open worksheet Worked solutions

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
$Profit = 275; \frac{275}{2500} = 0.11$ .
11%
Cost AUD 1200; net receipts AUD 1110. Find ROI.
2 marks
$Profit = - 90; \frac{- 90}{1200} = - 0.075$ .
$- 7.5$ %
An investment earns AUD 480 profit at an ROI of 12%. Find its initial cost.
2 marks
$P = \frac{480}{0.12} = 4000$ .
AUD 4,000.00
Compare AUD 200 profit on AUD 1000 with AUD 300 profit on AUD 2000.
2 marks
$\frac{200}{1000} = 0.20$ .
$\frac{300}{2000} = 0.15$ .
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
${1.331}^{\frac{1}{3}} - 1 = 0.10$ .
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.

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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 ↗

In this lesson

Understand the idea.

Build the return calculation

Consider the time period

See the method in action.

Worked example

Find the net profit.

Compare profit with the initial cost.

Evaluate the percentage return.

Worked example

Calculate the total profit and total ROI.

Set up an equivalent annual compound rate.

Take the positive growth-factor root.

State the annualised rate separately.

Try it yourself.

Check your understanding

Keep practising