IB Business Management HLTopic 3 — Finance and AccountsPaper 1 & 2Core skill~7 min read
Average Rate of Return
Payback tells a business how fast its money comes back. The average rate of return, or ARR, tells it how much money it makes. Because the answer is a percentage, you can hold it up against a bank interest rate, against a rival project, or against the firm’s own target.
What you need to know
ARR compares the average yearly profit of an investment with the money originally spent on it.
Total profit = total returns − initial cost. The cost is subtracted once, not every year.
Divide total profit by the number of years to get average annual profit.
Then divide by the initial cost and multiply by 100 to get a percentage.
ARR uses all the cash flows, which payback does not.
It ignores the timing of those cash flows, which is where NPV comes in.
The formula
Average rate of return
(average annual profit ÷ initial cost) × 100
Average annual profit
(total returns − initial cost) ÷ number of years
If your ARR comes out enormous, you have probably forgotten to divide by the number of years.
WORKED EXAMPLE 1
A single project
Rani’s Bakery is considering a $60,000 investment in a new production line. It expects total returns of $87,000 over five years. Calculate the average rate of return. [4]
Step 1: total profit87,000 − 60,000 = $27,000Step 2: average annual profit27,000 ÷ 5 = $5,400 a yearStep 3: divide by the initial cost5,400 ÷ 60,000 = 0.09Step 4: turn it into a percentage0.09 × 100ARR = 9.00%The project returns an average of 9 cents a year for every dollar invested. Compare that with what the bank pays before deciding.
Comparing two projects
ARR earns its keep when a business has to choose. Because the answer is a percentage, the size of each project stops mattering — a small project can beat a large one.
The two projects make identical total profit. Only the percentage reveals which uses the firm’s money better.
WORKED EXAMPLE 2
Choosing between two projects
Project A costs $60,000 and returns $87,000 over five years. Project B costs $45,000 and returns $72,000 over six years. Calculate the ARR of each and recommend one. [5]
Step 1: Project A(87,000 − 60,000) ÷ 5 = 27,000 ÷ 5 = $5,400(5,400 ÷ 60,000) × 100 = 9.00%Step 2: Project B(72,000 − 45,000) ÷ 6 = 27,000 ÷ 6 = $4,500(4,500 ÷ 45,000) × 100 = 10.00%Choose Project BB gives a higher return on every dollar and needs $15,000 less up front, which also helps cash flow. But B ties the money up for an extra year, so a firm expecting fast change in its market might still prefer A.
Notice how the two projects make exactly the same total profit. The whole point of ARR is that total profit on its own is misleading until you know what it cost and how long it took.
Judging the ARR method
Advantages
Disadvantages
Uses every net cash flow the project generates, not just the ones before payback
Because it averages, it ignores when the cash actually arrives
The answer is a percentage, so projects of any size can be compared fairly
Opportunity cost is ignored — no adjustment for interest rates or inflation
Can be compared directly with interest rates or the firm’s target return
Relies on forecasts of returns years into the future, which may be wrong
Easy to explain to owners, investors and lenders
A project that earns everything in year one scores the same as one that earns everything in year six
Use ARR and payback together. Payback measures risk, ARR measures reward. A project with a fast payback and a high ARR is an easy decision. When they disagree, the firm’s cash position usually decides.
Exam tip
Read carefully whether the question gives total returns or annual cash flows. If annual, add them up first.
Subtract the initial cost once only, at step one.
Give the answer to two decimal places with a percentage sign.
Always compare the ARR with something — a rival project, the interest rate, or the firm’s target.
Mention qualitative factors: staff impact, the environment, brand reputation, and the firm’s objectives.
If you are asked to recommend, commit to one option. Sitting on the fence loses the judgement mark.
Common mix-up
Forgetting to subtract the initial cost. That turns a return into total revenue and gives a wild percentage.
Dividing by the number of years twice. It happens once, at step two.
Dividing by total returns instead of the initial cost. The bottom of the fraction is what was spent.
Comparing ARR with the payback period. One is a percentage, the other is a length of time.
Assuming the higher ARR always wins. A cash-poor firm may need the faster payback instead.
Treating a forecast as a fact. Every figure here is an estimate of the future.
Up next: HL Net Present Value — the method that finally deals with the fact that money next year is worth less than money today.
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