Calculate payback and accounting rate of return
Calculate payback from cumulative cash flows and ARR from average profit and average investment, then explain what each method omits.
Cambridge International AS & A Level Business 9609, 2026–2028 syllabus and 2029 syllabus, section 10.3.2. Ratio calculations use the formulae listed in the relevant Cambridge syllabus. Written practice is self-checked. Specialist review has not been completed for this lesson; these exercises do not award an official mark or establish exam readiness.
Before you begin
- Read the figures, dates and assumptions supplied in the question before calculating or interpreting an accounting result.
Work on paper. Try each question before revealing help, and explain why your method works.
Quick readiness check
What does payback measure?
What you will learn
- Calculate and interpret payback from project cash flows
- Calculate ARR using Cambridge's formula
- Compare each result's use and limitations
Payback measures time to recover outlay
Payback is the time required for cumulative net cash inflows to recover the initial investment. Add the cash inflows in sequence; if recovery occurs partway through a year and the flow is assumed even, the fraction is unrecovered balance ÷ that year's cash inflow.
A shorter payback can help assess liquidity exposure or a firm's recovery target. Basic payback ignores cash flows after the recovery point and does not account for the time value of money unless a discounted-payback method is explicitly specified.
ARR measures average accounting return
Cambridge formula: ARR = (average profit ÷ average investment) × 100. Use the average profit and average investment figures supplied or calculate them from the assumptions given. When the question specifies no residual value and the usual straight-line pattern, average investment may be estimated as (initial investment + residual value) ÷ 2; state the convention used.
ARR is a percentage based on accounting profit, so it depends on depreciation and other accounting estimates and does not show when cash arrives. A higher ARR may be attractive, but compare the target, project life, risk and cash-flow timing.
Pause and explain
A project costs $50,000 and receives $20,000, then $30,000 in successive years. What is payback?
Worked example
A project costs $60,000 and is expected to generate cash inflows of $15,000, $20,000, $25,000 and $30,000 over four years. Total project profit is estimated at $30,000; assume zero residual value and use average investment=(initial cost+residual value)÷2. Calculate payback and ARR.
Show the worked solution
- Cumulative inflows after years 1 and 2 are $15,000+$20,000=$35,000.
- The remaining $25,000 is recovered during year 3, when the inflow is $25,000: payback=3 years.
- Average profit=30,000÷4=$7,500; average investment=(60,000+0)÷2=$30,000; ARR=7,500÷30,000×100=25%.
Answer Payback is 3 years and ARR is 25% using the stated average-investment convention.
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Test this topic →From guided practice to a new situation
Write your answer and reasoning first. Use a hint only if you are stuck. The model solution is for self-checking; your written work is not automatically marked.
A project costs $80,000 and generates inflows of $30,000, $25,000 and $40,000 over three years. Find payback, assuming even cash flow during the recovery year.
Give me a hint
Track the unrecovered balance after each full year.
Compare my reasoning
- After two years, cumulative inflow=30,000+25,000=$55,000.
- Unrecovered balance=80,000−55,000=$25,000.
- Fraction of year 3=25,000÷40,000=0.625.
Payback is 2.625 years (about 2 years and 7.5 months), assuming year-three cash flow arrives evenly.
Look for these in your work
- Cumulative cash flow is correct
- Unrecovered balance is correct
- Fractional year assumption is stated
Average annual profit is $18,000 and average investment is $120,000. Calculate ARR and interpret it carefully.
Give me a hint
Divide average profit by average investment, then multiply by 100.
Compare my reasoning
- ARR=18,000÷120,000×100.
- State the result as a percentage.
- Compare with the firm's target and other evidence, not as a guarantee.
ARR is 15%. It is an average accounting return based on the stated figures; whether it is acceptable depends on the target, risk, project life and cash-flow timing.
Look for these in your work
- Correct denominator is used
- Percentage is calculated
- Interpretation is qualified
Project X pays back in 2 years; Project Y pays back in 3.5 years but produces larger later inflows. Explain why payback alone may choose poorly.
Give me a hint
Payback stops crediting a project once the initial outlay is recovered.
Compare my reasoning
- X recovers its outlay sooner.
- Basic payback ignores later cash flows and usually ignores time value.
- Compare full project cash flows, risk and NPV as well as the firm's liquidity needs.
X offers earlier recovery, which may suit a cash-constrained or high-risk setting, but basic payback ignores Y's larger post-recovery inflows. Compare project-life cash flows, risk and discounted value as well; payback is one decision aid, not a total-return measure.
Look for these in your work
- Liquidity use is recognised
- Post-payback omission is explicit
- Alternative evidence is recommended
Common mistakes
- Using annual profit instead of cash flow for payback
- Including cash flows after recovery in the payback calculation
- Calculating ARR with total rather than average profit
What can you explain now?
What does payback measure?
Compare with the explanation
Time until cumulative net cash inflows recover the initial outlay
It is a time measure based on project cash flows.
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Make it stick
How are payback and ARR calculated, and what different information does each one leave out?
If you needed the solution, close it and solve the problem again from a blank page. A correct answer is stronger when you can explain the reason for each step.