How the problems are made
Each project is invented: a cost in year 0 and three to seven years of net cash flows in thousands, sometimes with a loss in year 1, a payback that lands exactly on a year end, or a residual value. Levels run from payback with the same cash flow every year to two projects compared on all three methods. Discount factors are printed to 2 decimal places, as in AQA mark schemes, and every answer is worked from the printed table.
An example from set PAY278
Ashgrove Farm Shop's café extension costs £150,000 and should bring in £60,000, £60,000, £50,000, £50,000, £25,000 and £30,000 over six years. The cumulative cash flow in £000s runs −150, −90, −30, 20, 70, 95 and 125, so it turns positive in year 3. After 2 years, 30 is still needed out of year 3's 50: 30 ÷ 50 × 12 = 7.2 months. Rounded up, payback is 2 years 8 months; to the nearest month it is 2 years 7 months. Open set PAY278
What each course asks for
AQA 7132 and 7138: ARR = average annual return ÷ initial cost of project × 100 (formula 40 in the 7138 annex). Edexcel 9BS0: simple payback (cost ÷ average yearly net cash flow) when the cash flow is the same every year; with uneven cash flows Pearson's mark schemes use the cumulative total, as this page does. ARR = average profit per year ÷ cost of initial investment × 100. OCR H431 and H436: ARR = average profit ÷ initial cost × 100, with discount factors given. Cambridge 9609: ARR = average profit ÷ average investment × 100, so the residual value matters. On the % sign: OCR mark schemes give at most 3 of 4 marks to an ARR with no unit, and Cambridge examiners ask for the unit, so this page marks a missing % as close for those courses. Pearson's 9BS0 examiners gave full marks to a worked answer without it.
Questions
How do you calculate the payback period in years and months?
Add up the net cash flows year by year, starting with the cost as a negative in year 0. Payback ends in the year the total turns positive. Divide what is still needed at the start of that year by that year's cash flow, then multiply by 12 for months or by 365 for days.
Do you round the months up or to the nearest month?
None of the specifications sets a rule. AQA's teaching guide rounds 2 years and 4.8 months up to 2 years and 5 months. Ask your teacher which style they mark to, and pick it above: every sheet and key says which one it uses.
Is ARR divided by the initial cost or the average investment?
AQA, Edexcel and OCR divide the average annual profit by the initial cost. Cambridge 9609 divides it by the average investment, which is (initial cost + residual value) ÷ 2. In both, the average is the total of the cash flows minus the cost, divided by the number of years.
Why is my NPV different from a calculator's?
Exam questions print the discount factors. AQA prints them to 2 decimal places: 0.91, 0.83 and 0.75 at 10%. A calculator uses 0.909, 0.826 and 0.751, so its answer drifts. Marks come from the factors on the paper, so this page works only from the printed table.
Is year 0 included in the NPV?
Yes, as the cost. Its discount factor is 1.00, so its present value is the cost itself. NPV is the total of the present values of years 1 onwards minus the initial cost, which is the same as adding all the present values with year 0 as a negative.
What does a negative NPV mean?
At the discount rate used, the future cash flows are worth less today than the project costs, so on financial grounds it should be rejected. A positive NPV means accept. Between two projects, the one with the higher positive NPV adds the most value.
Can the three methods disagree?
Often. Payback rewards quick returns and ignores everything after it. ARR uses all the years but not their timing. NPV allows for timing but depends on the rate chosen. The exam-style level makes you rank two projects on each method, then choose.
Sources, checked 28 October 2026: AQA AS and A-level Business 7137/7138 specification (PDF), annex formulae 39 to 41; AQA teaching guide: investment appraisal; AQA 7132/2 June 2023 mark scheme (PDF); Pearson Edexcel A level Business 9BS0 specification (PDF), 3.3.2; Pearson calculation questions for 9BS0 (PDF); Pearson International A level WBS13/01 January 2022 mark scheme (PDF); Pearson 9BS0/02 June 2019 examiner report (PDF), question 1(b), Pearson 9BS0/03 June 2022 mark scheme (PDF), question 2(d); OCR A Level Business H436 specification (PDF), 7.4.1; OCR H031/01 June 2017 mark scheme (PDF), question 4; Cambridge AS and A Level Business 9609 syllabus 2026 to 2028 (PDF), 10.3; Cambridge 9609 June 2024 principal examiner report (PDF).