This mini-lesson covers AQA 7132 section 3.7.8 — investment appraisal. You will calculate, in full, the payback period, the average rate of return (ARR) and the net present value (NPV) using discount factors, run a sensitivity analysis, and weigh the non-financial factors that decide whether a project with excellent numbers should actually go ahead.
Work through each screen, answer the questions as you go (some are analysis, some are calculations) and collect ⭐ stars. Every number here is worked through step by step. Press Start when you're ready.
3.7.8 · the problem
Why investment appraisal exists
A capital investment means paying out a large sum now in exchange for a stream of cash later. Investment appraisal answers two questions: is this project worth doing at all? and if we can only do one, which?
AQA requires three methods, and each answers a different question:
Payback — how quickly do we get our money back? (a liquidity and risk question)
Average Rate of Return (ARR) — what percentage return does it earn? (a profitability question)
Net Present Value (NPV) — is it worth more than it costs, once we account for the fact that money arrives later? (a value question — and the theoretically correct one)
Data — Project Aurora
Initial investment (Year 0): £360,000
Net cash inflows: Year 1 £120,000 · Year 2 £150,000 · Year 3 £180,000 · Year 4 £170,000 · Year 5 £100,000 (total £720,000)
3.7.8 · payback
Payback period
Run a cumulative cash flow column and find the moment it turns positive.
Cumulative net cash flow
Year 0: −£360,000
Year 1: −£360,000 + £120,000 = −£240,000
Year 2: −£240,000 + £150,000 = −£90,000
Year 3: −£90,000 + £180,000 = +£90,000 — so payback happens during Year 3.
Part-year = (amount still owed ÷ cash flow in that year) × 12= (£90,000 ÷ £180,000) × 12 months = 0.5 × 12 = 6 months
Calculate
Your turn — payback period
1State Project Aurora's payback period in years, as a decimal (e.g. 3.25 would mean 3 years 3 months).
years
Hint: £90,000 was still owed at the end of Year 2, and Year 3 brings in £180,000. £90,000 ÷ £180,000 = 0.5 of a year. So payback = 2 years + 0.5.
3.7.8 · ARR
Average Rate of Return
ARR (%) = (average annual profit ÷ initial investment) × 100average annual profit = (total net cash inflows − initial investment) ÷ number of years
Average annual profit = £360,000 ÷ 5 years = £72,000
ARR's great strength is that it produces a percentage — so it can be compared directly with the interest rate the firm pays to borrow, with the return on a different project, or with a board-set criterion rate ("we do not proceed below 15%").
?Project Aurora pays back in 2.5 years and has an ARR of 20%. What is the single biggest weakness that both methods share?
3.7.8 · discounting
Net Present Value and the time value of money
£100 today is worth more than £100 in a year, because today's £100 can be invested. To compare cash flows arriving at different times, we convert them all back to today's money using a discount factor.
Present value = future cash flow × discount factorNPV = (sum of all the present values of the inflows) − initial investment
The discount rate reflects the firm's cost of capital and the riskiness of the project. A higher rate means future cash is discounted more heavily — so it reduces NPV, and it hurts long-dated projects most.
Discounting Project Aurora at 10%
Year 1: £120,000 × 0.909 = £109,080
Year 2: £150,000 × 0.826 = £123,900
Year 3: £180,000 × 0.751 = £135,180
Year 4: £170,000 × 0.683 = £116,110
Year 5: £100,000 × 0.621 = £62,100
Notice how the factors shrink: by Year 5, a pound is worth only 62p in today's money. Distant cash flows carry far less weight — which is the whole point.
Calculate
Your turn — total present value
3Add up the five present values above to find the total present value of Project Aurora's inflows, in £.
4Now calculate Project Aurora's NPV at a 10% discount rate, in £.
£
Hint: NPV = total present value − initial investment = £546,370 − £360,000.
3.7.8 · the decision rule
Reading the NPV
NPV positive → ACCEPTthe project returns more than the firm's cost of capital: it creates value NPV negative → REJECT: the money would be better used elsewhere
Project Aurora, summarised
Payback 2.5 years · ARR 20% · NPV at 10% +£186,370
All three agree: on the numbers, this is a good project. It recovers its cash quickly, it earns 20% against a 10% cost of capital, and after fully accounting for the timing of every pound it is still worth £186,370 more than it costs.
When methods disagree — and they often do — NPV wins. It is the only method that uses all the cash flows and accounts for their timing. Payback favours short, safe projects and would reject a pharmaceutical programme that pays back in year 9 and then earns billions. ARR ignores timing entirely. Use payback as a risk filter and ARR as a quick comparator, but let NPV decide.
3.7.8 · sensitivity
Sensitivity analysis
Every appraisal rests on forecasts. Sensitivity analysis asks: how wrong could we be before the decision changes? Change one variable at a time — the discount rate, the sales forecast, the initial cost — and watch what happens to NPV.
Suppose the firm's cost of capital rises to 15%. The discount factors become 0.870, 0.756, 0.658, 0.572 and 0.497.
Project Aurora, discounted at 15%
Year 1: £120,000 × 0.870 = £104,400
Year 2: £150,000 × 0.756 = £113,400
Year 3: £180,000 × 0.658 = £118,440
Year 4: £170,000 × 0.572 = £97,240
Year 5: £100,000 × 0.497 = £49,700
Total present value = £483,180
Calculate
Your turn — NPV under sensitivity
5Calculate Project Aurora's NPV at a 15% discount rate, in £.
£
Hint: NPV = £483,180 − £360,000.
Quick check
Reading a sensitivity test
?Raising the discount rate from 10% to 15% cuts Aurora's NPV from £186,370 to £123,180. What does this tell the board?
Sort it
Which appraisal method?
Tap a characteristic, then tap the method it describes.
⏱️ Payback
📊 ARR
💰 NPV
Match it
Match each term to its definition
Tap an item on the left, then its partner on the right.
Term
Definition
3.7.8 · other influences
Factors influencing investment decisions
The arithmetic never decides on its own. Weigh:
Investment criteria — the board's own hurdles: "payback within three years", "ARR above 15%". These are policy, and they may rule out a positive-NPV project.
The reliability of the forecasts. Every figure beyond Year 1 is an estimate. Five-year forecasts in a volatile market are close to fiction, and NPV's precision (£186,370) gives them a spurious authority.
Risk and uncertainty. Risk can be modelled (probabilities, sensitivity analysis). Uncertainty cannot — a technology shift or a regulatory ban does not appear in any spreadsheet.
Non-financial factors — the firm's objectives and mission, the impact on employees and the community, environmental effects, ethics, brand and reputation, the reaction of competitors, and whether the project builds or destroys a core competence.
Availability of finance and opportunity cost. A positive NPV is irrelevant if the firm cannot raise the £360,000 — or if another project has a higher NPV and the money can only be spent once.
Quick check
When payback beats NPV
?A firm must choose between two projects. Project X: payback 1.8 years, NPV +£40,000. Project Y: payback 4.2 years, NPV +£310,000. The firm is currently under severe cash-flow pressure and has a large overdraft. What is the best advice?
Quick check
Criticising NPV properly
?Which criticism of NPV is most valid?
Evaluation
Thinking like an examiner
Each method answers a different question. Payback = risk and liquidity. ARR = profitability. NPV = value. Quote all three and say what each contributes.
NPV is theoretically superior — but not automatically decisive. A firm short of cash, or bound by a board criterion, may rationally choose the faster-paying project.
Interrogate the inputs. Where did the Year 5 forecast come from? What discount rate was used, and why? Run the sensitivity.
Say what the numbers cannot see. Ethics, environment, employees, brand, core competences, the competitor's response — and the opportunity cost of the project not chosen.
Recap
The big ideas to know
Payback: cumulative cash flow reaches the outlay. Part-year = (amount owed ÷ that year's cash flow) × 12. Ignores later cash flows and timing.
ARR: (average annual profit ÷ initial investment) × 100, where average annual profit = (total inflows − outlay) ÷ years. Ignores timing.
NPV: present value = cash flow × discount factor. NPV = total PV − initial outlay. Positive → accept.
Discount rate: a higher rate discounts the future more heavily → lower NPV, and it hurts long-dated projects most.
Sensitivity: change one variable and see whether the decision changes. It tests robustness, not accuracy.
Judgement: NPV is theoretically best, but liquidity, board criteria, forecast reliability, risk, ethics and opportunity cost all bear on the decision.
Press Finish to see your score.
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Mini-lesson complete!
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You've worked through Analysing strategic options: investment appraisal for AQA A-level Business (7132). 🎉