Average annual profit = Total net cash flows ÷ Number of years
Example: Investment £200,000; total net cash flows over 5 years = £300,000 → Profit = £100,000; Annual average = £20,000; ARR = (20,000 ÷ 200,000) × 100 = 10%
Decision rule: Accept if ARR > target rate (e.g. cost of capital or minimum required return)
Pros: Uses all cash flows over project life; expressed as % easy to compare; familiar concept for managers
Cons: Ignores timing of cash flows; does not account for time value of money; uses averages which can hide poor early performance
Method 3: Most Sophisticated
Net Present Value (NPV)
Time Value of Money
£1 today is worth more than £1 in the future — due to inflation, opportunity cost and risk. NPV discounts future cash flows back to their present value using discount factors.
Decision Rule
NPV = Sum of all discounted cash inflows − Initial investment
Accept if NPV > 0 (project generates more than the cost of capital). Reject if NPV < 0.
Year
Cash Flow (£)
Discount Factor @10%
Present Value (£)
1
50,000
0.909
45,450
2
60,000
0.826
49,560
3
70,000
0.751
52,570
Total PV of inflows
147,580
Less: Initial Investment
−120,000
NPV
+27,580 → ACCEPT
Method Comparison
Strengths & Weaknesses
Payback — Best for:
Cash-constrained SMEs needing quick returns
Fast-changing markets where long forecasts are unreliable
Simple comparison between projects
Weakness: Ignores total profitability
ARR — Best for:
Comparing % returns across projects of different sizes
When all future cash flows are equally important
Weakness: Timing ignored; averages distort
NPV — Theoretically Superior
Accounts for time value of money; uses all cash flows; gives absolute £ value added. Best for: large strategic investments; comparing projects over different timeframes. Weakness: Requires accurate discount rate and long-term forecasts — both uncertain. Complex for non-financial managers.
Beyond the Numbers
Qualitative Factors in Investment Decisions
Strategic fit: Does the investment align with corporate objectives and long-term direction?
Risk profile: How certain are the forecast cash flows? High uncertainty warrants shorter payback preference
Stakeholder impact: Will the investment affect employees, local community, suppliers — and are these acceptable?
Environmental/ethical: ESG constraints increasingly filter investment choices at board level
Opportunity cost: What is foregone by not making an alternative investment? All capital allocation involves opportunity cost
A-Level evaluation: A positive NPV is necessary but not sufficient for approval. Qualitative factors — strategic fit, risk, stakeholder concerns — can override strong financial metrics. Real-world investment decisions always combine both.
Risk & Uncertainty
Managing Investment Risk
Sensitivity analysis: Test how changes in key assumptions (sales volume, costs, discount rate) affect NPV — identifies critical variables
Scenario planning: Model optimistic, base and pessimistic scenarios — understand the range of possible outcomes
Staged investment: Invest in phases with review gates — reduces commitment risk; more flexible but may miss economies of scale
Higher discount rate: Apply a risk premium to the discount rate for riskier projects — e.g. use 15% instead of 10%
Practice Question 1
A business invests £80,000. Year 1 inflow: £30,000; Year 2: £30,000; Year 3: £40,000. What is the payback period?
A2 years 3 months
B2 years 6 months
C3 years exactly
D2 years 9 months
B is correct. After Year 1: cumulative = £30,000 (deficit £50,000). After Year 2: cumulative = £60,000 (deficit £20,000). In Year 3, £40,000 arrives — need £20,000 more: 20,000 ÷ 40,000 × 12 = 6 months into Year 3. Total payback = 2 years 6 months.
Practice Question 2
A project costs £250,000 and generates total cash inflows of £400,000 over 4 years. What is the ARR?
A60%
B15%
C37.5%
D40%
B is correct. Total net profit = £400,000 − £250,000 = £150,000. Average annual profit = £150,000 ÷ 4 = £37,500. ARR = (£37,500 ÷ £250,000) × 100 = 15%. A common mistake is dividing total inflows (not profit) by investment, which gives 40% — remember to subtract the initial cost first.
Practice Question 3
A project has a positive payback period but a negative NPV. A manager recommends rejecting it. Which evaluation of this recommendation is most appropriate?
AThe recommendation is wrong — positive payback means the project is profitable
BThe recommendation is likely correct — a negative NPV means the project destroys value in real terms once time value of money is considered
CThe recommendation is wrong — NPV ignores all cash flows after payback
DThe recommendation is correct because payback should always be used ahead of NPV
B is correct. A negative NPV means the discounted present value of cash inflows is less than the initial cost — the project earns less than the required rate of return. The manager's recommendation to reject is sound. A positive payback only means cash is recovered — it does not account for the time value of money or the opportunity cost of capital.
Practice Question 4
A retailer assesses two projects. Project A: NPV = +£150,000, payback = 5 years. Project B: NPV = +£90,000, payback = 2 years. The business has severe short-term cash flow pressure. Which should it choose?
AProject A — higher NPV means it creates more value
BProject B — faster payback is more important when cash flow is under pressure
CProject A — NPV is always the most important criterion
DNeither — both have positive NPVs so neither should be prioritised over the other
B is correct. Despite having a lower NPV, Project B's 2-year payback is critical when the business faces cash flow pressure. A 5-year wait to recover £150,000 may cause insolvency if the business cannot survive that long. Investment appraisal is context-dependent — the "best" method depends on the firm's financial position and risk tolerance.
Summary
Key Takeaways
Payback: Time to recover investment; simple; favoured by cash-constrained firms; ignores total returns
ARR: Average annual profit as % of investment; easy to compare; ignores timing
NPV: Accounts for time value of money using discount factors; theoretically superior; requires accurate forecasts
Accept NPV > 0; reject NPV < 0 — NPV positive means project returns exceed cost of capital
Qualitative factors: Strategic fit, risk, stakeholder impact and opportunity cost must complement quantitative analysis