A project costs 60,000 and returns 20,000 a year. Calculate the payback period. [2 marks]

Over five years a 100,000 project returns total cash flow of 150,000. Calculate the ARR. [3 marks]

WJEC Eduqas Eduqas 2020-style practice: A machine costs 80,000 and is expected to generate net cash flows of 25,000 a year. Calculate the payback period and the average rate of return over four years. (6)

A Component 2 calculation rewarding both methods, working and units. Payback: the machine returns 25,000 a year, so it repays 80,000 in 80,00025,000 = 3.2 years. The 0.2 of a year is 0.2 × 12 = 2.4 months, so payback is about 3 years and 2 to 3 months. ARR: total cash flow over four years = 25,000 × 4 = 100,000. Total profit = 100,000 - 80,000 = 20,000. Average annual profit = 20,0004 = 5,000. ARR = 5,00080,000 × 100 = 6.25\%. Markers reward the correct payback and ARR with units. The common errors are forgetting to subtract the initial cost when finding profit for ARR, and confusing cash flow with profit.

EnglandBusinessSyllabus dot point

How do businesses decide whether a long-term investment is worthwhile?

Investment appraisal methods: payback period, average rate of return and net present value; the calculation and interpretation of each; the use of discounting and the time value of money; and the strengths, limitations and qualitative factors in investment decisions.

A focused answer to the Eduqas A-Level Business statement on investment appraisal. Covers the payback period, the average rate of return and net present value, the calculation and interpretation of each, discounting and the time value of money, and the strengths, limitations and qualitative factors in investment decisions, with worked calculations.

Generated by Claude Opus 4.814 min answerUpdated 2026-06-02

Reviewed by: AI editorial process; not yet individually human-reviewed

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Quick answer

Investment appraisal judges whether a long-term investment is worthwhile. Payback is how long the investment takes to repay its cost (it favours liquidity but ignores cash after payback and the time value of money). The average rate of return (ARR) expresses average annual profit as a percentage of the investment, $\tfrac{\text{average annual profit}}{\text{initial investment}} \times 100$ (it shows profitability but ignores timing). Net present value (NPV) discounts future cash flows to today's value using discount factors, then subtracts the initial cost; a positive NPV adds value, and it is the only method that accounts for the time value of money. No method is perfect, so firms use them together alongside qualitative factors (risk, strategy, ethics).

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What this theme is asking
The payback period
The average rate of return
Net present value and the time value of money
Strengths, limitations and qualitative factors
Examples in context
Try this

What this theme is asking

Eduqas wants you to appraise a long-term investment using three methods, payback, the average rate of return and net present value, to calculate and interpret each, to understand discounting and the time value of money, and to weigh the strengths, limitations and qualitative factors. Investment appraisal is a core Component 2 quantitative technique and a frequent source of evaluation marks.

The payback period

When cash flows are even, payback is the cost divided by the annual cash flow. When uneven, add the cash flows year by year until the cost is recovered, then find the fraction of the final year. Payback is simple and good for risk and liquidity, but it ignores cash earned after payback and the time value of money.

The average rate of return

Net present value and the time value of money

A positive NPV means the project earns more than the cost of capital and adds value; a negative NPV destroys value. NPV is the strongest method because it accounts for the time value of money, but it depends heavily on the chosen discount rate and on uncertain forecasts.

Worked example: payback, ARR and NPV for one project

A machine costs $\pounds 80{,}000$ and earns net cash flows of $\pounds 25{,}000$ a year for four years. The discount factors at the firm's cost of capital are $0.91$ , $0.83$ , $0.75$ and $0.68$ .

step 1: payback period

\text{Payback} = \frac{80{,}000}{25{,}000} = 3.2 \text{ years} \approx 3 \text{ years } 2\text{-}3 \text{ months}

step 2: ARR

Total cash flow $= 25{,}000 \times 4 = \pounds 100{,}000$ ; total profit $= 100{,}000 - 80{,}000 = \pounds 20{,}000$ ; average annual profit $= \tfrac{20{,}000}{4} = \pounds 5{,}000$ .

\text{ARR} = \frac{5{,}000}{80{,}000} \times 100 = 6.25\%

step 3: NPV

Present values: $25{,}000 \times 0.91 = 22{,}750$ ; $\times 0.83 = 20{,}750$ ; $\times 0.75 = 18{,}750$ ; $\times 0.68 = 17{,}000$ . Sum $= \pounds 79{,}250$ .

\text{NPV} = 79{,}250 - 80{,}000 = -\pounds 750

step 4: interpret

Payback ( $3.2$ years) and a positive ARR ( $6.25\%$ ) look acceptable, but the NPV is negative ( $-\pounds 750$ ), meaning that once the time value of money is allowed for, the project just fails to earn the cost of capital. NPV gives the most complete picture, so on these figures the firm should be cautious, and the decision turns on the discount rate and the reliability of the forecasts.

Strengths, limitations and qualitative factors

Each method has a role: payback for risk and liquidity, ARR for headline profitability, NPV for value created allowing for time. Firms usually use them together. But appraisal rests on forecast cash flows that are uncertain, especially for long projects, and on assumptions (the discount rate). It also ignores qualitative factors that often decide investments: the firm's objectives and strategy, the risk and the state of the economy, the impact on staff and customers, ethical and environmental considerations, and competitor reactions. Good decisions combine the numbers with judgement.

Examples in context

A delivery firm uses payback to choose the van that repays its cost fastest, prioritising liquidity. A manufacturer uses ARR to compare two machines' profitability. A large firm uses NPV to appraise a multi-year factory investment, discounting future cash flows. In each case qualitative factors, such as fit with strategy and risk, shape the final decision alongside the figures.

Try this

Q1. A project costs $\pounds 60{,}000$ and returns $\pounds 20{,}000$ a year. Calculate the payback period. [2 marks]

Cue. $\tfrac{60{,}000}{20{,}000} = 3$ years.

Q2. Over five years a $\pounds 100{,}000$ project returns total cash flow of $\pounds 150{,}000$ . Calculate the ARR. [3 marks]

Cue. Total profit $= 150{,}000 - 100{,}000 = \pounds 50{,}000$ ; average annual profit $= \tfrac{50{,}000}{5} = \pounds 10{,}000$ ; ARR $= \tfrac{10{,}000}{100{,}000} \times 100 = 10\%$ .

Exam-style practice questions

Practice questions written in the style of WJEC Eduqas exam questions on this dot point, with worked answer explainers. The year tag is the paper they imitate, not the source.

Eduqas 20206 marksA machine costs

\pounds 80{,}000

and is expected to generate net cash flows of

\pounds 25{,}000

a year. Calculate the payback period and the average rate of return over four years. (6)

Show worked answer →

A Component 2 calculation rewarding both methods, working and units.

Payback: the machine returns $\pounds 25{,}000$ a year, so it repays $\pounds 80{,}000$ in $\tfrac{80{,}000}{25{,}000} = 3.2$ years. The $0.2$ of a year is $0.2 \times 12 = 2.4$ months, so payback is about $3$ years and $2$ to $3$ months.

ARR: total cash flow over four years $= 25{,}000 \times 4 = \pounds 100{,}000$ . Total profit $= 100{,}000 - 80{,}000 = \pounds 20{,}000$ . Average annual profit $= \tfrac{20{,}000}{4} = \pounds 5{,}000$ . ARR $= \tfrac{5{,}000}{80{,}000} \times 100 = 6.25\%$ .

Markers reward the correct payback and ARR with units. The common errors are forgetting to subtract the initial cost when finding profit for ARR, and confusing cash flow with profit.

Eduqas 202210 marksEvaluate whether net present value is always the best method of investment appraisal for a business. (10)

Show worked answer →

A levels-of-response evaluation. For NPV: it is the only common method that accounts for the time value of money, discounting future cash flows to today's value, so it reflects that money received later is worth less and shows whether the project earns more than the cost of capital; a positive NPV adds value. Against: NPV depends heavily on the chosen discount rate and on cash-flow forecasts that are uncertain for long projects, it is harder to calculate and explain than payback or ARR, and it ignores liquidity (a firm short of cash may prefer fast payback). Evaluation: NPV is theoretically the strongest method and best for comparing the value created, but it is not always best in practice: a firm worried about risk or cash may weight payback, and a simple comparison may use ARR. The best decision uses NPV alongside payback and qualitative factors, and depends on the firm's objectives and the reliability of the forecasts. The top band judges and applies.

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Sources & how we know this

Eduqas A Level Business Specification (A510) — Eduqas (2015)