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

The methods of capital investment appraisal (payback period, accounting rate of return and net present value), how to calculate and interpret each, the time value of money, and the quantitative and qualitative factors in an investment decision.

A focused answer to AQA A-Level Accounting 3.2, covering the methods of capital investment appraisal (payback period, accounting rate of return and net present value), how to calculate and interpret each, the time value of money, and the factors in an investment decision.

Generated by Claude Opus 4.812 min answerUpdated 2026-06-02

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What this dot point is asking
Payback period
Accounting rate of return
Net present value and the time value of money
Qualitative factors
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What this dot point is asking

AQA wants you to calculate and interpret the three appraisal methods (payback, accounting rate of return and net present value), explain the time value of money, and weigh the quantitative and qualitative factors in a decision. This is unit 3.2.5, and a full NPV calculation using given discount factors, with an accept or reject decision, is a high-tariff Paper 2 task.

Payback period

Payback is calculated by accumulating the net cash inflows until they equal the initial outlay. With even annual inflows, $\text{payback} = \dfrac{\text{initial cost}}{\text{annual inflow}}$ ; with uneven inflows, accumulate year by year and pro-rate the final part-year. Payback is popular because it is simple and focuses on liquidity and risk, but it is a crude measure of profitability.

Accounting rate of return

Note that ARR uses profit, not cash, so depreciation is deducted, in contrast to the cash-based payback and NPV. Average annual profit is the total profit over the project's life divided by the number of years.

Net present value and the time value of money

The time value of money is the principle that money received later is worth less than money now, because money now could be invested to earn a return (and because of risk and inflation). Net present value (NPV) applies this by discounting each future cash flow to its present value using a discount factor, then subtracting the initial cost. A positive NPV means the project earns more than the discount rate and adds value, so it should be accepted; a negative NPV means it destroys value.

Working all three methods

A machine costs £100,000 and generates net cash inflows of £30,000 a year for five years. The required rate of return (discount rate) is 10%.

Step 1: Calculate the payback period

Payback accumulates the annual inflows until the initial cost is recovered. With even inflows of £30,000 a year, after three full years the cumulative inflow is £90,000. The remaining £10,000 is recovered partway through year four.

\text{payback} = 3 + \frac{10{,}000}{30{,}000} \approx 3.3 \text{ years}

Step 2: Calculate the accounting rate of return (ARR)

ARR uses profit rather than cash, so we first deduct the cost of the investment. Total cash inflow is £150,000, giving total profit of £50,000 over five years. Dividing by five gives average annual profit, which is then expressed as a percentage of the initial outlay.

\text{average annual profit} = \frac{150{,}000 - 100{,}000}{5} = \frac{50{,}000}{5} = £10{,}000

\text{ARR} = \frac{10{,}000}{100{,}000} \times 100 = 10\%

Step 3: Calculate the net present value (NPV)

Because money received in the future is worth less than money now, each year's £30,000 inflow is discounted back to its present value using the given 10% discount factors. Multiplying each inflow by its factor, then summing, gives the total present value of all inflows.

Year	Inflow (£)	Discount factor	Present value (£)
1	30,000	0.909	27,270
2	30,000	0.826	24,780
3	30,000	0.751	22,530
4	30,000	0.683	20,490
5	30,000	0.621	18,630

\text{total present value} = 27{,}270 + 24{,}780 + 22{,}530 + 20{,}490 + 18{,}630 = £113{,}700

Step 4: Make the accept or reject decision

Subtracting the initial cost from the total present value of inflows gives the NPV. A positive NPV means the project earns more than the 10% required return and adds value in today's money, so it should be accepted.

\text{NPV} = 113{,}700 - 100{,}000 = +£13{,}700

Final answer: Payback 3.3 years; ARR 10%; NPV +£13,700. Accept the project because the NPV is positive.

Qualitative factors

A decision also depends on factors beyond the numbers: the risk and reliability of the forecasts (longer projects are more uncertain), the firm's objectives (growth, market share, sustainability), the availability of finance, the effect on staff and reputation, and how the project fits the firm's strategy. The appraisal methods inform the decision; they do not make it.

Try this

Q1. A project costs $60{,}000$ and returns $15{,}000$ a year. Calculate the payback period. [2 marks] $\dfrac{60{,}000}{15{,}000} = 4$ years.

Q2. Explain why NPV is often preferred to ARR. [3 marks] NPV accounts for the time value of money and uses all the cash flows, whereas ARR ignores timing and uses accounting profit.

Exam-style practice questions

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

AQA 20198 marksA project costs

100,000 and generates net cash inflows of

30,000 a year for five years. Using a discount rate of 10% (discount factors: year 1 0.909, year 2 0.826, year 3 0.751, year 4 0.683, year 5 0.621), calculate the payback period and the net present value, and state whether the project should be accepted.

Show worked answer →

A full worked NPV; the discounting is the main marking point.

Payback: $30,000 a year recovers$ 90,000 after three years; the remaining $10,000 takes$ 10,000 / $30,000 = one-third of year four, so payback is about 3.3 years (2 marks).

Present values: year 1 30,000 times 0.909 = $27,270; year 2 times 0.826 =$ 24,780; year 3 times 0.751 = $22,530; year 4 times 0.683 =$ 20,490; year 5 times 0.621 = $18,630. Total present value of inflows =$ 113,700 (4 marks).

NPV: $113,700 minus the$ 100,000 cost = +$13,700 (1 mark). Accept the project, because a positive NPV means it earns more than the 10% required return and adds value (1 mark). Markers reward each discounted inflow, the sum, subtracting the cost, and the accept decision.

AQA 20215 marksEvaluate the use of net present value compared with the payback period for appraising a long-term investment.

Show worked answer →

A 5-mark "Evaluate" answer compares strengths and weaknesses and concludes.

NPV strengths: it accounts for the time value of money, uses all the cash flows over the project's life, and gives an absolute money measure of value added (2 marks). Weaknesses: it needs an accurate discount rate and reliable long-term forecasts, and it is harder to calculate and explain.

Payback strengths: simple, focuses on liquidity and risk by favouring quick recovery (1 mark). Weaknesses: ignores cash flows after payback and the time value of money.

Judgement: NPV is theoretically superior for a value-maximising decision, but payback is a useful supplementary measure where cash flow or risk is a concern; many firms use both (2 marks). Markers reward a balanced comparison ending in a supported conclusion.

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Sources & how we know this

AQA A-level Accounting (7127) specification — AQA (2017)