Notes · AccountingUK · A-Levels

Capital investment appraisal

Capital investment appraisal evaluates whether a long-term investment - buying a machine, opening a branch - is worthwhile. This chapter covers the three methods on the specification: the payback period, the accounting rate of return, and net present value, which allows for the time value of money through discounting. It works each method on the same project and evaluates their strengths, weaknesses and the non-financial factors that inform the final decision.

4 sections~18 min reading time3 competenciesLevel Standard 2 · Advanced 2

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Exam profile

AO1 · Understand the appraisal methods and the time value of moneyAO2 · Calculate payback, the accounting rate of return and net present value, and rank projectsAO3 · Analyse and evaluate the methods and recommend whether to proceed, including non-financial factors

Operators:calculateexplainappraiseanalyseevaluaterecommendassess

basic level

AS-Level expects the payback period and the accounting rate of return.

higher level

The full A-Level adds net present value and the discounting of cash flows, and the evaluated recommendation of an investment decision.

Depth

Text

Contents · 4 sections

Capital investment appraisal

The payback period#

StandardAQA 7127 3.13

Cumulative cash flow and payback

Fig. 1The cumulative cash flow crosses zero during year 3 - the payback point. The firm needs £20,000 of year 3's £30,000, so payback is 2 years 8 months.

The payback period is the time a project takes to recover its initial investment from its net cash inflows - how long before the business gets its money back. It is found by accumulating the project's cash inflows year by year until the cumulative total equals the initial outlay. Where the cash flows are even, payback is simply the initial investment divided by the annual cash inflow; where they are uneven (the usual case), the cumulative cash flow is tracked and the point at which it turns from negative to positive is the payback point, with the part-year found by interpolation. Payback is measured in cash flows, not accounting profits, so depreciation (a non-cash item) is ignored.

A worked calculation shows the method. A project costs £100,000 and generates net cash inflows of £40,000, £40,000, £30,000 and £30,000 over four years. The cumulative cash flow is -£100,000 at the start, -£60,000 after year 1, -£20,000 after year 2, and +£10,000 after year 3 - so the investment is repaid during year 3. At the start of year 3 the firm still needs £20,000, and year 3 brings in £30,000, so the fraction of the year needed is £20,000 / £30,000 = 0.67, or about 8 months. The payback period is therefore 2 years and 8 months. Presenting the cumulative cash flow, and showing the interpolation, is what earns full marks.

Payback's appeal is its simplicity and its focus on risk and liquidity. It is easy to calculate and to understand, it favours projects that return cash quickly (which reduces the risk of being wrong about the distant future and eases cash flow), and it is useful when technology or markets change fast so that later cash flows are highly uncertain. A firm short of cash, or operating in a fast-moving industry, may sensibly prefer the project with the shortest payback because getting the money back quickly matters more than the total return. Many businesses set a maximum acceptable payback period and reject projects that exceed it.

But payback has serious weaknesses that a full answer must weigh. It ignores all cash flows after the payback point, so it takes no account of a project's total profitability - a project that pays back quickly but earns little thereafter would be preferred to one that pays back more slowly but earns far more over its life. It ignores the time value of money (a pound received in year 1 is treated the same as a pound in year 3). And the cut-off period is somewhat arbitrary. So payback is a useful measure of risk and liquidity and a good first screen, but it should not be the sole basis for a decision - which is exactly why it is used alongside the accounting rate of return and net present value.

\text{Payback (even flows)} = \frac{\text{Initial investment}}{\text{Annual net cash inflow}}

Payback with even cash flows

With uneven flows, accumulate the cash inflows and interpolate the part-year: (amount still needed / that year's inflow).

Worked example

Calculating the payback period

A machine costs £100,000 and is expected to generate net cash inflows of £40,000 (year 1), £40,000 (year 2), £30,000 (year 3) and £30,000 (year 4). Calculate the payback period.

Accumulate the cash flows
Cumulative: end of year 1 = -£60,000; end of year 2 = -£20,000; end of year 3 = +£10,000. So the £100,000 is recovered during year 3.
Interpolate the part-year
At the start of year 3, £20,000 is still needed; year 3 brings £30,000, so the fraction of the year = £20,000 / £30,000 = 0.67, which is about 8 months.
State the payback
Payback period = 2 years + 0.67 of year 3 = 2 years and about 8 months.

Result: The project pays back in 2 years and 8 months, when the cumulative cash inflows first equal the £100,000 outlay.

Typical mistakes

Using accounting profit (after depreciation) instead of cash flow for payback.
Stating payback as a whole number of years without interpolating the part-year.

Active revision

A project costs £100,000 and returns cash of £40,000, £40,000, £30,000 and £30,000 over four years. Calculate its payback period.

Active recall

Recall the key points — then reveal.

Sources: AQA A-level Accounting 7127 specification (AQA)

The accounting rate of return#

StandardAQA 7127 3.13

The accounting rate of return (ARR) measures a project's average annual accounting profit as a percentage of the investment, so unlike payback it is based on profit and considers the whole life of the project. It is calculated as the average annual profit divided by the investment, expressed as a percentage. The average annual profit is the total accounting profit over the project's life divided by the number of years, where accounting profit is the net cash inflow less depreciation (because ARR uses profit, not cash flow, the depreciation of the asset must be deducted). The result is a percentage return that can be compared with a target rate or with the returns on other projects.

A worked calculation continues the same project. The machine costing £100,000 generates cash inflows totalling £140,000 over four years (£40,000 + £40,000 + £30,000 + £30,000). Assuming the £100,000 is fully depreciated over the four years (no residual value), total depreciation is £100,000, so the total accounting profit is £140,000 - £100,000 = £40,000, and the average annual profit is £40,000 / 4 = £10,000. Using the initial investment as the base, ARR = £10,000 / £100,000 x 100 = 10%. (Some definitions divide by the average investment, here £50,000, giving 20%; whichever base is used, it must be stated and used consistently.)

ARR's strengths are that it uses profit (the measure owners and managers focus on and that appears in the accounts), it considers all the years of the project rather than stopping at payback, and it gives a percentage that is easy to compare with a required rate of return or with other investments and with the return on capital employed. Because it is expressed in the same terms as ROCE, it fits naturally with the way a business judges its overall performance, and a project whose ARR exceeds the firm's target return or its cost of capital looks attractive on this measure.

ARR's weaknesses are significant and mirror those of accounting profit generally. Like payback, it ignores the time value of money - it averages profits across the years without regard to when they arise, so a pound of profit in year 4 counts the same as a pound in year 1. It is based on accounting profit, which depends on depreciation policy and other accounting choices, so two firms could compute different ARRs for the same project. And averaging can hide the pattern of returns - two projects with very different profiles can have the same ARR. So ARR is a useful profitability measure that complements payback's liquidity focus, but it too is incomplete, which is the case for using net present value alongside them.

ARR = \frac{\text{Average annual profit}}{\text{Initial investment}} \times 100\%

Accounting rate of return

Average annual profit = (total cash inflows - total depreciation) / years. Here 10,000 / 100,000 = 10% (or 20% on average investment).

Worked example

Calculating the accounting rate of return

A machine costs £100,000, has a four-year life and no residual value, and produces net cash inflows of £40,000, £40,000, £30,000 and £30,000. Calculate the accounting rate of return on the initial investment.

Total profit
Total cash inflows = £140,000. Total depreciation = £100,000 (cost fully written off, no residual). Total accounting profit = £140,000 - £100,000 = £40,000.
Average annual profit
Average annual profit = total profit / life = £40,000 / 4 = £10,000.
ARR
ARR = average annual profit / initial investment x 100 = £10,000 / £100,000 x 100 = 10% (or 20% if the £50,000 average investment is used as the base).

Result: The accounting rate of return is 10% on the initial investment (£10,000 average annual profit on £100,000) - to be compared with the firm's target return before deciding.

Typical mistakes

Using cash flow instead of accounting profit (forgetting to deduct depreciation) in ARR.
Switching between the initial-investment and average-investment bases within a question.

Active revision

A project costs £100,000 (no residual value), lasts four years and produces cash inflows totalling £140,000. Calculate its accounting rate of return on the initial investment.

Active recall

Recall the key points — then reveal.

Sources: AQA A-level Accounting 7127 specification (AQA)

Net present value and discounting#

AdvancedAQA 7127 3.13

Net present value schedule

Fig. 2Discounting each cash flow at 10% and summing gives a positive NPV of £12,420, so the project earns more than its cost of capital and should be accepted.

Net present value (NPV) is the most sophisticated of the three methods because it allows for the time value of money - the principle that a pound received today is worth more than a pound received in the future, because today's pound can be invested to earn a return (and because of risk and inflation). To compare cash flows arising at different times fairly, each future cash flow is discounted back to its present value using a discount rate that reflects the firm's cost of capital. The present value of a future cash flow is that cash flow multiplied by the discount factor for its year, and the discount factor for year n at rate r is 1 divided by (1 + r) to the power n, which is read from a discount-factor table.

The net present value of a project is the sum of the present values of all its cash flows, including the initial outlay (a present-value cash flow at year 0). If the NPV is positive, the project earns more than the cost of capital and adds value, so it should be accepted; if negative, it earns less than the cost of capital and should be rejected; and between competing projects, the one with the higher NPV is preferred. NPV thus gives a clear, money-valued decision rule that takes account of the whole life of the project and the timing of every cash flow - the two things payback and ARR each miss.

A worked NPV uses the same project and a 10% cost of capital. The discount factors at 10% are 0.909 (year 1), 0.826 (year 2), 0.751 (year 3) and 0.683 (year 4). The present values are: year 1, £40,000 x 0.909 = £36,360; year 2, £40,000 x 0.826 = £33,040; year 3, £30,000 x 0.751 = £22,530; year 4, £30,000 x 0.683 = £20,490. The total present value of the inflows is £112,420. Deducting the £100,000 initial outlay gives a net present value of £12,420. Because the NPV is positive, the project earns more than the 10% cost of capital and should be accepted - it adds £12,420 of value in today's money.

The discount rate is central to NPV and to its interpretation. A higher discount rate (a higher cost of capital, or a riskier project) reduces the present value of distant cash flows more heavily, lowering the NPV - so a project that is worthwhile at 10% might not be at 15%. This is why the choice of discount rate matters and why it embodies both the cost of finance and the risk of the project. NPV's assumptions - that the cost of capital is known and constant, and that the future cash flows are reliably estimated - are also its vulnerabilities: the technique is only as good as the cash-flow forecasts and the discount rate fed into it. But conceptually it is the soundest method, because it alone values a project correctly for the timing and the opportunity cost of money.

\text{Discount factor}_n = \frac{1}{(1 + r)^n}

Discount factor

The present value of £1 received in year n at rate r. At 10%: year 1 = 0.909, year 2 = 0.826, year 3 = 0.751, year 4 = 0.683.

NPV = \sum \left( \text{Cash flow}_n \times \text{Discount factor}_n \right) - \text{Initial investment}

Net present value

Positive NPV: accept (adds value); negative: reject. Here 112,420 - 100,000 = +12,420.

Worked example

Calculating net present value

A machine costs £100,000 and generates net cash inflows of £40,000, £40,000, £30,000 and £30,000 over four years. The cost of capital is 10% (discount factors 0.909, 0.826, 0.751, 0.683). Calculate the NPV and advise whether to invest.

Discount each inflow
Year 1: £40,000 x 0.909 = £36,360. Year 2: £40,000 x 0.826 = £33,040. Year 3: £30,000 x 0.751 = £22,530. Year 4: £30,000 x 0.683 = £20,490.
Sum the present values
Total present value of inflows = £36,360 + £33,040 + £22,530 + £20,490 = £112,420.
Net off the outlay and advise
NPV = £112,420 - £100,000 = +£12,420. Because the NPV is positive, the project earns more than the 10% cost of capital and should be accepted.

Result: The NPV is +£12,420: the project's discounted inflows of £112,420 exceed the £100,000 outlay, so it adds value at a 10% cost of capital and should be accepted.

Typical mistakes

Forgetting to include the year 0 outlay, or discounting it (its discount factor is 1.000).
Reading the discount factors from the wrong year or rate, or adding the cash flows without discounting.

Active revision

A project costs £100,000 and returns £40,000, £40,000, £30,000 and £30,000 over four years. Using 10% discount factors (0.909, 0.826, 0.751, 0.683), calculate the NPV and advise.

Active recall

Recall the key points — then reveal.

Sources: AQA A-level Accounting 7127 specification (AQA)

Evaluating the methods and the decision#

AdvancedAQA 7127 3.13

Comparing the appraisal methods

Fig. 3The three methods answer different questions - payback (liquidity/risk), ARR (profitability), NPV (value after the time value of money) - and are strongest used together.

Each method answers a different question, so they are best used together rather than in isolation. Payback asks how quickly the money comes back (a measure of risk and liquidity); ARR asks what average percentage return the project earns on the investment (a profitability measure comparable with ROCE); and NPV asks whether, allowing for the time value of money, the project adds value at the cost of capital (the theoretically soundest measure). For the illustrative project, all three point the same way - payback 2 years 8 months, ARR 10%, NPV +£12,420 - which strengthens the case; but where they conflict, the firm must weigh what matters most to it.

NPV is generally regarded as the best single method because it alone accounts for both the whole life of the project and the timing of every cash flow, and it gives a clear money-valued decision rule. But it is not infallible: it depends entirely on the accuracy of the cash-flow forecasts and on the choice of discount rate, both of which involve estimation and judgement, and small changes in either can flip the decision. Payback and ARR, though cruder, are simpler to compute and communicate, and payback's focus on early cash recovery is genuinely valuable for a cash-constrained firm or a fast-changing market. So the methods complement one another, and a rounded appraisal reports all three.

Numbers, however, never settle an investment decision on their own, and the non-financial (qualitative) factors are often decisive. These include the effect on the workforce and on morale; the impact on customers, quality and the firm's reputation; the fit with the firm's long-term objectives and strategy; the environmental and social consequences; the reliability of any new technology or supplier; and the availability of finance and the risk the project brings. A project with a positive NPV might still be rejected because it damages the firm's reputation or stretches its finances too far, and a marginal project might be accepted because it is strategically essential. Recognising that the calculation informs but does not replace judgement is the hallmark of a strong evaluation.

A sound recommendation therefore does three things: it calculates and reports the financial measures accurately; it weighs the methods against one another, acknowledging their assumptions and limitations; and it considers the non-financial factors and the reliability of the forecasts before reaching a reasoned conclusion. For the illustrative project, the recommendation would be to accept - the positive NPV shows it adds value, the ARR beats a modest target, and the payback is reasonable - subject to confidence in the cash-flow estimates and the discount rate, and to the non-financial factors being favourable. This blend of calculation, comparison and judgement is exactly what the analysis-and-communication chapter develops, and what the top assessment band rewards.

Worked example

Making a reasoned recommendation

A project has a payback of 2 years 8 months, an ARR of 10% and an NPV of +£12,420 at a 10% cost of capital. Recommend whether to proceed and identify factors that could alter the decision.

Weigh the financial measures
All three measures are favourable: the NPV is positive (adds value at the cost of capital), the ARR of 10% would beat a modest target, and the payback of under three years is reasonable - a consistent financial case to accept.
Test the assumptions
The NPV depends on the cash-flow forecasts and the 10% discount rate; a sensitivity check (what if inflows were 10% lower, or the rate 15%?) would show how robust the positive NPV is before committing.
Consider non-financial factors and conclude
Weigh the effect on staff, customers, reputation, the environment and strategic fit, and the availability of finance. Subject to reasonable confidence in the forecasts and favourable qualitative factors, recommend acceptance - a positive-NPV project that also satisfies payback and ARR.

Result: Recommend proceeding: the positive NPV (backed by an acceptable ARR and payback) shows the project adds value, provided the cash-flow forecasts and discount rate are reliable and the non-financial factors - staff, customers, reputation, finance and strategy - are favourable.

Typical mistakes

Recommending purely on one method without weighing the others or the qualitative factors.
Treating the NPV as certain, ignoring that it depends on estimated cash flows and the chosen discount rate.

Active revision

For a project with a payback of 2 years 8 months, an ARR of 10% and an NPV of +£12,420 at 10%, make and justify a recommendation, and state two non-financial factors that could change it.

Active recall

Recall the key points — then reveal.

Sources: AQA A-level Accounting 7127 specification (AQA) · Ofqual - GCE AS and A level qualifications (Ofqual)

References & sources

Sources

AQA

AQA A-level Accounting 7127 specification

Ofqual

Ofqual - GCE AS and A level qualifications

Capital investment appraisal

4 sections~18 min reading time3 competenciesLevel Standard 2 · Advanced 2

Capital investment appraisal

Key points

Calculating the payback period

Key points

Calculating the accounting rate of return

Key points

Calculating net present value

Key points

Making a reasoned recommendation

Sources

Capital investment appraisal

Key points

Calculating the payback period

Key points

Calculating the accounting rate of return

Key points

Calculating net present value

Key points

Making a reasoned recommendation

Sources