the meaning, calculation and interpretation of accounting rate of return (ARR)

10.3 Investment Appraisal – Pay‑back, ARR and NPV

Learning Objective

Understand the purpose, calculation and interpretation of the three quantitative techniques used in investment appraisal – Pay‑back period, Accounting Rate of Return (ARR) and Net Present Value (NPV) – and be able to combine them with qualitative (non‑financial) factors when making capital‑investment decisions.

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10.3.0 Syllabus Context

In the Cambridge International AS‑Level Business (9609) specification the investment‑appraisal content is coded 10.3.1 – 10.3.4. It sits within the wider Business Studies programme, which also covers:

• Finance & accounting strategy (10.4)
• Operations strategy – lean, ERP, CPA (9.3)
• Quality management, location & scale, international marketing, HRM, business strategy and the core finance topics (5‑9).

All of these units feed into the same decision‑making process, so students should be able to see how the quantitative results from this chapter are used alongside strategic, operational and qualitative considerations.

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10.3.1 What is Investment Appraisal?

• Systematic analysis of the expected costs and benefits of a capital project before a commitment is made.
• Helps managers allocate scarce resources, compare alternative projects and ensure that investments support the organisation’s strategic objectives.
• Quantitative techniques covered in the syllabus:
  1. Pay‑back period
  2. Accounting Rate of Return (ARR)
  3. Net Present Value (NPV)
• Qualitative (non‑financial) factors must also be considered before a final decision is taken.

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10.3.2 Pay‑back Period

Definition

The pay‑back period is the length of time (in years or months) required for the cumulative cash inflows from an investment to equal the initial cash outlay.

Formula

\[ \text{Pay‑back Period}= \text{Full years before recovery} + \frac{\text{Unrecovered amount at start of final year}}{\text{Cash inflow in the final year}} \]

Steps to Calculate

1. List the expected cash inflows for each year of the project’s life.
2. Subtract each year’s inflow from the initial outlay to obtain the cumulative cash balance.
3. Identify the year in which the cumulative balance first becomes zero or positive.
4. Apply the formula above to obtain a more precise figure (including fractions of a year).

Worked Example

A company is considering a new printing press costing £80 000. Expected cash inflows are shown below.

Year	Cash Inflow (£)	Cumulative Balance (£)
0 (initial outlay)	-80,000	-80,000
1	30,000	-50,000
2	30,000	-20,000
3	25,000	+5,000

Pay‑back = 2 years + ( £20,000 unrecovered ÷ £25,000 in year 3 ) = 2 + 0.8 = 2.8 years

Interpretation

• If the pay‑back period is shorter than the company’s maximum acceptable period (the “hurdle”), the project is considered acceptable.
• Useful for assessing liquidity risk and for projects where rapid cash recovery is a priority.

Advantages & Limitations

Advantages	Limitations
Very simple to calculate and understand. Highlights cash‑flow recovery – important for firms with tight cash constraints.	Ignores cash flows after the pay‑back point. No consideration of the time value of money. Based on cash flows only – does not reflect profitability.

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10.3.3 Accounting Rate of Return (ARR)

Definition (syllabus wording)

ARR measures the profitability of an investment by comparing the average accounting profit generated each year with the initial capital outlay (or with the average investment). It is expressed as a percentage and uses accounting (book) figures rather than cash flows.

Formulas (both accepted by the syllabus)

1. ARR based on initial investment \[ \text{ARR}= \frac{\text{Average Annual Accounting Profit}}{\text{Initial Investment}} \times 100\% \]
2. ARR based on average investment \[ \text{ARR}= \frac{\text{Average Annual Accounting Profit}}{\text{Average Investment}} \times 100\% \] where \[ \text{Average Investment}= \frac{\text{Initial Investment} + \text{Residual (Salvage) Value}}{2} \]

Key Concepts

• Average annual accounting profit = (Total accounting profit over the project’s life) ÷ (Number of years).
• Depreciation must be accounted for; the example below uses straight‑line depreciation.
• ARR does not discount future profits – each year’s profit is weighted equally.

Steps to Calculate ARR

1. Determine the depreciation method and calculate annual depreciation.
2. Prepare a profit‑and‑loss forecast for each year (including depreciation).
3. Sum the accounting profits for all years and divide by the project life to obtain the average profit.
4. Choose either the initial‑investment or average‑investment denominator and apply the relevant formula.

Worked Example – Using Initial Investment

Project data:

• Machine cost: £120 000
• Useful life: 5 years
• Residual value: £20 000
• Straight‑line depreciation = (£120 000 – £20 000) ÷ 5 = £20 000 per year

Year	Accounting Profit (£) (after depreciation)
1	30,000
2	28,000
3	26,000
4	24,000
5	22,000

1. Total accounting profit = £130,000
2. Average annual profit = £130,000 ÷ 5 = £26,000
3. Initial investment = £120,000
4. ARR = (£26,000 ÷ £120,000) × 100% = 21.7 % (rounded to one decimal)

Worked Example – Using Average Investment

Average investment = (£120,000 + £20,000) ÷ 2 = £70,000.

ARR = (£26,000 ÷ £70,000) × 100% = 37.1 %.

Interpretation

• Compare the calculated ARR with the firm’s required rate of return (the “hurdle rate”).
• If ARR ≥ hurdle rate, the project is acceptable; otherwise it is rejected.
• A higher ARR indicates a more profitable use of capital, all else being equal.

Advantages & Limitations

Advantages	Limitations
Uses information already available in the income statement – no extra data collection required. Easy to communicate to non‑financial managers.	Ignores the timing of profits; early and late profits are weighted equally. Depends on accounting policies (e.g., depreciation method), which can be manipulated. No discounting – the time value of money is omitted. Residual value is only reflected indirectly (in the average‑investment formula).

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10.3.4 Net Present Value (NPV)

Definition

NPV is the difference between the present value of all cash inflows and the present value of all cash outflows associated with a project. Future cash flows are discounted at the firm’s required rate of return (the discount rate).

Key Formula

\[ \text{NPV}= \sum_{t=0}^{n} \frac{C_{t}}{(1+r)^{t}} \]

• C₀ = initial cash outlay (negative).
• Cₜ = net cash flow in year t (positive or negative).
• r = discount rate (company’s required rate of return).
• n = project life (years).

Steps to Calculate NPV

1. Identify the required discount rate (the “hurdle rate”).
2. Prepare a cash‑flow forecast for each year, including any residual (salvage) value.
3. Calculate the present‑value factor for each year: \(\frac{1}{(1+r)^{t}}\).
4. Multiply each year’s cash flow by its factor to obtain the present value.
5. Sum all present values – the result is the NPV.

Worked Example

Project details:

• Initial outlay: £80 000
• Annual cash inflows: £30 000 (years 1‑3)
• Residual (salvage) value at end of year 3: £10 000
• Discount rate: 10 %

Year (t)	Cash Flow (£)	PV Factor 1/(1+0.10)ᵗ	Present Value (£)
0	-80,000	1.000	-80,000
1	30,000	0.909	27,270
2	30,000	0.826	24,780
3	30,000 + 10,000 = 40,000	0.751	30,040
NPV			+2,090

Because NPV = +£2,090, the project adds value and would be accepted (assuming the discount rate reflects the firm’s required return).

Interpretation

• NPV > 0 → accept the project.
• NPV = 0 → the project earns exactly the required return – decision can be based on other criteria.
• NPV < 0 → reject the project.

Advantages & Limitations

Advantages	Limitations
Considers the time value of money. Uses cash flows – the figure that matters for liquidity. Provides a direct estimate of the increase in wealth.	Requires an estimate of the appropriate discount rate, which can be subjective. More complex to calculate than pay‑back or ARR. Relies on accurate cash‑flow forecasts; errors can significantly affect the result.

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10.3.5 Qualitative (Non‑Financial) Factors – A Decision Framework

Even when a project scores well on the quantitative techniques, managers must weigh a range of qualitative considerations. The table below links each factor to a simple decision rule (Accept / Reject / Investigate further).

Qualitative Factor	Typical Impact on Decision
Strategic fit (e.g., aligns with long‑term growth or diversification plans)	Accept if strong alignment; otherwise investigate.
Risk & uncertainty (technological change, market volatility, regulatory risk)	High risk may lead to rejection or demand for a higher hurdle rate.
Environmental & social impact (sustainability, community relations)	Negative impact may outweigh a positive NPV; may require mitigation.
Resource constraints (availability of skilled staff, production capacity)	Insufficient resources → reject or defer.
Legal & ethical considerations (compliance, ethical standards)	Legal barriers → reject; ethical concerns may require mitigation.
Stakeholder reaction (employees, shareholders, suppliers, customers)	Strong opposition → reject or modify the proposal.

When presenting a recommendation, students should summarise the quantitative results (pay‑back, ARR, NPV) and then complete a concise “pros‑cons” table that reflects the above qualitative factors.

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10.3.6 Comparison of the Three Quantitative Techniques

Technique	Focus	Primary Use	Time‑value of Money?	Cash vs. Accounting	Key Strength	Key Weakness
Pay‑back Period	Liquidity – speed of cash recovery	Screening projects with tight cash constraints	No	Cash flows only	Very simple, intuitive	Ignores post‑pay‑back cash flows and discounting
ARR	Profitability (accounting profit)	Assessing return relative to capital cost	No	Accounting profit (after depreciation)	Uses information already in accounts	Depreciation choices affect result; no discounting
NPV	Value creation (wealth increase)	Final investment decision, ranking alternatives	Yes	Cash flows	Considers timing and risk via discount rate	Requires reliable cash‑flow forecasts and a suitable discount rate

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10.3.7 Syllabus Checklist – What Else Must Be Studied?

Syllabus Block	Code	Status in This Set of Notes
Investment appraisal (Pay‑back, ARR, NPV)	10.3.1‑10.3.4	Fully covered
Finance & accounting strategy (budgeting, dividend policy, growth planning)	10.4.1‑10.4.2	Brief overview – see Section 10.3.0
Operations strategy (lean production, ERP, continuous process improvement)	9.3	Referenced – not detailed
Quality management (total quality, ISO standards)	9.2	Not covered – to be studied elsewhere
Location & scale decisions	9.1	Not covered – to be studied elsewhere
International marketing (exporting, joint ventures)	8.2	Not covered – to be studied elsewhere
Human resource management (recruitment, motivation, training) – A‑level extension	7.1‑7.4	Not covered – to be studied elsewhere
Business strategy (vision, mission, objectives, SWOT)	6.1‑6.2	Not covered – to be studied elsewhere
Core finance (ratio analysis, sources of finance)	5.1‑5.5	Not covered – to be studied elsewhere

Students should ensure they have completed the above blocks before attempting the final Cambridge 9609 examination questions on investment appraisal.

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Summary

• Pay‑back, ARR and NPV each provide a different perspective on a capital project – liquidity, accounting profitability and wealth creation respectively.
• All three techniques must be interpreted against a pre‑set hurdle rate or acceptable period.
• Qualitative factors can overturn a favourable quantitative result; a balanced recommendation always includes both.
• Understanding how these techniques fit into the wider business‑strategy, operations and finance context is essential for the Cambridge AS‑Level Business exam.