Skip to content
Marlbridge
Free trial

Revision Notes

A Level Accounting: Investment appraisal (Cambridge 9706) – Revision Notes

Condensed revision notes on payback, ARR, NPV, IRR, cash flows and non-financial factors for Cambridge A Level Accounting 9706 section 4.4.

Subject
Accounting
Level
A LEVEL
Topic
Cost and management accounting
Author
Marlbridge Academic Team
Updated
Reviewed by
Zain Ud Din Ahmed (what this means)

Aligned to Cambridge A Level Accounting (9706), 2026-2028. Official specification .

Syllabus page (what it covers and how it is assessed): Cambridge A Level Accounting.

Syllabus points this page covers

9706 (A Level)

  • 4.4 Investment appraisal

Found an error? Report a correction.

Need help with this topic? Request a free trial class for A Level Accounting (9706).

These notes condense 4.4 Investment appraisal (4.4.1), A Level content in Topic 4, for the Cambridge International AS & A Level Accounting 9706 syllabus for 2026, 2027 and 2028. For full explanations and worked examples, read the study guide. Then test yourself with the practice questions, the course hub, the checklist and the free diagnostics. All businesses and figures are invented, in dollars.

The syllabus says questions on discounted payback and on a residual value at the end of a project will not be set.

Core definitions

Term Meaning
Net cash flow Cash in minus cash out caused by the project in a period
Accounting profit Revenue less expenses on the accruals basis, after depreciation
Time value of money Cash received sooner is worth more than the same cash later
Cost of capital The return the project must earn, used as the discount rate
Discount factor 1 / (1 + r)ⁿ
Present value Cash flow × discount factor
NPV Sum of present values, outlay negative
IRR Discount rate that gives an NPV of zero

Formulas and decision rules

Technique Calculation Accept when
Payback Years until cumulative net cash inflow equals the outlay Within the target period
ARR (Average profit / average investment) × 100 At or above the target return
NPV Sum of cash flow × discount factor Positive
IRR Lower rate + [NPV low / (NPV low − NPV high)] × rate gap Above the cost of capital

Average profit = (total net cash inflows − cost) / years. Average investment = (initial investment + value at end) / 2, which is half the cost when there is no residual value. Always follow the definition a question gives.

The same 25,000 average profit is shown as a slice of two bars: initial cost 240,000 gives 10.4% and average investment 135,000 gives 18.5%.
ARR changes with the investment base, so state which one you use.

Method boxes

Profit to net cash flow

  1. Start with the forecast profit for each year.
  2. Add back depreciation (non-cash).
  3. Add back any apportioned cost that continues whether or not the project goes ahead.
  4. Leave out costs already paid and that cannot be recovered.
  5. Show the purchase of the asset as an outflow in year 0.

Payback with uneven flows

  1. Write cumulative cash flow for each year.
  2. Find the year in which it turns from negative to positive.
  3. Payback = full years + (amount still needed / that year’s inflow).
  4. Convert the fraction to months by multiplying by 12.

NPV

  1. List net cash flows, year 0 first.
  2. Multiply each by the factor for the year (year 0 has a factor of 1).
  3. Add them. Interpret the sign.

IRR

  1. Calculate NPV at a rate you choose.
  2. Choose a second rate, higher if NPV was positive, lower if it was negative, until the signs differ.
  3. Interpolate with the formula above and say it is an estimate.
  4. Compare with the cost of capital.

Worked reminder

Quillmore Textiles is considering a loom costing 60,000. Net cash inflows are 30,000, 28,000 and 26,000 over three years. Cost of capital is 12%.

  • Payback: cumulative inflow is 30,000 then 58,000, so 2,000 is still needed in year 3. 2 + 2,000 / 26,000 = 2.08 years, about 2 years 1 month.
  • ARR: total inflows 84,000 − 60,000 = 24,000 profit. Average profit 8,000. Average investment 30,000. ARR = 26.7%.
  • NPV at 12%: (60,000) + 26,787 + 22,322 + 18,507 = 7,616. Accept.
  • IRR: NPV is 4,354 at 15% and (512) at 20%. IRR = 15 + [4,354 / (4,354 + 512)] × 5 = 19.5%, above 12%. Accept.
Tarnhaven net cash inflows of 40, 45, 50, 35 and 30 thousand total 200,000. Less the 120,000 cost, total profit is 80,000, so average profit is 16,000 and average investment 60,000. ARR is 26.7%.
ARR works from total inflows less cost, then divides average profit by average investment.

Worked reminder: profit to cash flow

Kelsterne Signs may buy a cutting table for 48,000, depreciated on the straight line over 4 years with no residual value, which is 12,000 a year. Forecast profits after depreciation are 3,000, 6,000, 8,000 and 5,000.

Year Profit Depreciation added back Net cash inflow Cumulative
0 (48,000) (48,000)
1 3,000 12,000 15,000 (33,000)
2 6,000 12,000 18,000 (15,000)
3 8,000 12,000 20,000 5,000
4 5,000 12,000 17,000 22,000

Payback is 2 years plus 15,000 / 20,000, which is 2.75 years (2 years 9 months). Total profit is 22,000, equal to the 70,000 of cash inflows less the 48,000 outlay. At 10% the present values are 13,636, 14,875, 15,026 and 11,611, so NPV = 55,148 − 48,000 = 7,148.

Oswick Printworks: three stacked bars add profit, 30,000 depreciation and 5,000 apportioned costs to reach cash inflows of 42,000, 48,000 and 51,000. Inflows total 141,000 against an outlay of 90,000, while profits total only 36,000.
Depreciation and apportioned costs are deducted in profit but are not cash flows, so add them back.
Each year of Tarnhaven cash flow is shown beside its present value at 10 percent: 40,000 becomes 36,364, 45,000 becomes 37,188, 50,000 becomes 37,565, 35,000 becomes 23,905 and 30,000 becomes 18,627. These total 153,649, and after the 120,000 outlay the NPV is 33,649.
Later cash is worth less today, and a positive NPV means the project beats the required return.
A waterfall of Tarnhaven present values at 10%: outlay -120,000, then 36,364, 37,188, 37,565, 23,905 and 18,627, reaching an NPV of 33,649.
Each year is cash flow times its discount factor; year 0 stays at 1.0000.
Pairs of bars compare each cash flow with its present value after multiplying by 0.909, 0.826, 0.751 and 0.683. Present values total 155,754; less the 120,000 outlay gives NPV of 35,754.
Discounting turns later cash into smaller present values; NPV is their total less the outlay.

Writing a recommendation

  1. State each result with its unit: years, percentage or dollars.
  2. Compare it with the criterion: the target payback, the target ARR, a zero NPV, or the cost of capital.
  3. Say where the techniques agree or disagree, and which you give most weight to. NPV is usually weighted most because it measures value added in present terms.
  4. Bring in at least one non-financial factor and explain how it could change the decision.
  5. Finish with a clear decision and one reason for it, plus a reservation, such as the reliability of the forecasts.
Machine X and Machine Y are compared on payback (1.75 and 2.4 years), ARR (25.0% and 37.5%), NPV at 10% (13,537 and 18,495) and IRR (20.9% and 19.7%). Payback and IRR favour X; ARR and NPV favour Y, which adds about 4,958 more value but later.
Techniques can disagree, so a recommendation needs a reasoned choice.
A grid of payback, ARR, NPV and IRR against four criteria: counts every year, uses cash, allows for time value, shows dollar value added. Only NPV has all four; payback answers in years, ARR and IRR in percent.
The four techniques differ in what they count and what they tell you.
Running totals for Alder and Birch cross zero at 2 years 6 months and 3 years 10 months. NPV bars at 8% show Alder 11,610 and Birch 17,545. Payback favours Alder, NPV favours Birch, and Birch relies on later years.
Payback and NPV can recommend different projects, so evaluate with both.

Strengths and weaknesses

Technique Strengths Weaknesses
Payback Simple; shows how fast cash returns; limits exposure to distant forecasts Ignores later cash flows and the time value of money; target period is arbitrary
ARR Uses all profits; percentage easy to compare with a target Uses profit not cash; ignores timing; hides project size
NPV Time value of money; all cash flows; shows value added in dollars Needs a cost of capital; harder to explain; relies on forecasts
IRR Time value of money; percentage compared with the cost of capital Interpolation is an estimate; no dollar value; can rank differently from NPV

Non-financial factors

  • Employees: jobs, retraining, morale.
  • Customers: quality, service and reputation.
  • Environment: pollution, energy use, legal compliance.
  • Community and suppliers.
  • Strategic fit and the risk of changing technology.
  • Quality of the forecasts behind the figures.

A good recommendation compares the financial results, then says which non-financial factors could change the decision and why.

Six cards list employees, customers, environment, suppliers and community, strategic fit and forecast risk. A positive NPV project may be rejected for environmental harm and a weak-return project accepted for strategic fit.
Numbers can say yes while non-financial factors say no, so weigh both.

Must-know distinctions

  • Profit versus cash flow: depreciation is an expense but not a cash flow.
  • Payback and ARR ignore the time value of money; NPV and IRR include it.
  • NPV is a dollar amount; IRR and ARR are percentages.
  • ARR uses profit; the other three use cash flows.
  • The cost of capital is an input to NPV, but a comparison point for IRR.
  • Payback measures speed of recovery and liquidity; NPV measures the value created. A project can pass one and fail the other.
  • A higher cost of capital lowers every present value, so NPV falls as the rate rises and IRR is the rate at which it reaches zero.
  • Sunk costs and continuing overheads are not relevant cash flows, however they appear in the profit forecast.

Quick self-test

  1. What is the discount factor for year 3 at 8%, to four decimal places?
  2. A project has a forecast profit of 9,000 after depreciation of 6,000 and an apportioned overhead of 1,500 that would be paid anyway. What is the net cash inflow?
  3. A machine costs 36,000 and brings in 9,000 a year. What is the payback?
  4. A project costs 50,000 and returns 15,000, 20,000, 25,000 and 10,000 in years 1 to 4. What is the payback?
  5. A project costs 40,000 and lasts 4 years with total net cash inflows of 56,000. Calculate the ARR, assuming no residual value.
  6. A project costs 30,000 and returns 12,000 a year for 3 years. Factors at 10% are 0.9091, 0.8264 and 0.7513. Calculate the NPV and give the decision.
  7. NPV is 2,000 at 12% and (1,500) at 16%. Estimate the IRR.
  8. If the cost of capital is 15%, what should be done with the project in question 7?
  9. Name two techniques that ignore the time value of money.
  10. Give one reason why a project with a positive NPV might still be rejected.

Answers

  1. 0.7938.
  2. 9,000 + 6,000 + 1,500 = 16,500.
  3. 36,000 / 9,000 = 4 years.
  4. Cumulative 15,000, 35,000, 60,000. Needs 15,000 of year 3’s 25,000: 2 + 0.6 = 2.6 years (2 years 7 months).
  5. Profit 16,000. Average profit 4,000. Average investment 20,000. ARR = 20%.
  6. 10,909 + 9,917 + 9,016 = 29,842. NPV = 29,842 − 30,000 = (158). Reject.
  7. 12 + [2,000 / 3,500] × 4 = 14.3% (approximately).
  8. IRR of 14.3% is below 15%, so reject on this measure.
  9. Payback and ARR.
  10. For example, an environmental or employee impact, or unreliable forecasts. Any well-explained non-financial or risk reason.
Total inflows of 200,000 less the 120,000 cost give 80,000 profit, or 16,000 a year over 5 years. The investment falls to nil over 5 years so the average is 60,000. ARR is 16,000 divided by 60,000, which is 26.7 percent.
ARR divides average yearly profit by average investment, which is half the cost with no residual value.
NPV falls as the discount rate rises: 33,649 at 10 percent, 2,452 at 20 percent and minus 9,433 at 25 percent. Joining the 20 and 25 percent points with a straight line crosses zero at about 21.0 percent, the IRR, above the 10 percent cost of capital.
The IRR is the rate at which NPV is zero; interpolation estimates it from two rates.
NPV against discount rate for Tarnhaven: 33,649 at 10%, 2,452 at 20% and -9,433 at 25%. The straight line between 20% and 25% crosses zero near 21.0%, the IRR estimate, above the 10% cost of capital.
IRR is the rate where NPV is zero, estimated by a straight line between two rates.
Wexcombe Cider example. Counted: canning line, installation, sale of old fillers (year 0 outlay 216,000) and resale in year 5. Left out and crossed: depreciation, engineer fee, head-office share and loan interest, with a reason for each.
Include only future cash caused by the project; leave out depreciation, sunk costs, unchanged overheads and (OxfordAQA) loan interest.
Bars show the running total of cash for the Kestrel press from -120 to +80 thousand pounds. The total crosses zero between years 2 and 3. 34,000 divided by 52,000 times 12 gives 7.8 months, so payback is 2 years 8 months.
Payback is when the running total of cash turns positive.
Two bars compare Wexcombe inflows added up (314,000) with the same inflows in today's money (210,969) against the 216,000 outlay. The discounted total is 5,031 short, so NPV is negative and the project is rejected.
A project can recover its cost undiscounted yet still have a negative NPV.
NPV falls as the discount rate rises. A straight line joins +34,060 at 10% and -4,555 at 16% and crosses zero at about 15.3%, above the 10% WACC, so the project is accepted.
IRR is the rate at which NPV is zero, estimated by interpolation and compared with WACC.

Where marks are usually lost

  • Discounting the year 0 outlay.
  • Using profit instead of cash flow in payback, NPV or IRR.
  • Not adding depreciation back when converting profit to cash.
  • Stopping at the number in payback, ARR, NPV or IRR without a decision.
  • Interpolating from two NPVs of the same sign.
  • Calling an IRR exact when it is an estimate from interpolation.
  • Giving a one-sided recommendation with no reference to non-financial factors.
  • Listing strengths and weaknesses of a technique without applying them to the figures.

Frequently asked questions

What is the decision rule for IRR? Accept the project if the IRR is higher than the cost of capital, the business’s required rate of return.

What is the decision rule for NPV? A positive NPV means the project earns more than the required return, so it should be accepted on financial grounds.

Is the year 0 outlay discounted? No. The year 0 outlay has a discount factor of 1, so it is not discounted. Discounting it is a common mistake.

Why is an interpolated IRR only an estimate? Interpolation assumes NPV falls in a straight line between the two discount rates, which it does not exactly, so the IRR should not be described as exact.

Official syllabus

Cambridge International, AS & A Level Accounting 9706 syllabus for 2026, 2027 and 2028, section 4.4 Investment appraisal.

Get free revision emails (optional)

Occasional emails with practice questions, worked explanations and links to free resources for the qualification and subjects you choose. No spam, and you can unsubscribe from any email. The free tools on this site never need an email.

Subjects (optional, up to 6)

Choose a qualification to see its subjects.

Related resources

Related articles

Studying this with a teacher

Working through Accounting A LEVEL?

This page is free and stays free. If you would rather be taught it, Marlbridge runs Accounting classes one-to-one and in small groups of up to 15, online in your own time zone. The first trial class is free. WhatsApp replies within an hour (8am–11pm Pakistan time, every day); email the same day.

Cambridge Accounting teachers at Marlbridge

Request a free trial Meet the teachers