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3.10a · Cost-benefit Analysis · Sub-skill

The cost–benefit principle

Decide whether a project is worthwhile by comparing total costs and benefits — and learn why sunk costs must be ignored.

See it first

Watch it happen

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Build it up, step by step

The cost–benefit principle — the key ideas

Click each step below to reveal it — work through them in order the first time round.

Step 1 · The principle

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The cost–benefit principle says: do something if its benefits are greater than its costs. To compare them, put both in the same units — usually money — and add up over the whole time period. Net benefit = total benefits − total costs.

Step 2 · Comparing options

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For several options, choose the one with the highest net benefit. The benefit–cost ratio (benefits ÷ costs) shows value for money: above 1 means benefits exceed costs. The payback period is how long it takes the savings to repay the original cost.

Step 3 · Sunk costs

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A sunk cost is money already spent that cannot be got back. It should not affect the decision, because it is the same whichever option you choose. Compare only future costs and benefits.

Step 4 · Beyond the numbers

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Some costs and benefits are hard to put a price on (safety, enjoyment, the environment). A good answer mentions them, notes who gains and who pays, and says how uncertain the figures are.

Worked example

A council could build a crossing for £120,000 that saves £30,000 a year for 5 years. Is it worthwhile?

Benefits = 5 × 30,000 = £150,000. Costs = £120,000. Net benefit = £30,000; benefit–cost ratio = 150,000 ÷ 120,000 = 1.25. Benefits exceed costs, so yes on this measure.

Test yourself

Past-paper style question

A company can install solar panels for £8,000. They save £1,100 a year on electricity for 10 years. Maintenance costs £150 a year.

(a) Find the total benefit over 10 years.
(b) Find the total cost and the net benefit.
(c) How long will it take for the panels to pay for themselves? Give your answer to 1 decimal place. [5 marks]

Show the answer

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(a) 10 × £1,100 = £11,000. (1 mark)

(b) Total cost = 8,000 + 10 × 150 = £9,500. Net benefit = 11,000 − 9,500 = £1,500. (2 marks)

(c) Net saving each year = 1,100 − 150 = £950. Payback = 8,000 ÷ 950 = 8.42… ≈ 8.4 years. (2 marks)

Practice

The cost–benefit principle worksheet

Five short questions. Work through them, then reveal the mark scheme to check.

  1. Benefits total £450,000 and costs total £380,000. Find the net benefit.
  2. Benefits total £240,000 and costs total £200,000. Find the benefit–cost ratio.
  3. Option A costs £50k and gives benefits of £70k. Option B costs £80k and gives benefits of £95k. Which has the higher net benefit?
  4. A £5,000 machine saves £800 a year. How long to pay back?
  5. A firm has already spent £30,000 developing a product. Finishing it costs another £20,000 and will bring in £35,000. Should it finish? Explain.

Mark scheme

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  1. 450,000 − 380,000 = £70,000.
  2. 240,000 ÷ 200,000 = 1.2.
  3. A: 70 − 50 = £20k. B: 95 − 80 = £15k. A has the higher net benefit.
  4. 5,000 ÷ 800 = 6.25 years.
  5. Yes. The £30,000 is a sunk cost and must be ignored. Future net benefit = 35,000 − 20,000 = £15,000 > 0.
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