Expected cost and risk matrices — Cost-benefit Analysis

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Expected cost and risk matrices — the key ideas

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Step 1 · Risk as expected cost

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A risk is something that might happen and cost money if it does. Its expected cost is: probability of it happening × cost if it does happen. For example, a 5% chance a year of £40,000 flood damage has an expected cost of 0.05 × 40,000 = £2,000 a year.

Step 2 · Adding up several risks

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For several risks, work out the expected cost of each and add them to get the total expected cost. Over several years, multiply the yearly expected cost by the number of years (as an estimate).

Step 3 · Risk matrices

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A risk matrix is a grid with likelihood on one axis and impact on the other. Risks that are both likely and serious (top right) are the highest priority; unlikely and minor ones (bottom left) the lowest. It is a quick way to rank risks when exact numbers are not known.

Step 4 · Comparing risks

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A rare risk with a huge cost can have a larger expected cost than a common risk with a small cost, so compare the numbers, not just the probabilities. The matrix and the expected cost should tell the same story.

Worked example

The probability of a flood in any year is 0.05 and the damage would cost £40,000. Find the expected annual cost.

Expected cost = 0.05 × £40,000 = £2,000 per year. Over 10 years this is about £20,000 in expected damage.

Test yourself

Past-paper style question

A company identifies three risks. R1: probability 0.1 per year, cost £20,000. R2: probability 0.02 per year, cost £150,000. R3: probability 0.3 per year, cost £4,000.

(a) Find the expected annual cost of each risk.
(b) Which risk has the highest expected cost?
(c) Find the total expected annual cost.
(d) Describe R2 using the words likelihood and impact. [5 marks]

Show the answer

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(a) R1: 0.1 × 20,000 = £2,000. R2: 0.02 × 150,000 = £3,000. R3: 0.3 × 4,000 = £1,200. (2 marks)

(b) R2. (1 mark)

(c) 2,000 + 3,000 + 1,200 = £6,200. (1 mark)

(d) R2 has a low likelihood but a high impact. (1 mark)

Practice

Expected cost and risk matrices worksheet

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

A risk has probability 0.2 and cost £5,000. Find its expected cost.
Risk X: probability 0.05, cost £12,000. Risk Y: probability 0.1, cost £3,000. Find the total expected cost.
Which has the greater expected cost: a 1% chance of a £50,000 loss, or a 10% chance of a £6,000 loss?
A risk has a probability of 0.9 and a cost of only £100. Where does it go on a risk matrix?
A 4% yearly chance of a £25,000 loss. Estimate the expected cost over 10 years.

Mark scheme

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0.2 × 5,000 = £1,000.
0.05 × 12,000 = 600; 0.1 × 3,000 = 300. Total = £900.
0.01 × 50,000 = £500; 0.1 × 6,000 = £600. The 10% chance of £6,000 is greater.
High likelihood, low impact.
0.04 × 25,000 = £1,000 per year → 10 × 1,000 = £10,000.

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