Control measures, insurance and uncertainty — Cost-benefit Analysis

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Control measures, insurance and uncertainty — the key ideas

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Step 1 · Control measures

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A control measure reduces the probability or the impact of a risk (an alarm, a guard, a better lock, staff training). The risk left over afterwards is the residual risk. Work out the expected cost before and after.

Step 2 · Is it worth it?

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A control measure is worthwhile if the saving in expected cost is greater than the cost of the measure. Net benefit = (expected cost before − expected cost after) − cost of the measure. If it is positive, it is worth doing.

Step 3 · Insurance

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Insurance transfers the risk: you pay a premium and the insurer pays the loss. On average the premium is more than your expected loss (the insurer must make a profit), but insurance protects you from a large loss you could not afford. Compare the premium with the expected cost — and think about whether you could cope with the loss.

Step 4 · Uncertainty

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Probabilities and costs are estimates. Always comment on how reliable they are, and check how sensitive your decision is: how much would an estimate have to change for the decision to flip? A decision that only just breaks even is not a safe one.

Worked example

A risk has a 0.15 chance each year of causing £40,000 of loss. A control measure costing £2,000 a year reduces the chance to 0.05. Is it worthwhile?

Before: 0.15 × 40,000 = £6,000. After: 0.05 × 40,000 = £2,000. Saving = £4,000.

Net benefit = 4,000 − 2,000 = £2,000 per year, so the measure is worthwhile.

Test yourself

Past-paper style question

A shop owner estimates a 6% chance each year of a burglary costing £8,000. An alarm costs £300 a year and reduces the chance to 2%.

(a) Find the expected annual cost of burglary with and without the alarm.
(b) Is the alarm worth buying? Show your working.
(c) Give one reason why your answer may be unreliable. [5 marks]

Show the answer

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(a) Without: 0.06 × 8,000 = £480. With: 0.02 × 8,000 = £160. (2 marks)

(b) Saving = 480 − 160 = £320. Cost of alarm = £300. Net benefit = 320 − 300 = £20 a year — worthwhile, but only just. (2 marks)

(c) The probabilities (6% and 2%) are only estimates; a small change would remove the £20 benefit, so the decision is very sensitive. (1 mark)

Practice

Control measures, insurance and uncertainty worksheet

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

A risk has probability 0.2 and cost £1,000. A control measure reduces the probability to 0.05. Find the saving in expected cost.
The control measure in question 1 costs £100. Is it worthwhile?
Suppose the same measure cost £200 instead. Is it worthwhile?
What is meant by 'residual risk'?
The £100 measure reduces the probability from 0.2 to a new probability $p$. For what values of $p$ is the measure NOT worthwhile?

Mark scheme

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Before: 0.2 × 1,000 = £200. After: 0.05 × 1,000 = £50. Saving = £150.
Net = 150 − 100 = +£50, so yes.
Net = 150 − 200 = −£50, so no.
The risk that remains after a control measure has been put in place.
Saving = (0.2 − $p$) × 1,000 must be more than 100, so 0.2 − $p$ > 0.1, $p$ < 0.1. Not worthwhile if $p \geq 0.1$.

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