Two Estimates and a Reserve
A city council is budgeting a £600,000 project to digitise 40,000 paper planning files. The lead estimator has produced three-point estimates for the main work packages, including the scanning package: optimistic 60 person-days, most likely 90, pessimistic 180, because file condition is unknown. The finance director wants a single figure for the business case and has asked for 'the most likely number'. A separate risk has been identified: the chosen scanning supplier may fail its quality audit, forcing re-scanning of 15% of files at a cost of £45,000; the supplier's own quality manager puts the chance at 30%. The finance director has already allocated a 5% contingency on the total budget and does not want another line. Last year a similar council project ran 22% over budget after a supplier dispute.
1. Calculate the expected value of the scanning work package and explain why the finance director's request for the most likely figure is unsafe for a business case.
Read the worked answer
PERT expected value = (O + 4M + P) / 6 = (60 + 360 + 180) / 6 = 100 person-days, against a most likely figure of 90.
Standard deviation = (P − O) / 6 = (180 − 60) / 6 = 20 person-days, so the range that covers roughly two-thirds of outcomes is about 80 to 120 days.
Why 90 is unsafe:
- The distribution is skewed upward. The optimistic case is only 30 days below the mode, while the pessimistic case is 90 days above it. So 90 is not a representative central value; it sits below the mean and offers roughly a 50% chance of being exceeded.
- It is a point estimate presented as a commitment, which removes the range the business case actually needs for sensitivity testing.
- The estimate is in person-days of effort, not elapsed time or cost; converting it requires rates and productivity assumptions that should be shown.
The constructive response is to give the director the 100-day expected value, the range, and a commitment figure at a chosen confidence level, plus a recommendation to sample-audit around 500 files to narrow the range.
2. Calculate the expected monetary value of the supplier risk and recommend how it should be funded given the existing 5% contingency.
Read the worked answer
EMV = probability × impact = 0.30 × £45,000 = £13,500.
Funding recommendation:
- The 5% contingency is £30,000. It covers identified risks such as this one, whereas a management reserve covers unknown-unknowns. The re-scan risk belongs in the risk-based contingency calculation, not in a new line item of its own.
- Check whether the £30,000 is already allocated to other quantified risks. If the summed EMV of all identified risks exceeds it, the contingency is underfunded and the gap must go to the board, not be absorbed silently.
- Spend part of the money to reduce exposure rather than only to pay for it: a pre-audit on a sample batch may cut the probability substantially at modest cost, which reduces both the EMV and the chance of a November-style dispute.
- Benchmark the reserve: last year's comparable project ran 22% over, which is £132,000 on this budget. A 5% contingency needs explicit justification if it is to stand.
The project manager should show the board the EMV calculation, the total quantified exposure, the residual exposure after mitigation, and the confidence level the reserve provides.
3. Recommend two risk responses for the supplier risk and state what the project manager should record and monitor for each.
Read the worked answer
1. Mitigate (reduce probability). Require the supplier to pass a pre-audit on a representative sample batch before full production begins, with the sample results accepted by the council's records team. Record: the action, the owner, the due date before production, the trigger (sample audit result), the estimated cost, and the reduction in probability from 30% to a stated target. Monitor at each status cycle and at the pre-production gate.
2. Transfer (reduce impact). Insert a contract clause making the supplier bear the cost of re-scanning caused by its own quality failures, and confirm insurance cover. Record: the clause reference, the residual impact after transfer, the credit risk if the supplier disputes or fails, and the evidence needed to prove a failure. Monitor through contract reviews and change control.
Acceptance with reserve is the fallback if neither is achievable, and must be explicitly approved. In all three cases the risk register entry needs an owner, a cause and effect description, a rating before and after response, a trigger, and a review date, so the board can see that the residual risk is a decision, not an oversight.