Coastline Council Waste Fleet: Ranking Under Optimism Bias
Coastline Council must decide how to maintain its 180-vehicle waste fleet. Three options are on the shortlist. Option A (do minimum) keeps the current fleet with reactive repairs: annual cost £1.2m, no measurable savings. Option B refurbishes 40 vehicles: capital £3.0m in year 0, then operating savings of £0.9m a year for five years. Option C replaces the fleet with electric vehicles: capital £7.0m in year 0, savings of £1.4m a year for five years, and a residual value of £1.0m at the end of year 5. The finance team requires optimism bias of +20% on capital costs and -15% on benefits. The discount rate is 3.5%; the five-year annuity factor is 4.517 and the year-5 discount factor is 0.843. The capital programme is already fully committed for the next two years.
1. Calculate the optimism-bias-adjusted NPV of each option and state the ranking. Show your workings.
Read the worked answer
Option A: NPV = -1.2 x 4.517 = -£5.42m (costs only, no benefits).
Option B: capital 3.0 x 1.20 = £3.60m. Annual benefit 0.9 x 0.85 = £0.765m; PV = 0.765 x 4.517 = £3.46m. NPV = 3.46 - 3.60 = -£0.14m.
Option C: capital 7.0 x 1.20 = £8.40m. Annual benefit 1.4 x 0.85 = £1.19m; PV = 1.19 x 4.517 = £5.38m. Residual £1.0m x 0.843 = £0.84m; if the -15% bias is also applied to the residual, £0.72m. NPV = 5.38 + 0.84 - 8.40 = -£2.18m.
Ranking: B (-0.14) > C (-2.18) > A (-5.42).
All three options are net costs, so the question is which cost stream is smallest over the appraisal period. The apparently cheap do-minimum is the most expensive, which is the finding that matters. The ranking is insensitive to how the residual is treated; the magnitude is not.
2. The portfolio holder says 'C is the greenest option, so choose C.' Calculate the switching value for C's annual benefit and explain what it implies.
Read the worked answer
For C to match B, its NPV must reach -£0.14m.
Required PV of benefits = 8.40 - 0.84 - 0.14 = £7.42m. Required annual benefit = 7.42 / 4.517 = £1.64m.
Against the bias-adjusted £1.19m, that is a 38% increase; against the unadjusted £1.40m it is 17%.
Implication: 'greenest' is not by itself a sufficient reason, because the appraisal has not monetised the environmental benefits that make C attractive. There are two defensible routes and one indefensible one. The defensible routes are: quantify carbon, air quality and noise benefits and add them to the appraisal, which may close the gap; or choose C on explicit non-monetary grounds that the board records and defends. The indefensible route is to assert the preference and work backwards to justify it.
A 38% gap is too wide to be closed by optimism or rounding. It needs new evidence, not a stronger assertion.
3. None of the options delivers a positive NPV, and the capital programme is committed for two years. Advise the board on how to proceed.
Read the worked answer
A negative NPV is not automatically a rejection. Value for money is relative, and the do-minimum may be undeliverable on compliance or service grounds as the fleet ages. But the board should not approve B as presented.
Options worth testing before a decision:
- Re-examine the appraisal period. Vehicles last considerably longer than five years; a 10 or 15-year period with a residual may reverse the sign.
- Re-scope, for example refurbishing 60 vehicles to improve the benefit-to-capital ratio.
- Defer into years 3-4 to fit the committed capital programme, accepting delayed benefits and re-running the NPV.
- Use leasing or an operating model to cut year-0 capital, while testing whole-life cost.
- Strengthen the evidence behind the £0.9m saving, which is the single largest driver and the least evidenced.
Recommend a revised shortlist with sensitivity analysis rather than approval or rejection now.