Would a higher fare make the express ferry worth running?
Compare two services before and after a berth restriction.
The question
North Quay Ferries is a fictional UK commuter operator. It can run one service during a five-weekday trial. The two services use different berths. There are no switch costs. All amounts in the exhibit are per weekday.
| Conventional | Express | |
|---|---|---|
| Forecast journeys | 400 | 350 |
| Journey capacity | 420 | 360 |
| Fare, GBP per journey | 5 | 7 |
| Variable cost, GBP per journey | 2 | 3 |
| Fixed cost, GBP per day | 900 | 1050 |
Demand forecasts reflect each fare. Each fixed cost includes one vessel and crew.
“Which service should run? Show the operating surplus, then respond when the express berth can serve only 260 journeys per day.”
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A strong answer, step by step
Open each step in turn. This is one strong answer, not the only one.
Step 1: What should the operator compare?
What would you do here? Open the move you’d make.
Compare contribution per journey.
Tempting, but it misses something. It tells you the unit economics but leaves out the number served and fixed costs.
Compare daily surplus at the number of journeys each service can serve.
The strong move. It puts both options on the same decision metric and period.
Compare forecast revenue before costs.
Tempting, but it misses something. Revenue measures demand value but cannot establish which service earns more.
See how a strong candidate says it
“I would compare daily operating surplus. Served journeys equal the lower of demand and capacity. Multiply them by fare less variable cost, then subtract the fixed cost of the chosen service.”
Why it works: A higher fare or margin per journey can lose when fewer people travel or fixed costs rise.
Step 2: How much does each service earn in one day?
What would you do here? Open the move you’d make.
Use 400 and 350 journeys, then subtract each service’s fixed cost.
The strong move. Both forecasts are under capacity, and the comparison includes both fixed costs.
Use capacity of 420 and 360 journeys as sales.
Tempting, but it misses something. The exhibit does not forecast enough passengers to fill either service.
Use only the difference in fares and subtract the express fixed cost.
Tempting, but it misses something. The options serve different numbers of passengers and both have fixed costs.
See how a strong candidate says it
“Conventional: 400 × (5 − 2) − 900 = GBP300/day. Express: 350 × (7 − 3) − 1,050 = GBP350/day. The express adds GBP50/day, or GBP250 over five days.”
Why it works: Use forecast journeys where demand is below capacity.
Step 3: What do you recommend before the restriction?
What would you do here? Open the move you’d make.
Keep conventional because it serves more journeys.
Tempting, but it misses something. Volume can matter for access, but the stated objective is surplus. Name a different objective if you use it.
Approve a permanent express schedule based on the trial forecast.
Tempting, but it misses something. The exhibit supports a short conditional decision only.
Run the express trial if the berth can serve the forecast.
The strong move. It states the gain and the assumption that can remove it.
See how a strong candidate says it
“I would run the express trial if the berth and demand assumptions hold. The forecast gain is GBP50/day. I would confirm usable capacity and avoid treating a five-day forecast as a permanent service decision.”
Why it works: Conventional is defensible if the operator explicitly values forecast risk; the exhibit does not price that risk.
Step 4: The express berth drops to 260 journeys. What changes?
What would you do here? Open the move you’d make.
Reduce both forecasts to 260 journeys.
Tempting, but it misses something. The conventional service uses a different berth and its capacity is unchanged.
Recalculate express at 260 and compare with the unchanged conventional surplus.
The strong move. This applies the new constraint only to the affected option.
Run express if it can reach its own break-even volume.
Tempting, but it misses something. An express service that breaks even still earns less than the conventional service.
See how a strong candidate says it
“Express now earns 260 × GBP4 − GBP1,050 = −GBP10/day. Conventional stays at GBP300/day. I would run conventional, which earns GBP310 more per day. Express needs at least 338 whole journeys to beat it.”
Why it works: The berth restriction applies only to express. Breaking even at 263 journeys does not beat conventional.
The answer, in short
- Decision
- Run conventional during dredging.
- Because
- At the new cap, conventional earns GBP300/day and express loses GBP10/day.
- What would change it
- At 338 express journeys per day, the express would beat conventional under the stated prices and costs.
Common traps
- Using capacity as demand.
- Comparing a daily figure with a five-day figure.
- Using break-even as the threshold for beating the alternative.
Check your answer
- Did you cap journeys at capacity?
- Did you show GBP/day for both services?
- Did you state the initial recommendation and its assumption?
- Did you recalculate only the affected service?
Last reviewed Nov 11, 2026