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9609 · 4.3.1

Significance and measurement of capacity utilisation — practice questions

Practice and worked examples for 9609 Significance and measurement of capacity utilisation. Short previews only — attempt the full question in MarkScheme against the official scheme.

Worked example 1

A factory has a maximum output of 50,000 units per month and monthly fixed costs of $200,000. It is currently producing 35,000 units. Calculate the current capacity utilisation and the fixed cost per unit at both current and full capacity.

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Utilisation = (35,000 ÷ 50,000) × 100 = 70%

Fixed cost per unit now: $200,000 ÷ 35,000 = $5.71/unit

At full capacity: $200,000 ÷ 50,000 = $4.00/unit

Implication: The 30% of idle capacity adds $1.71 to each unit's fixed cost burden. This reduces the profit margin per unit and may make the firm's pricing uncompetitive.

Worked example 2

A hotel has 80 rooms. On average, 55 rooms are occupied each night. The hotel is considering a marketing campaign costing $6,000 per month, which is forecast to increase average occupancy to 70 rooms per night. The average contribution per room-night is $80. Calculate the current and forecast capacity utilisation, and advise whether the campaign is financially viable.

Show solution outline

Step 1: Calculate Current Capacity Utilisation Utilisation = (Current Occupancy ÷ Maximum Capacity) × 100 Utilisation = (55 ÷ 80) × 100 = 68.75%

Step 2: Calculate Forecast Capacity Utilisation Forecast Utilisation = (Forecast Occupancy ÷ Maximum Capacity) × 100 Forecast Utilisation = (70 ÷ 80) × 100 = 87.5%

Step 3: Evaluate Financial Viability

  • Increase in occupied rooms per night = 70 - 55 = 15 rooms.
  • Assuming a 30-day month, total increase in room-nights = 15 rooms/night × 30 nights = 450 room-nights.
  • Increase in monthly contribution = 450 room-nights × $80/room-night = $36,000.
  • Cost of marketing campaign = $6,000.
  • Net financial gain = Increase in contribution - Campaign cost
  • Net financial gain = $36,000 - $6,000 = $30,000.

Advice: The campaign is financially viable. It is projected to generate a net gain of $30,000 per month and increases capacity utilisation to a more efficient level of 87.5% without overstretching resources.

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