Larnaca Components: bottleneck plan, outsourcing and a below-normal export order
Larnaca Components Ltd operates one bottleneck machine with 20,000 hours available in 2025. It makes three components, all using the same machine. Per-unit data: Component A sells for €50, variable cost €30, uses 2 machine hours, annual demand 4,000 units. Component B sells for €40, variable cost €22, uses 3 hours, demand 3,000 units. Component C sells for €30, variable cost €12, uses 1 hour, demand 5,000 units. Fixed overhead of €480,000 is allocated to products at €8 per machine hour and is unavoidable except for €25,000 of supervision cost specific to Component C if C is discontinued. An external supplier has offered to supply all 5,000 units of C at €19 each, delivered. If C is outsourced, the freed machine hours can only be used to make additional B, up to demand. Separately, a one-off export enquiry offers €38 for 1,000 units of A; accepting it would require €5,000 of setup cost and would displace existing B production because the machine is fully loaded.
1. Calculate the optimal production plan and total contribution, ranking products by contribution per machine hour.
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Contribution per unit: A €20, B €18, C €18. Contribution per machine hour: A €10, B €6, C €18. Demand consumes 8,000 hours for A, 9,000 for B and 5,000 for C, totalling 22,000 hours against 20,000 available, so the machine is the limiting factor.
Ranking: C first, then A, then B.
- C: 5,000 units × 1 hour = 5,000 hours; contribution 5,000 × €18 = €90,000.
- A: 4,000 units × 2 hours = 8,000 hours; contribution 4,000 × €20 = €80,000.
- Remaining hours = 20,000 − 5,000 − 8,000 = 7,000 hours. B units = 7,000 / 3 = 2,333 units; contribution 2,333 × €18 = €41,994 (approximately €42,000).
Total contribution is approximately €212,000. The €480,000 fixed overhead and the €8 per hour allocation are irrelevant to the short-term plan because they do not change with the mix; only the €25,000 C-specific supervision cost becomes relevant if C is discontinued.
2. Evaluate the outsourcing offer for Component C using relevant costing, including opportunity cost, and advise management.
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Relevant cost of making C for 5,000 units:
- Variable cost: 5,000 × €12 = €60,000.
- Avoidable supervision cost: €25,000.
- Opportunity cost of freed hours: 5,000 hours could make 1,666 additional B units, but demand only supports 667 more B units beyond the current plan of 2,333. Opportunity cost = 667 × €18 = approximately €12,000. The remaining freed hours have no alternative use.
- Total relevant cost of making = €60,000 + €25,000 + €12,000 = €97,000.
Relevant cost of buying = 5,000 × €19 = €95,000. Outsourcing saves only €2,000, about 2% of the relevant cost, which is marginal. The allocated fixed overhead is irrelevant. Management should also consider supplier reliability, quality certification, delivery risk, loss of in-house expertise, workforce consequences and the possibility that B demand recovers, which would raise the opportunity cost. The quantitative case is weak, so a long-term contract should not be signed without secure quality and continuity safeguards.
3. Evaluate the one-off export order for 1,000 units of A at €38 and advise whether to accept it, addressing qualitative factors.
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The order uses 1,000 × 2 = 2,000 machine hours, which must displace B production. Displaced B units = 2,000 / 3 = 667 units; lost contribution = 667 × €18 = approximately €12,000. Relevant analysis:
- Incremental revenue: 1,000 × €38 = €38,000.
- Incremental variable cost: 1,000 × €30 = €30,000.
- Setup cost: €5,000.
- Opportunity cost of displaced B: €12,000.
- Net relevant benefit = €38,000 − €30,000 − €5,000 − €12,000 = −€9,000.
On financial grounds the order should be rejected. Qualitative factors could change the decision only if they are genuinely strategic: entry to a new export market, a reference customer, learning effects, or use of otherwise idle capacity in a later period. Management must also consider price precedent and anti-dumping or competitor reactions. If the order is accepted at €38, it should be ring-fenced and time-limited so that it does not become the normal selling price.