Make-or-Buy with Constrained Capacity and a Sunk Cost Trap
Tūī Components Ltd manufactures three components (A, B and C) on a single machine that runs 4,000 hours per year and is fully utilised. Per-unit data:
| A | B | C | |
|---|---|---|---|
| Selling price | $120 | $90 | $75 |
| Direct materials | $30 | $25 | $20 |
| Direct labour | $20 | $15 | $12 |
| Variable overhead | $10 | $8 | $6 |
| Machine hours | 2.0 | 1.0 | 0.5 |
| Annual demand (units) | 800 | 1,200 | 1,600 |
Fixed overhead is $240,000 per year and is allocated on machine hours. An external supplier has offered to supply component B for $62 per unit. Last year Tūī spent $45,000 redesigning component B's tooling; the redesign is now complete and the tooling cannot be used for anything else. The sales manager argues B should be outsourced because its full cost of $94 exceeds the $62 quote.
1. Determine whether Tūī should outsource component B, showing the relevant costing and the opportunity cost of the constrained resource.
Read the worked answer
The sales manager's comparison uses full cost including allocated fixed overhead, which is not relevant. The $45,000 tooling redesign is a sunk cost - it is already incurred and cannot be recovered - so it is excluded.
Step 1 - Contribution per unit and per machine hour:
| A | B | C | |
|---|---|---|---|
| Contribution/unit | 60 | 42 | 37 |
| Machine hours | 2.0 | 1.0 | 0.5 |
| Contribution per machine hour | 30 | 42 | 74 |
Ranking by contribution per constrained hour: C (74) > B (42) > A (30). C is the most profitable use of the bottleneck.
Step 2 - Relevant cost of making B: variable cost = 25 + 15 + 8 = $48 per unit. Buying costs $62. On a pure avoidable-cost basis, making B saves $14 per unit - before considering what the freed capacity could earn.
Step 3 - Opportunity cost. If B is outsourced, the 1,200 hours freed (1,200 units × 1.0 hr) would be redeployed to the next-best product. Demand for C is 1,600 units = 800 hours, already fully met, so the freed hours cannot all go to C. Demand for A is 800 units = 1,600 hours, currently unmet. So freed hours go to A at $30 contribution per hour: 1,200 hours × $30 = $36,000 of additional contribution.
Step 4 - Net effect of outsourcing B:
- Extra purchase cost: 1,200 × ($62 − $48) = $16,800 outflow
- Contribution from redeployed capacity: $36,000 inflow
- Net benefit of outsourcing B = $19,200
Recommendation: outsource B, because the opportunity cost of the bottleneck capacity exceeds the purchase premium. The examiner is testing whether you (a) strip out fixed overhead and sunk costs, and (b) recognise that in a constrained setting the relevant comparison is contribution per scarce hour, not unit cost.
2. Explain how your answer would change if the machine could be operated for an extra 1,000 hours per year at an additional fixed cost of $25,000.
Read the worked answer
Adding capacity changes the scarcity assumption, and that is the pivot on which the whole analysis turns.
With 1,000 extra hours available, the constraint binds less tightly. Total demand requires: A 1,600 hrs + B 1,200 hrs + C 800 hrs = 3,600 hours, which is within the expanded 5,000-hour capacity. If all demand can be met internally, there is no opportunity cost to making B - the freed hours would simply sit idle.
So the comparison reverts to the simple relevant-cost test: making B costs $48 variable, buying costs $62, a $14 per unit penalty for buying, or $16,800 per year. That exceeds nothing, so keep B in-house.
But the extra capacity itself costs $25,000 per year in additional fixed cost, and it is only worth paying for if the contribution it unlocks exceeds that. The additional contribution from meeting currently unmet demand for A (800 units × $60 = $48,000) exceeds $25,000 by $23,000. So the better decision may be to buy the extra capacity and keep B in-house: net benefit = $48,000 − $25,000 = $23,000, versus $19,200 from outsourcing B with no capacity expansion.
Caveats worth flagging: the extra capacity is only justified if demand for A is genuinely firm; if A's demand is soft, the $25,000 becomes a stranded fixed cost. Also, qualitative factors - supplier reliability, quality risk on B, loss of know-how - may outweigh a $3,800 difference between the two options.