Relevant costing for a special order with a constrained resource
Tasman Components makes two products, Alpha and Beta, using the same machine, which has a capacity of 10,000 machine hours per year. Alpha uses 2 hours per unit and sells for $90 with variable costs of $50. Beta uses 4 hours per unit and sells for $160 with variable costs of $90. Current demand is 3,000 Alpha and 1,000 Beta, using 10,000 hours in total. A customer offers a one-off order for 500 units of a modified Alpha at $70 per unit. The modification requires an additional $8 of variable cost per unit and 2.5 machine hours per unit. Fixed costs are $200,000 per year and are unaffected by the order. The customer will not accept a price above $70.
1. Calculate the contribution per machine hour for Alpha and Beta and determine the optimal production mix before the special order.
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Contribution per unit
- Alpha: 90 - 50 = $40; per hour = 40 / 2 = $20/hour.
- Beta: 160 - 90 = $70; per hour = 70 / 4 = $17.50/hour.
Optimal mix
Alpha yields the higher contribution per constrained hour, so prioritise Alpha. Demand for Alpha uses 3,000 x 2 = 6,000 hours. Remaining hours = 4,000, allowing 1,000 Beta (4,000 / 4). This exactly meets demand, so the current plan is optimal: 3,000 Alpha and 1,000 Beta. Total contribution = (3,000 x 40) + (1,000 x 70) = 120,000 + 70,000 = $190,000.
2. Evaluate whether the special order should be accepted, considering the opportunity cost of the constrained machine hours.
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Incremental analysis
Special order price = $70. Incremental variable cost = 50 + 8 = $58. Contribution per unit = $12. Hours per unit = 2.5, so contribution per hour = 12 / 2.5 = $4.80/hour.
Opportunity cost
The order needs 500 x 2.5 = 1,250 hours. These must come from existing production. The lowest-contribution use displaced is Beta at $17.50/hour. Opportunity cost = 1,250 x 17.50 = $21,875.
Total incremental contribution = 500 x 12 = $6,000. Net benefit = 6,000 - 21,875 = -$15,875.
Conclusion: Reject the order. Although it shows a positive unit contribution, it destroys value once the constrained resource is valued at its next-best use. The $70 price is below the relevant cost of $70 + (2.5 x 17.50) = $113.75 per unit equivalent. Fixed costs are irrelevant because they do not change.
3. The customer returns and offers $95 per unit for 500 units, but requires delivery within the current capacity. Advise management, showing the minimum acceptable price.
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Minimum price
Relevant cost per unit = incremental variable cost $58 + opportunity cost per unit (2.5 x 17.50 = $43.75) = $101.75.
At $95, contribution per unit = 95 - 58 = $37; total = $18,500. Opportunity cost = $21,875. Net = -$3,375. Still value-destroying.
Alternative: If management can displace Alpha instead (only if Beta demand cannot be met), opportunity cost per hour is $20, giving relevant cost = 58 + (2.5 x 20) = $108. Either way $95 is insufficient.
Advice: Decline at $95 unless non-financial benefits (market entry, future orders) are quantified and judged to exceed $3,375. If accepted, disclose the strategic rationale. The minimum price is $101.75 assuming Beta is displaced.