Special Order in a Constrained Machine Shop
Gampaha Manufacturing produces two components, Alpha and Beta, on the same CNC machine, which has 20,000 machine hours available per month. Alpha sells for LKR 4,500, uses 0.5 machine hours, and has variable cost LKR 2,700. Beta sells for LKR 6,000, uses 1.2 machine hours, and has variable cost LKR 3,300. Monthly fixed costs are LKR 18 million. Current demand is 24,000 Alpha and 8,000 Beta. A new export customer offers a one-off order for 5,000 units of a modified Alpha at LKR 3,900 each. The modification requires an additional LKR 300 per unit variable cost and a one-time tooling cost of LKR 1.2 million. The export customer requires delivery within the month, so the order must displace existing production. The sales director wants acceptance because the price exceeds the existing variable cost; the production manager warns that Beta has a higher contribution per unit. The company is operating at full capacity and has no alternative machine capacity.
1. Calculate the contribution per machine hour for Alpha and Beta and determine the optimal monthly production plan at full capacity. Show the ranking.
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Alpha: selling price LKR 4,500 minus variable cost LKR 2,700 equals contribution of LKR 1,800 per unit. Machine hours are 0.5. Contribution per machine hour is 1,800 divided by 0.5, equal to LKR 3,600.
Beta: LKR 6,000 minus LKR 3,300 equals LKR 2,700 per unit. Hours are 1.2. Contribution per machine hour is 2,700 divided by 1.2, equal to LKR 2,250.
Alpha ranks first. Available hours are 20,000. Demand for Alpha is 24,000 units multiplied by 0.5, equal to 12,000 hours. Remaining hours are 8,000, which produce Beta at 1.2 hours each, equal to 6,666.67 units, so 6,666 whole units. Fixed costs of LKR 18 million do not affect the mix decision. Total contribution is Alpha 24,000 multiplied by 1,800, equal to LKR 43.2 million, plus Beta 6,666 multiplied by 2,700, equal to about LKR 18.0 million, giving LKR 61.2 million and profit of about LKR 43.2 million. The sales director's comparison of unit contribution ignores the bottleneck. The production manager is also wrong: Beta has higher contribution per unit but lower contribution per constrained hour.
2. Evaluate the special order using relevant costing. Calculate the minimum price per unit and recommend whether to accept.
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Relevant costs are the incremental variable cost of LKR 2,700 plus LKR 300, equal to LKR 3,000 per unit; the one-off tooling cost of LKR 1.2 million; and the opportunity cost of displaced production. The order needs 5,000 multiplied by 0.5, equal to 2,500 machine hours. At the optimal plan, all Alpha demand is already satisfied and the marginal hours produce Beta. The displaced product is therefore Beta, not Alpha, even though Alpha ranks first. Opportunity cost is 2,500 hours multiplied by LKR 2,250, equal to LKR 5.625 million.
Incremental revenue is 5,000 multiplied by LKR 3,900, equal to LKR 19.5 million. Incremental costs are 5,000 multiplied by LKR 3,000, equal to LKR 15 million, plus tooling LKR 1.2 million, plus opportunity cost LKR 5.625 million, total LKR 21.825 million. Net relevant loss is LKR 19.5 million minus LKR 21.825 million, equal to LKR 2.325 million. Reject on financial grounds.
Minimum price: variable cost LKR 3,000 plus opportunity cost per unit, 0.5 multiplied by LKR 2,250, equal to LKR 1,125, plus tooling per unit, LKR 1.2 million divided by 5,000, equal to LKR 240. Minimum price is LKR 4,365. At LKR 3,900, the order is LKR 465 per unit short. If the order were so large that it also displaced Alpha, the opportunity cost would rise to LKR 3,600 per hour and the minimum price would be higher.
3. Discuss the qualitative factors the board should consider before rejecting or accepting the order, and identify one non-financial condition that could change the decision.
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Qualitative factors include whether the export customer could become a long-term buyer, whether accepting a low price sets a precedent for existing customers, and whether the order opens a new market that supports future pricing. The board should also consider the risk of displacing regular Beta customers, possible penalties for late delivery, quality and warranty exposure on a modified product, and the learning effect from the new export relationship. The one-off tooling cost is sunk once incurred, so it should not affect later repeat orders, but the company must decide whether the tooling has alternative use. Capacity expansion may be possible but would take time and capital.
One non-financial condition that could change the decision is a binding commitment from the export customer for follow-on orders at a price above LKR 4,365, or a strategic supply agreement that improves access to a market the company cannot otherwise enter. Another is a customer requirement that the order be accepted to retain a larger contract. Without such a condition, the financial analysis shows a relevant loss of LKR 2.325 million, so rejection is the defensible decision.