Machine-Hour Constraint and a Thin Special Order (Subject: Commerce)
Sunrise Components Ltd makes three parts on the same machine. Budget data for the year: Part A - selling price ₹400, variable cost ₹260, 2 machine hours per unit, demand 6,000 units. Part B - price ₹300, variable cost ₹180, 1.5 machine hours per unit, demand 8,000 units. Part C - price ₹250, variable cost ₹170, 1 machine hour per unit, demand 10,000 units. Machine capacity is 30,000 hours and annual fixed costs are ₹12,00,000. A trading house offers a one-time export order of 2,000 units of Part A at ₹310 per unit, to be produced in the slack quarter when regular demand for A falls to 2,000 units and 4,000 machine hours would otherwise be idle. The order requires special packaging at ₹18 per unit and a one-time mould costing ₹50,000, which has no resale value. The sales manager argues that any price above variable cost must be accepted. The works manager points out that the slack quarter is exactly when preventive maintenance is scheduled, and the union has asked for overtime payments.
1. Determine the optimal production mix for the year and the resulting profit. Show why ranking products by selling price or by unit contribution is the wrong method.
Read the worked answer
Hours required at full demand: A 6,000 × 2 = 12,000; B 8,000 × 1.5 = 12,000; C 10,000 × 1 = 10,000. Total 34,000 hours against 30,000 available - a shortfall of 4,000 hours. Capacity is the binding constraint, so rank by contribution per machine hour.
| Part | Contribution per unit | Hours | Contribution per hour |
|---|---|---|---|
| A | 400 − 260 = ₹140 | 2.0 | ₹70 |
| B | 300 − 180 = ₹120 | 1.5 | ₹80 |
| C | 250 − 170 = ₹80 | 1.0 | ₹80 |
Allocation: meet C fully (10,000 units, 10,000 hours), meet B fully (8,000 units, 12,000 hours) - they tie at ₹80 per hour - leaving 8,000 hours for A, i.e. 4,000 units.
Contribution: C 10,000 × 80 = ₹8,00,000; B 8,000 × 120 = ₹9,60,000; A 4,000 × 140 = ₹5,60,000. Total ₹23,20,000. Less fixed costs ₹12,00,000 → profit ₹11,20,000.
Why other rankings fail: Part A has the highest selling price and the highest unit contribution, so price- or unit-contribution ranking would produce A first and give up ₹10 per hour against B and C - on 12,000 hours of A at full demand that is a ₹1,20,000 sacrifice. The scarce resource, not the product's price tag, determines the ranking.
2. Evaluate the export order using relevant costing. Should Sunrise accept ₹310, and at what price would the order become clearly worthwhile?
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Relevant cost per unit: variable cost ₹260 + special packaging ₹18 + mould amortised over 2,000 units ₹25 = ₹303. Price ₹310 gives ₹7 per unit, or ₹14,000 on the order - about 2.3% of the ₹6,20,000 order value.
Capacity check: the order needs 2,000 × 2 = 4,000 machine hours, exactly the hours idle in the slack quarter. So there is no displacement of regular contribution, and the ₹50,000 mould is a genuine incremental cost, not a sunk one. On pure relevant costing the order is marginally positive: accept rather than reject, because ₹14,000 beats zero.
But three qualifications decide the judgement:
- The margin is a rounding error. A ₹5 error in packaging, or a small quality rework, wipes it out. A counter-offer at ₹320 yields 2,000 × (320 − 278) − 50,000 = ₹34,000; ₹325 yields ₹44,000. The negotiation, not the accept/reject call, is where the value lies.
- Maintenance is a real cost, not a note. Using the 4,000 hours means rescheduling preventive maintenance. If breakdown risk or an outsourced maintenance slot costs more than ₹14,000, the answer flips to reject.
- No overtime. If the order cannot be completed inside normal hours, overtime premium becomes an incremental cost and destroys the margin entirely.
Verdict: accept only if maintenance is rescheduled with a documented plan, no overtime is needed, and the export sale is ring-fenced from domestic price expectations. Otherwise reject or negotiate upward.
3. The sales manager says the order must be accepted because it absorbs fixed costs. How should this argument be answered, and which qualitative factors should be recorded in the file?
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Answering the absorption argument:
Fixed costs of ₹12,00,000 are unchanged whether the order is taken or not, so they are irrelevant to the decision. 'Absorbing fixed cost' is an accounting presentation, not a cash consequence - the order either adds contribution above its incremental costs or it does not. Here it adds ₹14,000, which is the entire financial case; there is no hidden fixed-cost benefit to add on top. Equally, the argument that 'any price above variable cost is profit' is wrong because it ignores the ₹18 packaging, the ₹25 per-unit mould charge, the machine hours consumed and the maintenance displacement. The correct test is incremental revenue minus all incremental costs, including opportunity cost of any scarce resource used.
Qualitative factors to record:
- Price precedent: whether the export buyer or domestic customers can use ₹310 as a reference price; require separate branding, export-only packaging and a confidentiality clause.
- Maintenance risk: the rescheduled maintenance plan, the equipment criticality and the breakdown exposure during the quarter.
- Labour: union expectations of overtime and any precedent created by accepting a rush order.
- Repeat business and learning: whether the mould, though written off on this order, has value in future export orders at a better price.
- Capacity accuracy: confirm the slack quarter forecast, because if regular A demand revives, the 4,000 hours are no longer idle and the displaced contribution of ₹140 per unit (₹70 per hour) makes the order loss-making.
Record the decision, the numbers and these factors with the approving authority's signature, since a one-time order priced below the domestic price is the kind of transaction auditors query.