Machine-hour constraint, export order and product discontinuance
Zenith Components Ltd makes three components on a single CNC machine available for 60,000 machine hours a year. Product X sells for ₹1,200, has variable cost ₹720 and uses 4 hours; annual demand is 6,000 units. Product Y sells for ₹1,800, variable cost ₹1,080 and uses 6 hours; demand is 4,000 units. Product Z sells for ₹2,400, variable cost ₹1,800 and uses 10 hours; demand is 2,000 units. Fixed costs are ₹36 lakh a year and are absorbed at ₹60 per machine hour. The current plan, driven by Z's high selling price, produces all of Z and Y and fills the remaining hours with X. A customer has offered to buy 1,000 units of Z at ₹2,000 for an export order that must be accepted or rejected as a whole. Management also wants to drop Z because its product-line statement shows no profit after fixed-cost absorption.
1. Determine the contribution-maximising production plan, compare its profit with the current plan, and explain why contribution per machine hour, not contribution per unit, drives the ranking.
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Ranking by scarce resource
| Product | Contribution/unit (₹) | Hours/unit | Contribution/hour (₹) | Demand (units) |
|---|---|---|---|---|
| X | 480 | 4 | 120 | 6,000 |
| Y | 720 | 6 | 120 | 4,000 |
| Z | 600 | 10 | 60 | 2,000 |
X and Y earn the same contribution per machine hour and both beat Z. Produce X and Y to demand: 6,000 x 4 = 24,000 hours; 4,000 x 6 = 24,000 hours. Remaining hours = 60,000 - 48,000 = 12,000, enough for 1,200 units of Z.
Contribution = (6,000 x 480) + (4,000 x 720) + (1,200 x 600) = 28,80,000 + 28,80,000 + 7,20,000 = ₹64,80,000. Profit = ₹64,80,000 - ₹36,00,000 = ₹28,80,000.
Current plan
Z 2,000 units = 20,000 hours; Y 4,000 = 24,000 hours; X 4,000 = 16,000 hours. Contribution = 12,00,000 + 28,80,000 + 19,20,000 = ₹60,00,000; profit = ₹24,00,000. The optimal plan improves profit by ₹4,80,000.
The ₹60 per hour absorption rate is an allocation of a common fixed cost. It does not change the incremental value of a machine hour. Ranking by contribution per unit would wrongly favour Z because each Z unit earns ₹600, more than X's ₹480, even though Z consumes 10 hours against X's 4.
2. Evaluate the export order at ₹2,000 and state the minimum price at which it becomes acceptable, showing the opportunity cost.
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Incremental analysis of the export order
Revenue: 1,000 x ₹2,000 = ₹20,00,000. Variable cost: 1,000 x ₹1,800 = ₹18,00,000. Contribution = ₹2,00,000.
The order needs 10,000 machine hours. In the optimal plan there is no idle capacity, so the hours must be released by cutting X, the product at the margin. Each X unit gives ₹480 contribution in 4 hours, i.e. ₹120 per hour. Lost contribution = 10,000 x ₹120 = ₹12,00,000.
Net effect = ₹2,00,000 - ₹12,00,000 = -₹10,00,000. Reject the order at ₹2,000.
Minimum acceptable price: the order must recover variable cost ₹1,800 plus the opportunity cost of the displaced hours (10 hours x ₹120 = ₹1,200), i.e. ₹3,000 per unit. At ₹3,000 the company is indifferent; above ₹3,000 it gains. If genuine idle capacity existed, the minimum would fall to ₹1,800. Qualitative factors, such as export market entry, should not justify a price below the relevant cost unless treated as a separate strategic investment.
3. Should Z be discontinued? Quantify the effect and identify the conditions under which discontinuance would be justified.
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Do not discontinue Z on the product-line statement
The statement showing no profit for Z has allocated ₹36 lakh of common fixed cost to it. That allocation is not avoidable if Z is dropped. Z's contribution is ₹600 per unit.
From the current plan, dropping Z releases 20,000 hours. X has unmet demand of 2,000 units (8,000 hours), which can be made for extra contribution of 2,000 x ₹480 = ₹9,60,000. The remaining 12,000 hours have no alternative use. Lost contribution from Z = 2,000 x ₹600 = ₹12,00,000. Net change = ₹9,60,000 - ₹12,00,000 = -₹2,40,000. Profit falls.
From the optimal plan, X and Y are already at demand, so the 12,000 hours released by Z have no alternative use; the loss is the full ₹7,20,000 contribution of 1,200 Z units.
Discontinuance is justified only if avoidable fixed costs plus the contribution from redeployed capacity exceed Z's contribution, or if there are strategic reasons such as quality or customer exit. The manager should ask for a contribution statement, not an absorption-cost product-line statement.