Cobalt Packaging: Special Order in a Bottleneck
Cobalt Packaging prints cartons on a single printing machine that is its bottleneck. Monthly capacity is 10,000 machine hours. Product A sells for £40 and has a variable cost of £22; it uses 2 machine hours per unit. Product B sells for £55 and has a variable cost of £37; it uses 3 machine hours per unit. Monthly demand is 3,000 units of A and 2,000 units of B. Fixed costs are £60,000 per month.
A customer offers a one-off order for 1,000 units of a modified carton, product C, at £30 per unit. Each C would use 1.5 machine hours and incur variable cost of £19, including the modification. The order would have to be produced in the same month and would displace existing production. No additional fixed costs would be incurred. The sales director says the order should be accepted because £30 exceeds the £19 variable cost. The production manager warns that the machine is already fully committed to profitable work.
1. Determine the optimal production plan and total contribution for the month without the special order. Show the ranking of products and workings.
Read the worked answer
Contribution per unit: A = £40 − £22 = £18; B = £55 − £37 = £18. Machine hours per unit: A = 2; B = 3. Contribution per machine hour: A = £18 / 2 = £9; B = £18 / 3 = £6. Demand requires: A 3,000 × 2 = 6,000 hours; B 2,000 × 3 = 6,000 hours; total 12,000 hours, which exceeds 10,000. Rank A first. Produce 3,000 A using 6,000 hours. Remaining 4,000 hours produce 4,000 / 3 = 1,333.33 units of B. Assuming whole units, produce 1,333 B and leave 1 hour idle. Contribution = (3,000 × £18) + (1,333 × £18) = £54,000 + £23,994 = £77,994. With fractional units it is £78,000. Fixed costs are £60,000, so profit is about £18,000.
2. Evaluate the special order using relevant costing. Calculate the relevant cost per unit and total contribution from accepting it, and advise whether Cobalt should accept.
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Each C uses 1.5 hours and displaces B. B produces 1 unit per 3 hours, so 1.5 hours would have produced 0.5 units of B. Contribution forgone per C = 0.5 × £18 = £9. Relevant cost per C = variable cost £19 + opportunity cost £9 = £28. Price £30 − relevant cost £28 = £2 net contribution per C. For 1,000 C: net contribution = 1,000 × £2 = £2,000. Check: C uses 1,500 hours, displacing 500 B. New plan: A 3,000 (6,000 hours), C 1,000 (1,500 hours), B 833.33 units (2,500 hours). Contribution = £54,000 + £11,000 + £15,000 = £80,000, which is £2,000 above £78,000. On financial grounds accept, because the order adds contribution and no fixed costs. But check that the displaced B sales are genuinely lost, not merely deferred; if B demand is unmet and can be served later, the opportunity cost may be lower. Also consider qualitative factors: disruption, quality risk, future pricing, and whether the customer will expect repeat low prices.
3. The customer increases the order to 2,000 units of C. Recalculate the decision and discuss two qualitative factors that could change your recommendation.
Read the worked answer
At 2,000 C, machine hours = 3,000; displaced B = 1,000 units; contribution forgone = £18,000. Net contribution = 2,000 × (£30 − £19) − £18,000 = £22,000 − £18,000 = £4,000. Still positive, so the financial recommendation is to accept. The revised plan is A 3,000, C 2,000, and 333 B, giving contribution £54,000 + £22,000 + £5,994 = £81,994, about £4,000 above the original plan.
Qualitative factors: (1) If the B customers are long-term contractual customers, turning them away could lose future sales and damage relationships; the order may not be worth the strategic cost. (2) The special order may become a regular expectation at £30, which could undermine the normal price of B; quality and delivery risk may also affect reputation. Other factors include machine maintenance, overtime, staff fatigue, and whether the displaced B units can be made up later.