Aldergate Components Ltd: one machine, three products and a misleading full cost
Aldergate Components Ltd makes three products on a single machine limited to 10,000 hours per month. Product A sells for £60, has variable costs of £36 and takes 2 machine hours; monthly demand is 2,000 units. Product B sells for £45, has variable costs of £27 and takes 1 machine hour; demand is 3,000 units. Product C sells for £80, has variable costs of £56 and takes 3 machine hours; demand is 1,500 units. Fixed overhead is £100,000 per month and is absorbed at £10 per machine hour. A customer has offered to buy 1,000 units of A at £50 each, in addition to existing demand. Separately, the managing director, noting that C's full cost is £86 against a price of £80, has proposed dropping product C.
1. Rank the products and allocate the 10,000 machine hours to maximise monthly contribution. Show the resulting contribution, profit and unmet demand.
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Contribution per unit and per machine hour:
| Product | Contribution/unit | Hours | Contribution/hour | Rank |
|---|---|---|---|---|
| A | £24 | 2 | £12.00 | 2 |
| B | £18 | 1 | £18.00 | 1 |
| C | £24 | 3 | £8.00 | 3 |
Hours demanded: A 4,000 + B 3,000 + C 4,500 = 11,500 hours, against 10,000 available - a shortfall of 1,500 hours. Rank on contribution per machine hour, not per unit: C has the same contribution per unit as A but uses half as much again.
Optimal plan:
- B: 3,000 units × 1 hr = 3,000 hrs → contribution £54,000
- A: 2,000 units × 2 hrs = 4,000 hrs → contribution £48,000
- C: 3,000 remaining hrs = 1,000 units → contribution £24,000
Total contribution £126,000, less fixed overhead £100,000 = profit £26,000. Unmet demand: 500 units of C (1,500 hours). All of A's and B's demand is satisfied.
2. Evaluate the offer of 1,000 units of A at £50 each. Should it be accepted, and what would change your answer?
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Relevant cost is the variable cost, £36. Contribution per unit = £50 − £36 = £14, so on the face of it the order is profitable (1,000 × £14 = £14,000).
But the machine is a bottleneck, so contribution per machine hour decides: £14 ÷ 2 hours = £7.00 per hour.
Something must be displaced. The marginal hour is currently used for C, which earns £8.00 per hour. Accepting the order:
- gains 1,000 × £14 = £14,000
- loses 2,000 hours of C’s output = 667 units × £24 = £16,000
Net effect: profit falls by £2,000. Reject at £50. The breakeven price is where contribution per hour equals C's £8.00, i.e. £36 + (2 × £8) = £52 per unit. At £52 the company is indifferent; above £52 the order becomes worthwhile.
What would change the answer: spare capacity (e.g. if B's demand fell by 3,000 hours, any price above £36 adds profit); the order being recurring, which would justify expanding capacity; the risk of the £50 price leaking to existing customers; and any additional order-specific costs such as tooling or export packing.
3. The managing director argues that C should be dropped because its full cost of £86 exceeds its £80 price. Advise, with figures, and recommend how fixed overhead should be treated in the report.
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Dropping C would cut profit, not raise it. Under the current plan C absorbs 3,000 machine hours and earns £24,000 of contribution.
- Fixed overhead is £100,000 whatever happens. It is not avoidable by dropping C.
- The
lossof £6 per unit × 1,000 units = £6,000 is an artefact of charging £30 of absorbed overhead against C. - Dropping C frees 3,000 hours, but A's and B's demand is already fully met, so the hours have no alternative use in the short term (worth checking with marketing - if B's demand could grow, the freed hours might earn £18/hour).
Effect of closure: contribution falls by £24,000, fixed costs unchanged, profit falls from £26,000 to £2,000.
Recommendation: do not drop C. Instead investigate why sales of B are capped and whether C's price can rise - C's £8/hour is low because its price is weak relative to its variable cost, so a price increase or a machine-time reduction would fix the real problem.
Reporting: present contribution by product and by machine hour to the board, with fixed overhead shown as a period cost beneath the contribution line, plus a memo line of full cost per unit for pricing. A report built on absorbed full cost invites exactly this wrong decision.