Pennick Engineering: capacity constraint and a marginal special order
Pennick Engineering runs a single CNC machining cell with 8,000 hours available next quarter and no prospect of subcontracting or extra shifts. It makes two products. Product A sells for £78, uses £48 of variable cost and requires 2 machining hours. Product B sells for £120, uses £76 of variable cost and requires 4 machining hours. Maximum quarterly demand is 2,600 units of A and 1,200 units of B. A long-standing contract obliges Pennick to supply at least 900 units of B each quarter; there is no penalty clause, but the customer is strategically important. Fixed costs of £120,000 per quarter are absorbed at £15 per machining hour. A new customer has offered to buy 500 units of a variant at £82 each; variable cost would be £60 per unit and each unit needs 1.5 machining hours. The production director wants to reject the order because £82 is below the £82.50 full absorption cost, while the sales director argues that any order contributing towards fixed costs is worth taking.
1. Determine the optimal production plan for next quarter and the total contribution it generates.
Read the worked answer
Contribution per unit: A = £78 − £48 = £30, over 2 hours → £15 per machine hour. B = £120 − £76 = £44, over 4 hours → £11 per machine hour.
Rank A first. The B contract consumes 900 × 4 = 3,600 hours and earns 900 × £44 = £39,600. Remaining capacity = 8,000 − 3,600 = 4,400 hours, giving 4,400 ÷ 2 = 2,200 units of A (below maximum demand of 2,600), contribution 2,200 × £30 = £66,000.
Total contribution = £105,600; less fixed costs £120,000 = loss of £14,400.
Two points the board should hear: it is correct to leave 400 units of A demand unmet, because capacity is genuinely exhausted; and no B should be made above the contract minimum, because every hour switched from A to B forfeits £4 (15 − 11). The £15 absorption rate is irrelevant to the plan - fixed costs are identical under every feasible mix, so only contribution per limiting factor drives the decision.
2. Evaluate the 500-unit special order at £82, showing the opportunity cost involved, and state the minimum acceptable price.
Read the worked answer
Order contribution = 500 × (£82 − £60) = £11,000; hours required = 500 × 1.5 = 750 hours.
The hours must be released by A, since B is already at its strategic minimum. 750 hours = 375 units of A, forfeiting 375 × £30 = £11,250. Net effect = £11,000 − £11,250 = −£250: reject at £82.
Minimum price: contribution needed = £11,250 ÷ 500 = £22.50 per unit → £82.50. That happens to equal the full absorption cost (£60 + 1.5 × £15), but only because the opportunity cost per hour coincides with the absorption rate - a coincidence, not a principle. If the order could displace B instead, the opportunity cost would be 187.5 units × £44 = £8,250 and the order would be worth £2,750; the contract rules that out.
Note the sales director's rule is not wrong in principle - contribution does help cover fixed costs - but only where capacity is idle. Here it is not. Counter-offer at £84–£85 and probe whether £82 is a one-off or an opening price expectation.