Relevant Costing of a One-Off Order in a Machine-Constrained Plant
Perrin Components makes products X and Z on the same machine. Budgeted output is 20,000 X and 15,000 Z, using 36,000 machine hours against a capacity of 40,000. Budgeted fixed production overhead is £1,440,000, absorbed on machine hours at £40. X sells for £85, uses 1.2 machine hours and has a prime cost of £38; Z sells for £120, uses 1.6 hours and has a prime cost of £52. A customer has offered a one-off order for 6,000 units of a modified X at £62 each. The order would use 0.9 machine hours per unit, require £48,000 of tooling that has no other use, and extra variable cost of £6 per unit. It can only be met by cutting output of Z. The sales director says it must be profitable because £62 exceeds the £44 variable cost; the financial controller says it loses money because £62 is below the £80 full cost; the production manager notes 4,000 idle hours.
1. Calculate the relevant cost of accepting the order and the minimum price per unit at which acceptance would leave the company no worse off.
Read the worked answer
Principle. Include only future cash flows that differ between accepting and rejecting. Exclude absorbed fixed overhead, which does not change in total, and exclude any past cost.
Variable cost. 6,000 x (£38 prime + £6 modification) = £264,000, i.e. £44 per unit.
Tooling. £48,000 incremental, with no alternative use, so it is relevant.
Machine time and opportunity cost. The order needs 6,000 x 0.9 = 5,400 hours. Idle capacity is 4,000 hours, so 1,400 hours must be taken from Z. Z earns contribution of £120 - £52 = £68 per unit over 1.6 hours, i.e. £42.50 per machine hour. Opportunity cost = 1,400 x £42.50 = £59,500, equivalent to 875 units of Z.
Total relevant cost. £264,000 + £48,000 + £59,500 = £371,500, or £61.92 per unit.
Minimum price. £61.92 per unit, assuming the displaced Z output cannot be sold later and the 4,000 idle hours are genuinely available. At £62 the order adds only 6,000 x £0.08 = £500 to profit, which is within estimation error and should not be treated as a clear financial gain.
2. Reconcile the sales director's and controller's positions and recommend a decision with conditions.
Read the worked answer
The controller's £80. Variable cost £44 plus 0.9 hours x £40 absorption = £36, giving £80. The £40 per hour is a recovery rate for a fixed pool of £1,440,000. Accepting the order does not increase that pool, so charging £36 per unit to the order manufactures a loss of £18 per unit while leaving company overhead unchanged. Absorption costing is appropriate for inventory valuation, not for a short-term accept/reject decision with spare capacity.
The sales director's £44. This is also wrong, because the plant is capacity-constrained in the relevant sense: 1,400 hours of Z must be sacrificed at £42.50 per hour. Ignoring the opportunity cost overstates the benefit of the order by £59,500.
Recommendation. Financially the order is effectively neutral (£500), so the decision turns on qualitative factors:
- Whether £62 becomes a reference price and undermines the £85 list price for regular X;
- Whether disrupting 875 units of Z risks existing customers and future orders;
- Whether the tooling has any residual or future use;
- Whether the 4,000 idle hours are truly available after maintenance and demand variability;
- Strategic value of the new customer and the reliability of the volume forecast.
Conditions for acceptance. Written confirmation that the price is one-off; a check that Z demand is genuinely soft; and a price of at least £65 to give a meaningful buffer (6,000 x £3.08 = £18,500). Otherwise decline, or offer a smaller volume that uses only idle hours.