Relevant costing for a special order
Lindqvist Furniture makes 8,000 chairs a year, using 80% of its 10,000-unit capacity. Normal selling price is $120. Per-unit cost at 8,000 units: direct materials $38, direct labour $24, variable overhead $9, fixed overhead $20 (total $91). A hotel chain offers to buy 2,000 chairs at $72 each, badged with the hotel's logo. Accepting requires a one-off logo die costing $18,000 and $4 per unit extra labour for the custom finish. The order would displace no normal sales, but the sales manager earns commission of 5% of revenue on all sales, and the factory would need overtime, raising the variable overhead rate on the special order by 50%.
1. Determine whether the special order should be accepted. Show the relevant cost build-up per unit and in total.
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Relevant costs are future, incremental cash flows that differ between alternatives. Fixed overhead at $20/unit is an allocated existing cost - it does not change, so it is excluded (capacity is available).
Relevant cost per unit:
- Direct materials $38
- Direct labour $24 + $4 custom finish = $28
- Variable overhead $9 × 1.5 = $13.50
- Sales commission 5% × $72 = $3.60
- Total relevant cost = $83.10
Plus one-off die $18,000.
Revenue 2,000 × $72 = $144,000 Relevant costs 2,000 × $83.10 = $166,200 Die = $18,000 Net result = $144,000 − $166,200 − $18,000 = −$40,200
Contribution per unit is $72 − $83.10 = −$11.10; the order loses money before the die. Reject at $72.
Note the trap: the naive comparison of $72 against the $91 full cost looks like a loss, while comparing $72 to variable cost of $71 looks like a small profit. Neither is correct - the custom labour, overtime overhead, commission and die must all be included.
2. Calculate the minimum price per unit Lindqvist should accept, and explain why the sales commission treatment matters.
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Let P be the price. For the order to break even:
2,000 × (P − 38 − 28 − 13.50 − 0.05P) − 18,000 = 0 2,000 × (0.95P − 79.50) = 18,000 0.95P − 79.50 = 9 0.95P = 88.50 P = $93.16 (approximately)
Check: revenue $186,315; commission $9,316; materials/labour/overhead 2,000 × $79.50 = $159,000; die $18,000. Contribution = $186,315 − $9,316 − $159,000 = $17,999, less die $18,000 ≈ 0. ✓
Why commission matters: the 5% commission is a variable cost that scales with price, so it changes the break-even algebra - it is not a fixed $3.60. Treating it as a flat amount at $72 would understate the required price. It also raises a behavioural issue: the sales manager has an incentive to accept low-margin orders because commission is paid on revenue, not profit. Management should consider basing commission on contribution so incentives align with the firm's interests.
Qualitative points: the order uses spare capacity and does not displace normal sales, so it is not automatically bad - but at $72 it destroys value. Counter-offer near $95–$100, and confirm the hotel will not resell chairs in competition with Lindqvist's normal market.