Spare Capacity, a One-off Export Order and a Price Rise
Zaria Packaging Ltd produces cartons for food processors. Plant capacity is 120,000 cartons a year and current output is 96,000. Each carton sells for ₦1,500; variable cost is ₦900 and annual fixed cost is ₦48,000,000, giving a profit of ₦9,600,000.
A cocoa exporter offers a one-off order of 20,000 cartons at ₦1,050 each. The export specification adds ₦50 a carton to variable cost, and the order requires a die-cutting machine to be hired for ₦4,000,000 for the year. The production manager rejects the idea: '₦1,050 is below our cost of ₦1,400 a carton, so we would lose money on every box.' The sales director, whose bonus is 2% of revenue, wants to accept in order to 'grow the top line'.
Separately, marketing estimates that raising the domestic price by 10%, to ₦1,650, would reduce domestic volume by 12%. Fixed costs would not change.
1. Compute the break-even point and margin of safety, and comment on the production manager's ₦1,400 figure.
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Contribution and break-even Unit contribution = ₦1,500 − ₦900 = ₦600 (40% of sales). Break-even = ₦48,000,000 ÷ ₦600 = 80,000 cartons, or ₦120,000,000 of revenue, which is 66.7% of capacity.
Margin of safety 96,000 − 80,000 = 16,000 cartons (16.7%); profit = 16,000 × ₦600 = ₦9,600,000, which agrees with the stated figure.
The ₦1,400 'cost' ₦1,400 = ₦900 variable + (₦48,000,000 ÷ 96,000) = ₦900 + ₦500. That is an average full cost at one particular volume, not a relevant cost for a decision. The ₦48,000,000 of fixed cost is committed and will be incurred whether or not the export order is accepted, so it cannot be charged against the order again - doing so double-counts it.
For a spare-capacity decision the only relevant figures are the incremental cash flows: the extra ₦950 variable cost per carton and the ₦4,000,000 hire cost. Any price above the incremental cost adds to profit. The manager's rule would also imply rejecting any order below ₦1,400, which is exactly the reasoning that leaves 24,000 cartons of capacity idle.
2. Evaluate the export order and give a recommendation with conditions.
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Incremental analysis Incremental revenue: 20,000 × ₦1,050 = ₦21,000,000 Incremental variable cost: 20,000 × ₦950 = (₦19,000,000) Incremental contribution: ₦2,000,000 Incremental fixed cost (machine hire): (₦4,000,000) Net effect: (₦2,000,000) - reject as offered.
Where the deal would work Break-even price = ₦950 + (4,000,000 ÷ 20,000) = ₦1,150. At ₦1,200: (20,000 × ₦250) − ₦4,000,000 = ₦1,000,000 profit on the order. The required volume at ₦1,050 would be 4,000,000 ÷ 100 = 40,000 cartons, which exceeds both the order size and the 24,000 cartons of spare capacity.
Capacity check 120,000 − 96,000 = 24,000 spare, so 20,000 fits without displacing domestic sales - this is the assumption the whole analysis rests on. If domestic demand rose, the export order would displace ₦600 contribution per carton and become far worse.
Recommendation and conditions Reject at ₦1,050; counter-offer at ₦1,200 or above, or ask the exporter to share the machine cost. Before signing, consider: whether the die-cutter can also serve domestic work or be resold (which would reduce its effective cost); foreign-exchange and payment risk; whether a low export price could leak back and undermine the ₦1,500 domestic price; and the strategic value of an export reference customer against the risk of setting a low-price precedent. The sales director's 'grow the top line' rationale is not a reason to accept a negative-contribution order.
3. Assess the proposed 10% price rise, reconcile the revenue and profit effects, and comment on the sales director's incentive.
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Elasticity PED = %Δ quantity ÷ %Δ price = 12% ÷ 10% = 1.2 - demand is elastic, so revenue should fall.
Revenue New volume = 96,000 × 0.88 = 84,480 cartons. New revenue = 84,480 × ₦1,650 = ₦139,392,000, against ₦144,000,000 now - a fall of ₦4,608,000 (−3.2%). The elasticity prediction is confirmed.
Profit New unit contribution = ₦1,650 − ₦900 = ₦750 (up 25%). Total contribution = 84,480 × ₦750 = ₦63,360,000, against ₦57,600,000 - up ₦5,760,000. Less fixed costs ₦48,000,000 → profit = ₦15,360,000, against ₦9,600,000, a 60% increase.
Reconciliation A 12% volume loss against a 25% rise in unit contribution leaves total contribution higher. Elasticity governs revenue; the decision rule is total contribution. This is the trap: 'demand is elastic, therefore do not raise price' is only correct if variable cost is zero.
Caveats The 12% estimate is unverified and competitor reaction is unknown; test the increase on one segment or region first, and watch for volume drift.
Agency problem The sales director's 2% revenue bonus would make him oppose a decision that raises profit by 60% simply because revenue falls 3.2%. That is a goal-congruence failure caused by the performance measure, not by disloyalty. Rebase the bonus on contribution or gross margin, and note that a director also owes a fiduciary duty to act in the company's interest rather than in the interest of his own bonus.