Make-or-Buy Decision with a Scarce Machine Resource
Benin Rubber Products Ltd makes two components, X and Y, on the same machine, which has a capacity of 30,000 hours per year. Demand for X is 10,000 units and for Y is 8,000 units. Product X sells for ₦5,000 and has variable cost of ₦2,600; it uses 2 machine hours. Product Y sells for ₦7,000 and has variable cost of ₦4,000; it uses 3 machine hours. Fixed costs are ₦12m per year and are unaffected by the product mix. An external supplier has offered to supply up to 7,000 units of X per year at ₦3,600 each. The production manager wants to accept the offer because ₦3,600 is below the selling price of X. The sales director opposes it because the variable cost of X is only ₦2,600.
1. Determine the optimal production plan without the supplier and calculate total contribution and profit.
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Contribution per unit is selling price less variable cost: X = ₦5,000 − ₦2,600 = ₦2,400; Y = ₦7,000 − ₦4,000 = ₦3,000. Contribution per machine hour is X = ₦2,400 ÷ 2 = ₦1,200; Y = ₦3,000 ÷ 3 = ₦1,000. Because machine hours are the scarce resource, rank X first. Produce all 10,000 units of X using 20,000 hours. The remaining 10,000 hours produce 10,000 ÷ 3 = 3,333 units of Y (ignoring fractional units). Total contribution is (10,000 × ₦2,400) + (3,333 × ₦3,000) = ₦24m + ₦9.999m = ₦33.999m. Fixed costs are ₦12m, so profit is ₦21.999m. The key reasoning is that X generates more contribution per constrained hour than Y, even though Y has a higher contribution per unit. Ranking by contribution per unit would be wrong because it ignores the machine-hour constraint.
2. Evaluate the supplier offer using relevant costing and determine how many units of X should be outsourced.
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Making X in-house uses 2 hours and earns contribution of ₦2,400. If X is outsourced, those 2 hours can be used to make Y. Each unit of Y needs 3 hours and earns ₦3,000, so 2 hours produce 2/3 of a unit of Y and earn 2/3 × ₦3,000 = ₦2,000 of contribution. The relevant cost of making X is therefore the variable cost of ₦2,600 plus the opportunity cost of ₦2,000 = ₦4,600. The supplier price is ₦3,600, so outsourcing saves ₦1,000 per unit of X. The company should outsource as many units as possible until the freed hours are fully used to satisfy unmet Y demand. Without outsourcing, Y production is 3,333 units, leaving a gap of 8,000 − 3,333 = 4,667 units. That gap needs 4,667 × 3 = 14,001 hours. Each outsourced X frees 2 hours, so up to 7,000 units of X can be outsourced (the supplier’s limit). If 7,000 units are outsourced, in-house X is 3,000 units using 6,000 hours, leaving 24,000 hours for 8,000 units of Y. Contribution becomes: outsourced X 7,000 × (₦5,000 − ₦3,600) = ₦9.8m; in-house X 3,000 × ₦2,400 = ₦7.2m; Y 8,000 × ₦3,000 = ₦24m; total ₦41m. Profit rises to ₦29m, an increase of ₦7.001m.
3. Discuss the qualitative factors that the board should consider before accepting the outsourcing offer.
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The financial analysis favours outsourcing, but the board must also consider quality, reliability and control. The supplier may not maintain the same quality standards, which could damage the company’s reputation and lead to warranty claims. Delivery reliability is critical because the company is increasing Y production to full capacity; any supplier delay could disrupt customer orders. The company may lose technical knowledge and bargaining power if it stops making 7,000 units of X, and the supplier may increase prices after the company becomes dependent. There may be workforce implications, including idle labour, redundancies or industrial action. Confidentiality and intellectual property may be at risk if the component design is shared with the supplier. The board should also consider whether the supplier can scale up, whether the offer price is fixed, and whether the company can return to in-house production if needed. A pilot arrangement with strict service-level agreements and quality checks would reduce risk.