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Break-Even Point Between Two Machines

Easybreak-evencost comparison
Machine A has fixed costs of $40,000 per year and variable costs of $12 per unit. Machine B has fixed costs of $25,000 per year and $18 per unit. The annual output at which both cost the same is most nearly:
  1. A2,167 units
  2. B3,333 units
  3. C2,500 units
  4. D4,167 units
Show solution

Answer: C. 2,500 units

Equation: each machine's annual cost is fixed cost + (variable cost per unit) × Q. At break-even the two costs are equal: FA + vA·Q = FB + vB·Q, so Q = (FA − FB)/(vB − vA). Values: FA = $40,000 and vA = $12/unit for machine A; FB = $25,000 and vB = $18/unit for machine B. Step 1: difference in fixed costs, 40,000 − 25,000 = $15,000. Step 2: difference in variable costs, 18 − 12 = $6 per unit. Step 3: Q = 15,000/6 = 2,500 units. Below 2,500 units machine B is cheaper; above it, machine A is. 2,167 units adds the fixed costs and the variable costs instead of subtracting. 3,333 units uses machine A alone (40,000/12). 4,167 units divides B's fixed cost by the cost difference.
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