There are two ways to make a product: plan A (fixed costs ¥10 million, variable cost ratio 60%) and plan B, which automates the production line (fixed costs ¥16 million, variable cost ratio 45%). Above a certain level of sales, plan B earns more profit than plan A. Which is that level?

Answer: C. ¥40 million

If sales are S (in ¥ million), the profit of plan A is 0.4S − 10 and that of plan B is 0.55S − 16. They are equal when 0.15S = 6, that is, S = ¥40 million (both profits are then ¥6 million). Above this, plan B, with its higher contribution margin ratio, increases profit faster and is better; below it, plan A, with its lower fixed costs, is better. An investment such as automation that raises fixed costs to lower the variable cost ratio pays off when sufficient sales can be expected.

• A. This divides the ¥6 million difference in fixed costs by plan A's contribution margin ratio of 0.4. It must be divided by the difference between the two contribution margin ratios (0.15).
• B. This is plan B's break-even sales (16 ÷ 0.55). At this level plan B's profit is zero, while plan A already earns about ¥1.64 million.
• C. Correct. It is the sales at which the two plans earn the same profit; above it, plan B is better.