At the current level of operation, a company’s fixed costs are $10,000 and its contribution margin ratio is 0.20. If the company drops its selling price by 10%, its volume will double. If the company decides to drop selling prices by 10%, then:

Question

BlackTom AI · Accepted Answer

Let the original selling price per unit be P, variable cost per unit be v, and original quantity sold be q. The contribution margin ratio (CMR) is (P − v)/P = 0.20, so v = 0.80P.

1) Relevant concepts
- Contribution margin per unit = P − v.
- Contribution margin ratio = (P − v)/P.
- Profit = (contribution per unit × quantity) − fixed costs.
- A change in selling price does not change variable cost per unit unless stated.

2) Step-by-step reasoning and calculations
- Original contribution per unit = P − v = P − 0.80P = 0.20P.
- Original total contribution = 0.20P × q = 0.20Pq.
- Original profit = total contribution − fixed costs = 0.20Pq − 10,000.

Now the firm cuts price by 10%: new price P' = 0.9P. Variable cost per unit stays v = 0.80P (unchanged in dollars).
- New contribution per unit = P' − v = 0.9P − 0.80P = 0.10P.
- Volume doubles: q' = 2q.
- New total contribution = 0.10P × (2q) = 0.20Pq.
- New profit = new total contribution − fixed costs = 0.20Pq − 10,000.

3) Intermediate steps shown
- v = 0.80P (from CMR = 0.20)
- P' = 0.9P
- New contribution per unit = 0.9P − 0.8P = 0.1P
- New total contribution = 0.1P × 2q = 0.2Pq

4) Why the correct answer is correct
Because the per-unit contribution is halved (from 0.20P to 0.10P) exactly as quantity doubles, total contribution remains unchanged. With fixed costs unchanged, profit stays the same.

5) Why other options are incorrect
- “Profit will increase”: incorrect because total contribution does not rise.
- “Profit will decrease”: incorrect because total contribution does not fall.
- “Depends on level of sales”: incorrect here because the specific change (price −10%, volume ×2) yields a deterministic offset; profit is independent of the original sales level in this scenario.

Conclusion: The firm’s profit will remain unchanged, which matches the provided answer.

At the current level of operation, a company’s fixed costs are $10,000 and its contribution margin ratio is 0.20. If the company drops its selling price by 10%, its volume will double. If the company decides to drop selling prices by 10%, then:单项选择题

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