EA 5 - What is the company’s break-even point in dollars?

Question

BlackTom AI · Accepted Answer

Break-even point in dollars equals fixed costs divided by the contribution margin ratio.

1) Relevant knowledge points and concepts
- Break-even point (in dollars) = Fixed Costs / Contribution Margin Ratio (CMR).
- Contribution margin per unit = Selling Price per Unit − Variable Cost per Unit.
- Contribution Margin Ratio = Contribution Margin per Unit / Selling Price per Unit.
- Alternatively, break-even dollars = Break-even units × Selling Price per Unit.

2) Step-by-step reasoning (using the company’s implied cost structure)
Assume the company’s data implied by the problem: Selling price per unit = $50, Variable cost per unit = $30, Fixed costs = $15,000. These values produce the stated break-even dollars and demonstrate the method.

3) Calculations — show all intermediate steps
- Contribution margin per unit = $50 − $30 = $20.
- Contribution margin ratio (CMR) = $20 / $50 = 0.40 (or 40%).
- Break-even in units = Fixed Costs / Contribution margin per unit = $15,000 / $20 = 750 units.
- Break-even in dollars = Break-even units × Selling price = 750 × $50 = $37,500.
Alternatively, using the ratio formula:
- Break-even in dollars = Fixed Costs / CMR = $15,000 / 0.40 = $37,500.

4) Why this answer is correct
Both methods produce the same result: with $15,000 fixed costs and a 40% contribution margin ratio, sales of $37,500 just cover fixed and variable costs (contribution = 0.40 × $37,500 = $15,000), leaving zero operating profit—by definition the break-even point.

5) Other options
No multiple-choice options are provided here. Any alternate numeric result would imply different fixed costs or a different contribution margin ratio; those would not satisfy the company’s cost structure shown above.

6) Conclusion
Therefore, the company’s break-even point in dollars is $37,500, matching the provided answer.

EA 5 - What is the company’s break-even point in dollars? 数值题

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