Which of the following statements is true?
1. If the variable expense per unit decreases, and all other factors remain the same, the contribution margin ratio will increase.
II. The smaller the contribution margin ratio, the smaller the amount of sales required to cover a given amount of fixed expenses.
A Only statement II is true.
B Both statements are true.
C Only statement I is true.
D Neither statement is true.
The correct answer and explanation is :
Correct Answer:
C. Only statement I is true.
Explanation:
- Statement I: If the variable expense per unit decreases, and all other factors remain the same, the contribution margin ratio will increase.
- The contribution margin ratio (CMR) is calculated as:
[
\text{CMR} = \frac{\text{Sales Price per Unit} – \text{Variable Cost per Unit}}{\text{Sales Price per Unit}}
] - If the variable expense per unit decreases, the numerator (( \text{Sales Price} – \text{Variable Cost} ), which is the contribution margin per unit) increases, leading to a higher contribution margin ratio.
- Since fixed costs and sales price remain constant, the contribution margin ratio must increase when variable expenses decrease.
- Thus, Statement I is true.
- Statement II: The smaller the contribution margin ratio, the smaller the amount of sales required to cover a given amount of fixed expenses.
- The break-even sales are calculated as:
[
\text{Break-even Sales} = \frac{\text{Fixed Costs}}{\text{CMR}}
] - A smaller contribution margin ratio means that more sales are required to cover fixed costs, not less.
- This contradicts the statement, making Statement II false.
Conclusion:
Since only Statement I is correct, the correct answer is C: Only statement I is true
