If fixed costs increased and variable costs per unit decreased, the break-even point

Question

BlackTom AI · Accepted Answer

Break-even point in units equals Fixed Costs divided by Contribution Margin per unit (CM = Price − Variable Cost per unit). This relationship is the key concept.

1) Relevant concepts:
- Break-even units = Fixed Costs / (Price − Variable Cost per unit).
- An increase in Fixed Costs raises the numerator, tending to raise the break-even point.
- A decrease in Variable Cost per unit raises the contribution margin (denominator), tending to lower the break-even point.
Because both numerator and denominator change in opposite directions, the net effect depends on magnitudes.

2) Step-by-step reasoning with calculations:
- Let initial Fixed Costs = FC0, initial Variable Cost = VC0, Price = P. Initial BE0 = FC0 / (P − VC0).
- After the changes: FC1 > FC0 and VC1 < VC0, so BE1 = FC1 / (P − VC1).
- Without numerical values for FC0, FC1, VC0, VC1, and P we cannot compute BE1 − BE0.

3) Examples showing all possible outcomes:
- Example where BE remains the same: FC0 = 1000, P = 10, VC0 = 8 → BE0 = 1000/(10−8)=500. If FC1 = 1500 and VC1 = 7 → BE1 = 1500/(10−7)=1500/3=500 (no change).
- Example where BE decreases: FC1 = 1200, VC1 = 7 → BE1 = 1200/3=400 (BE falls from 500 to 400).
- Example where BE increases: FC1 = 2000, VC1 = 7 → BE1 = 2000/3 ≈ 667 (BE rises).

4) Why the correct answer is correct:
Because the effect of higher fixed costs (increasing BE) and lower variable costs (decreasing BE) work in opposite directions, the direction of the net change cannot be determined without specific numeric magnitudes.

5) Why other options are incorrect:
- "Would increase": assumes fixed-cost effect dominates—unsupported without numbers.
- "Would decrease": assumes variable-cost effect dominates—unsupported.
- "Would remain the same": only true in special cases where the changes exactly offset; not guaranteed.

Conclusion: Therefore, the correct choice is "cannot be determined from the data given," which matches the provided answer.

If fixed costs increased and variable costs per unit decreased, the break-even point单项选择题

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