Zipee Inc.'s unit selling price is $90, unit variable costs are $40.50, fixed costs are $170,000, and current sales are 12,000 units. How much will income from operations change if sales increase by 5,000 units?

Question

BlackTom AI · Accepted Answer

Contribution margin per unit = $90 − $40.50 = $49.50.

1. Relevant knowledge points and concepts
- Contribution margin per unit (selling price minus variable cost) shows how much each unit sold contributes toward covering fixed costs and then to operating income.
- Fixed costs remain constant within the relevant range; therefore, a change in operating income from a change in sales volume equals the contribution margin per unit multiplied by the change in units sold.

2. Step-by-step reasoning
- Compute the contribution margin per unit.
- Multiply that margin by the increase in units (5,000) because fixed costs do not change.
- The resulting product is the change in income from operations.

3. Calculations (all intermediate steps)
- Unit selling price = $90.00
- Unit variable cost = $40.50
- Contribution margin per unit = $90.00 − $40.50 = $49.50
- Increase in units = 5,000
- Change in operating income = Contribution margin per unit × Increase in units
- Change in operating income = $49.50 × 5,000
- $49.50 × 5,000 = $49.50 × (1,000 × 5) = ($49.50 × 1,000) × 5 = $49,500 × 5 = $247,500

4. Why the correct answer is correct
Because fixed costs are unchanged, each additional unit sold contributes $49.50 directly to operating income. Selling 5,000 more units therefore increases operating income by 5,000 × $49.50 = $247,500.

5. Why the other options are incorrect
- "$125,000 decrease": Wrong sign and magnitude; an increase in units cannot decrease operating income when contribution margin is positive.
- "$75,000 increase": This would imply a contribution margin of $15 per unit ($75,000/5,000), which contradicts the actual margin of $49.50.
- "$175,000 increase": That would imply a contribution margin of $35 per unit ($175,000/5,000), which does not match the true margin.

6. Conclusion
The operating income will increase by $247,500, which matches the provided correct answer: $247,500 increase.

Zipee Inc.'s unit selling price is $90, unit variable costs are $40.50, fixed costs are $170,000, and current sales are 12,000 units. How much will income from operations change if sales increase by 5,000 units? 单项选择题

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