A study has been conducted to determine if one of the departments in Parry Company should be discontinued. The contribution margin in the department is $50,000 per year. Fixed expenses charged to the department are $65,000 per year. It is estimated that $40,000 of these fixed expenses could be eliminated if the department is discontinued. These data indicate that if the department were discontinued, the company's overall operating income per year would change by how much?

Question

BlackTom AI · Accepted Answer

Contribution margin and avoidable (traceable) fixed costs determine the effect on overall operating income when a segment is discontinued.

1. Relevant knowledge points and concepts
- Contribution margin = Sales − Variable costs; it represents the amount available to cover fixed costs and profit. If a department is discontinued, its contribution margin is lost.
- Fixed costs can be avoidable (traceable to the department and eliminated if it closes) or unavoidable/common (remain even if the department closes). Only avoidable fixed costs affect the discontinuation decision.
- Change in overall operating income = (avoidable fixed costs saved) − (lost contribution margin).

2. Complete reasoning process step by step
- The department currently contributes $50,000 per year toward fixed costs and profit (contribution margin).
- The department is charged total fixed expenses of $65,000, but only $40,000 of those fixed expenses are avoidable if the department is discontinued. The remaining $25,000 (65,000 − 40,000) are unavoidable and will remain with the company.
- If discontinued, the company will lose the $50,000 contribution margin but will save $40,000 of fixed costs.

3. Calculations with intermediate steps
- Lost contribution margin = −$50,000
- Fixed costs saved = +$40,000
- Net change in operating income = (Fixed costs saved) + (Lost contribution margin)
  = $40,000 − $50,000
  = −$10,000

4. Why the correct answer is correct
Because the department’s contribution margin exceeds the avoidable fixed costs saved by $10,000, discontinuing the department would reduce overall operating income by $10,000 per year. The unavoidable $25,000 of fixed costs are irrelevant to this decision since they will remain regardless.

5. Why other multiple-choice options are incorrect
- Any answer showing an increase (±$10,000, +$15,000, +$25,000) is wrong because savings ($40,000) are less than the lost contribution margin ($50,000).
- A decrease of $25,000 would be the result only if no fixed costs were avoidable (or other numbers), which contradicts the given $40,000 avoidable amount.

6. Conclusion
The net effect is a decrease in operating income of $10,000 per year, which matches the provided correct answer: A decrease of $10,000.

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