A firm operated at 90% of capacity for the past year, during which fixed costs were $420,000, variable costs were 40% of sales, and sales were $1,000,000. Operating income was单项选择题
A
$180,000
B
$420,000
C
$1,080,000
D
$980,000

Question

A firm operated at 90% of capacity for the past year, during which fixed costs were $420,000, variable costs were 40% of sales, and sales were $1,000,000. Operating income was

BlackTom AI · Accepted Answer

Operating income = Sales − Variable costs − Fixed costs, so compute variable costs from the given percentage and subtract fixed costs.

1. Relevant knowledge and concepts
- Variable costs change with sales and are given as a percentage of sales (here, 40% of sales). 
- Fixed costs do not change with output in the relevant range (the $420,000 is the total fixed cost for the year).
- Operating income (also called operating profit) = Sales − Variable costs − Fixed costs.
- The fact that the firm operated at 90% of capacity affects per-unit fixed cost or capacity utilization analysis but does not change total fixed costs or the arithmetic with provided total sales and cost figures.

2. Step-by-step reasoning and calculations
- Given sales = $1,000,000.
- Variable costs = 40% of sales = 0.40 × $1,000,000.
  Intermediate step: 0.40 × $1,000,000 = $400,000.
- Contribution margin (Sales − Variable costs) = $1,000,000 − $400,000.
  Intermediate step: $1,000,000 − $400,000 = $600,000.
- Subtract fixed costs to find operating income: $600,000 − $420,000.
  Intermediate step: $600,000 − $420,000 = $180,000.

3. Why the correct answer is correct
- The algebra is straightforward: operating income equals the remaining revenue after covering variable costs and fixed costs. Using the numbers provided yields $180,000. The 90% capacity statement is extraneous for this calculation because total sales and total fixed costs are given.

4. Why the other options are incorrect
- $420,000: This equals the fixed costs, not operating income; it ignores variable costs.
- $1,080,000 and $980,000: Both exceed total sales ($1,000,000), so they cannot be operating income (operating income cannot exceed sales when variable costs are positive).

Conclusion: The operating income is $180,000, which matches the provided correct answer.

A firm operated at 90% of capacity for the past year, during which fixed costs were $420,000, variable costs were 40% of sales, and sales were $1,000,000. Operating income was单项选择题

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