Tanner Company's most recent contribution format income statement is presented below:

The company sells its only product for $15 per unit. There were no beginning or ending inventories.

Compute the total variable expenses at the break-even point.

Question

Tanner Company's most recent contribution format income statement is presented below:

The company sells its only product for $15 per unit. There were no beginning or ending inventories.

Compute the total variable expenses at the break-even point.

BlackTom AI · Accepted Answer

Contribution margin ratio is the key: from the statement CM = $30,000 on Sales $75,000 so CM ratio = 30,000/75,000 = 0.40 (40%).

1. Relevant knowledge points and concepts
- Contribution margin (CM) = Sales − Variable expenses.
- Contribution margin ratio = CM / Sales.
- Break-even sales (dollars) = Fixed expenses / CM ratio.
- Variable expense ratio = 1 − CM ratio (or Variable expenses / Sales).
- Variable expenses at break-even = Break-even sales × Variable expense ratio (or units at break-even × variable cost per unit).

2. Step‑by‑step reasoning
- Use the provided contribution format income statement to compute CM ratio and variable ratio.
- Compute break-even sales using fixed expenses and CM ratio.
- Convert break-even sales to total variable expenses using the variable expense ratio (or compute per unit and multiply by break-even units).

3. Calculations (all intermediate steps)
- From statement: Sales = $75,000; Variable expenses = $45,000; CM = $30,000; Fixed expenses = $36,000.
- CM ratio = CM / Sales = 30,000 / 75,000 = 0.40 (40%).
- Variable expense ratio = 1 − CM ratio = 1 − 0.40 = 0.60 (60%).
- Break-even sales = Fixed expenses / CM ratio = 36,000 / 0.40 = $90,000.
- Variable expenses at break-even = Break-even sales × Variable expense ratio = 90,000 × 0.60 = $54,000.
Alternate per‑unit method:
- Selling price per unit = $15. Variable cost per unit = 0.60 × 15 = $9. CM per unit = 15 − 9 = $6.
- Break-even units = Fixed / CM per unit = 36,000 / 6 = 6,000 units.
- Variable expenses = 6,000 units × $9 = $54,000.

4. Why the correct answer is correct
The $54,000 equals the total variable costs when sales just cover fixed costs (break-even). It follows directly from the fixed expenses divided by the CM ratio to find break-even sales, then applying the 60% variable cost proportion.

5. Why other options are incorrect
- $60,000 would result from incorrect break-even sales ($100,000) or a wrong ratio; it does not match fixed/CM calculations.
- $75,000 is current total sales, not variable costs at break-even.
- $112,500 is far larger than required and inconsistent with the given ratios and fixed costs.

6. Conclusion
Therefore, total variable expenses at break-even = $54,000, which matches the provided correct answer.

Tanner Company's most recent contribution format income statement is presented below: The company sells its only product for $15 per unit. There were no beginning or ending inventories. Compute the total variable expenses at the break-even point. 单项选择题

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