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 company's break-even point in units sold.

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 company's break-even point in units sold.

BlackTom AI · Accepted Answer

Break-even in units = Fixed expenses ÷ Contribution margin per unit.

Relevant concepts:
- Contribution margin (CM) = Sales − Variable expenses. CM can be expressed in total, per unit, or as a ratio.
- Break-even point (units) = Fixed expenses ÷ CM per unit. Equivalently, break-even in dollars = Fixed expenses ÷ CM ratio, then divide by unit price to get units.

Step-by-step reasoning and calculations:
1. From the contribution format statement:
   - Sales = $75,000
   - Variable expenses = $45,000
   - Contribution margin (total) = $30,000 (confirmed by 75,000 − 45,000)
   - Fixed expenses = $36,000

2. Compute the contribution margin ratio (CM%):
   CM ratio = Total CM / Sales = $30,000 / $75,000 = 0.40 (or 40%).

3. Compute contribution margin per unit:
   Unit selling price = $15.
   CM per unit = Price × CM ratio = $15 × 0.40 = $6 per unit.
   (Alternatively compute CM per unit = Total CM / Units sold; but units sold are not needed because price and CM ratio give per-unit CM.)

4. Compute break-even in units:
   Break-even units = Fixed expenses / CM per unit = $36,000 / $6 = 6,000 units.

Why this is correct:
- At 6,000 units, total contribution = 6,000 × $6 = $36,000 which exactly covers fixed expenses, producing zero operating profit (break-even).

Why the other choices are incorrect (briefly):
- 8,000 units would require a smaller CM per unit (e.g., $36,000/8,000 = $4.50) which contradicts the given CM ratio and price.
- 7,500 units implies total contribution of $45,000 (7,500 × $6), which would exceed fixed costs and produce profit, not break-even.
- 5,000 units gives total contribution $30,000, which is less than fixed expenses, so would still produce a loss.

Conclusion: The break-even point is 6,000 units, matching 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 company's break-even point in units sold.单项选择题

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