Matsunaga firms produce strawberries and raspberries. Annual fixed costs are $10,000. The variable cost is $0.50 per pint of strawberries and $1.40 per pint of raspberries. Strawberries sell for $1.00 per pint and raspberries for 2.00 per pint. If the dollar value of the sales is comprised of 50% strawberries and 50% raspberries, compute the break-even-point in dollars.

Question

BlackTom AI · Accepted Answer

Compute the weighted-average contribution margin per dollar of sales, since break-even in dollars equals Fixed Costs divided by the contribution margin ratio.

1) Relevant concepts
- Contribution margin per unit = Price − Variable cost.
- Contribution margin ratio (per dollar) = (Price − Variable cost) / Price.
- For a mix of products measured by dollar sales composition, use a weighted-average contribution margin ratio (weights = share of dollar sales).
- Break-even sales dollars = Fixed Costs / Weighted-average contribution margin ratio.

2) Step-by-step reasoning
- Find each product’s contribution margin and margin ratio.
- Use the 50%/50% sales-dollar mix to compute the weighted-average margin ratio.
- Divide fixed costs by that ratio to get break-even dollars.

3) Calculations (all intermediate steps)
- Strawberries: Price = $1.00, Variable cost = $0.50
  Contribution = $1.00 − $0.50 = $0.50
  Margin ratio = $0.50 / $1.00 = 0.50 (50%)
- Raspberries: Price = $2.00, Variable cost = $1.40
  Contribution = $2.00 − $1.40 = $0.60
  Margin ratio = $0.60 / $2.00 = 0.30 (30%)
- Weighted-average contribution margin ratio:
  = 0.5*(0.50) + 0.5*(0.30)
  = 0.25 + 0.15 = 0.40 (40%)
- Break-even in dollars:
  Fixed costs / CM ratio = $10,000 / 0.40 = $25,000

4) Why this is correct
Using dollar-based weights is appropriate because the problem states the sales mix in percentage of dollar value. The weighted-average margin ratio tells how much contribution is generated per dollar of mixed sales; dividing fixed costs by that rate gives the required sales dollars to cover fixed costs.

5) Why the other options are incorrect
- $27,272 would result from a different (incorrect) margin ratio (~36.7%), not supported by given prices/costs.
- $10,000 would imply a 100% contribution margin (no variable costs), which is false.
- $18,181 would correspond to a margin ratio of 55% (10,000/18,181 ≈ 0.55), inconsistent with the calculated mix.

6) Conclusion
The break-even point in dollars is $25,000, which matches the provided answer.

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