sales mix and break-even analysis

conley company has fixed costs of $17,802,000. the unit selling price, variable cost per unit, and contribution margin per unit for the companys two products follow:

product model | selling price | variable cost per unit | contribution margin per unit
--- | --- | --- | ---
yankee | $180 | $99 | $81
zoro | 225 | 135 | 90

the sales mix for products yankee and zoro is 80% and 20%, respectively. determine the break-even point in units of yankee and zoro.

a. product model yankee: units
b. product model zoro: units

Question

sales mix and break-even analysis

conley company has fixed costs of $17,802,000. the unit selling price, variable cost per unit, and contribution margin per unit for the companys two products follow:

product model | selling price | variable cost per unit | contribution margin per unit
--- | --- | --- | ---
yankee | $180 | $99 | $81
zoro | 225 | 135 | 90

the sales mix for products yankee and zoro is 80% and 20%, respectively. determine the break-even point in units of yankee and zoro.

a. product model yankee:   units
b. product model zoro:   units

Accepted Answer

{ "quality": "clear", "question_count": 2, "skills_matched": [ "step_cot", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Fixed Cost", "Break-Even Analysis" ], "new_concepts": [ "Sales Mix", "Weighted Average Contribution Margin" ], "current_concepts": [ "Fixed Cost", "Break-Even Analysis", "Sales Mix", "Weighted Average Contribution Margin" ] } ## Calculate the weighted-average contribution margin per unit $$ \begin{aligned} \text{WACM} &= (\text{CM}_{\text{Yankee}} \times \text{Mix}_{\text{Yankee}}) + (\text{CM}_{\text{Zoro}} \times \text{Mix}_{\text{Zoro}}) \ &= (\$81 \times 0.80) + (\$90 \times 0.20) \ &= \$64.80 + \$18.00 \ &= \$82.80 \end{aligned} $$ ## Determine the total break-even units $$ \begin{aligned} \text{Total Break-Even Units} &= \frac{\text{Fixed Costs}}{\text{WACM}} \ &= \frac{\$17,802,000}{\$82.80} \ &= 215,000 \text{ units} \end{aligned} $$ ## Calculate break-even units for each product $$ \begin{aligned} \text{Yankee Break-Even Units} &= 215,000 \times 0.80 = 172,000 \text{ units} \ \text{Zoro Break-Even Units} &= 215,000 \times 0.20 = 43,000 \text{ units} \end{aligned} $$ ## Question a a. Product Model Yankee: 172,000 units ## Question b b. Product Model Zoro: 43,000 units { "subject": "Business", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Business", "Accounting", "Cost-Volume-Profit Analysis" ] }

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QUESTION IMAGE

Question

Explanation:

Calculate the weighted-average contribution margin per unit

Determine the total break-even units

Calculate break-even units for each product

Answer:

Question a

Question b