The first step you need to do to solve this problem is to
calculate the contribution margin per unit for each model:
Model a12 b22 c124
Sales Price per unit 50 100 400
Less: Variable Cost per unit 35 70 300
Contribution Margin per unit 15 30 100
The next step is to calculate the weighted-average
contribution margin per unit for the sales mix using the following formula:
Model a12 CM per Unit ×
Model a12 Sales Mix Percentage<span>
+ Model b22 CM per Unit × Model b22 Sales Mix Percentage
+ Model c124 CM per Unit × Model c124 Sales Mix Percentage
<span>= Weighted Average Unit Contribution Margin (WACM)</span></span>
Contribution Margin per unit 15 30 100
X Sales Mix Percentage 60% 15% 25%
WACM 9 4.5 25
Weighted Average Unit Contribution Margin (sum) 38.5
The next step is to find the break-even point using the
WACM.
<span>
<span><span>
<span>
Total Fixed Cost
</span>
<span>
$269,500
</span>
</span>
<span>
<span>
÷ Weighted Average CM per Unit
</span>
<span>
$38.50
</span>
</span>
<span>
<span>
Break-even Point in Units of Sales Mix
</span>
<span>
7,000
</span>
</span>
</span></span>
The next step is to calculate the number of units of each
model at break-even point
<span>
<span><span>
<span>
Model
</span>
<span>
a12
</span>
<span>
b22
</span>
<span>
c124
</span>
</span>
<span>
<span>
Sales Mix Ratio
</span>
<span>
60%
</span>
<span>
15%
</span>
<span>
25%
</span>
</span>
<span>
<span>
× Total Break-even Units
</span>
<span>
7,000
</span>
<span>
7,000
</span>
<span>
7,000
</span>
</span>
<span>
<span>
Product Units at Break-even Point
</span>
<span>
4,200
</span>
<span>
1,050
</span>
<span>
1,750
</span>
</span>
</span></span>
<span> </span>