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>
