Question

Nofly corporation sells three different models of a mosquito "zapper." model a12 sells for $50 and has variable costs of $35. model b22 sells for $100 and has variable costs of $70. model c124 sells for $400 and has variable costs of $300. the sales mix of the three models is a12, 60%; b22, 15%; and c124, 25%. if the company has fixed costs of $269,500, how many units of each model must the company sell in order to break even?

Answer 1

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
+ Model b22 CM per Unit × Model b22 Sales Mix Percentage
+ Model c124 CM per Unit × Model c124 Sales Mix Percentage
= Weighted Average Unit Contribution Margin (WACM)

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.

Total Fixed Cost $269,500 ÷ Weighted Average CM per Unit $38.50 Break-even Point in Units of Sales Mix 7,000

 

The next step is to calculate the number of units of each model at break-even point

Model a12 b22 c124 Sales Mix Ratio 60% 15% 25% × Total Break-even Units 7,000 7,000 7,000 Product Units at Break-even Point 4,200 1,050 1,750