Yard Tools manufactures lawnmowers, weed-trimmers, and chainsaws. Its sales mix and unit contribution margin are as follows. Sales Mix Unit Contribution Margin
Lawnmowers 20% $33
Weed-trimmers 50% $21
Chainsaws 30% $37

Yard Tools has fixed costs of $4,200,000.

Required:
Compute the number of units of each product that Yard Tools must sell in order to break even under this product mix.

Lawnmowers’ break-even point in units = 29,787 units

Weed-trimmers’ break-even point in units = 74,468 units

Chainsaws' break-even point in units = 44,681 unit

Explanation:

Given:

                                    Sales Mix              Unit Contribution Margin

Lawnmowers                 20%                                     $33

Weed-trimmers              50%                                     $21

Chainsaws                     30%                                     $37

The number of units of each product that Yard Tools must sell in order to break even under this product mix can be computed using Weighted-Average Contribution Margin Ratio as follows:

Weighted contribution margin = (Sales Mix of Lawnmowers * Unit Contribution Margin of Lawnmowers) + (Sales Mix of Weed-trimmers * Unit Contribution Margin of Weed-trimmers) + (Sales Mix of Chainsaws * Unit Contribution Margin of Chainsaws) = (20% * $33) + (50% * $21) + (30% * $37) = $28.20

Total break-even point in units for the company = Fixed cost / Weighted contribution margin = $4,200,000 / $28.20 = 148,936 units

Therefore, we have:

Lawnmowers’ break-even point in units = Sales Mix of Lawnmowers * Total break-even point in units for the company = 20% * 148,936 = 29,787 units

Weed-trimmers’ break-even point in units = Sales Mix of Weed-trimmers * Total break-even point in units for the company = 50% * 148,936 = 74,468 units

Chainsaw’s break-even point in units = Sales Mix of Chainsaws * Total break-even point in units for the company = 30% * 148,936 = 44,681 units

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