Question

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 % $34
Weed-trimmers 50 % $24
Chainsaws 30 % $37
Yard total has fixed cost of $6,836,000

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

Answer 1

Lawnmowers= 45,726

Weed-trimmers= 114,314

Chainsaws= 68,589

Step-by-step explanation:

Giving the following information:

Sales Mix - Unit Contribution Margin

Lawnmowers 20 % $34

Weed-trimmers 50 % $24

Chainsaws 30 % $37

Yard total has fixed cost of $6,836,000

Based on the weighted average sales participation and the unit contribution margin, we can calculate the weighted average contribution margin for the whole company. We need it to calculate the break-even point in units.

Break-even point (units)= Total fixed costs / (weighted average selling price - weighted average variable expense)

Weighted average contribution margin= sales participation per product* unitary contribution margin

Weighted average contribution margin= (0.20*34) + (0.5*24) + (0.3*37)= 29.9

Break-even point (units)= 6,836,000/ 29.9= 228,629 units

Now, we can calculate the required units for each product:

Lawnmowers= 0.20*228,629= 45,726

Weed-trimmers= 0.50*228,629= 114,314

Chainsaws= 0.3*228,629= 68,589