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 % $30
Weed-trimmers 50 % $20
Chainsaws 30 % $40

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

Compute the number of units of each product that Yard Tools must sell in order to break even under this product mix. (Use Weighted-Average Contribution Margin Ratio rounded to 2 decimal places e.g. 0.25 and round final answers to 0 decimal places, e.g. 2,510.)

Lawnmowers


units
Weed-trimmers


units
Chainsaws


units

Answer 1

Lawnmowers= 30,000

Weed-trimmers= 75,000

Chainsaws= 45,000

Step-by-step explanation:

First, we need to calculate the weighted average contribution margin:

Weighted average contribution margin= sales proportion*unitary contribution margin

Weighted average contribution margin= (0.2*30) + (0.5*20) + (0.3*40)

Weighted average contribution margin= $28

Now, the break-even point in units for the whole company:

Break-even point (units)= Total fixed costs / Weighted average contribution margin

Break-even point (units)= 4,200,000 / 28

Break-even point (units)= 150,000

Finally, the number of units to be sold for each product:

Lawnmowers= 0.20*150,000= 30,000

Weed-trimmers= 0.5*150,000= 75,000

Chainsaws= 0.3*150,000= 45,000