Question

Lindon Company is the exclusive distributor for an automotive product that sells for $54.00 per unit and has a CM ratio of 30%. The company’s fixed expenses are $388,800 per year. The company plans to sell 28,600 units this year. Required: 1. What are the variable expenses per unit? 2. What is the break-even point in unit sales and in dollar sales? 3. What amount of unit sales and dollar sales is required to attain a target profit of $226,800 per year? 4. Assume that by using a more efficient shipper, the company is able to reduce its variable expenses by $5.40 per unit. What is the company’s new break-even point in unit sales and in dollar sales?

Answer 1

1.

Variable costs ratio = 1 - Contribution margin ratio

= 1 - 0.3

= 0.7

Variable expenses per unit = Selling price per unit * Variable costs ratio

= $54 * 0.7

= $37.8

2.

Contribution margin per unit = Selling price per unit - Variable expenses per unit

= $54 - $37.8

= $16.2

Break-even point in unit sales = Fixed expenses / Contribution margin per unit

= $388,800 / $16.2

= 24,000 units

Break-even point in dollar sales = Fixed expenses / Contribution margin ratio

= $388,800 / 0.3

= $1,296,000

3.

Unit sales required to attain a target profit = (Fixed expenses + Target profit) / Contribution margin per unit

= ($388,800 + $226,800) / $16.2

= 38,000 units

Dollar sales required to attain a target profit = (Fixed expenses + Target profit) / Contribution margin ratio

= ($388,800 + $226,800) / 0.3

= $2,052,000

4.

Variable expenses per unit = $37.8 - $5.4 = $32.4

Contribution margin per unit = Selling price per unit - Variable expenses per unit

= $54 - $32.4

= $21.6

Contribution margin ratio = Contribution margin per unit / Selling price per unit

= $21.6 / $54

= 0.4

Break-even point in unit sales = Fixed expenses / Contribution margin per unit

= $388,800 / $21.6

= 18,000 units

Break-even point in dollar sales = Fixed expenses / Contribution margin ratio

= $388,800 / 0.4

= $972,000