Question

Super Sales Company is the exclusive distributor for a high-quality knapsack. The product sells for $60 per unit and has a CM ratio of 40%. The company's fixed expenses are $360,000 per year. The company plans to sell 17,000 knapsacks this year.

Required:

1. What are the variable expenses per unit?
2. Answer the following questions independently:
   1. What is the break-even point in units and in sales dollars?
   2. What sales level in units and in sales dollars is required to earn an annual profit of $90,000?
   3. What sales level in units is required to earn an annual after-tax profit of $90,000 if the tax rate is 25%?
   4. Assume that through negotiation with the manufacturer, Super Sales Company is able to reduce its variable expenses by $3 per unit. What is the company's new break-even point in units and in sales dollars?

Answer 1

Variable cost ratio = 1 - Contribution margin ratio

= 1 - 0.4

= 0.6

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

= $60 * 0.6

= $36

a. Contribution margin per unit = Selling price per unit * Contribution margin ratio

= $60 * 0.4

= $24

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

= $360,000 / $24

= 15,000

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

= $360,000 / 0.4

= $900,000

b. Sales required in units = (Fixed costs + Desired profit) / Contribution margin per unit

= ($360,000 + $90,000) / $24

= 18,750

Sales required in dollars = (Fixed costs + Desired profit) / Contribution margin ratio

= ($360,000 + $90,000) / 0.4

= $1,125,000

c. Pretax profit = $90,000 / (1 - 0.25) = $120,000

Sales required in units = (Fixed costs + Desired profit) / Contribution margin per unit

= ($360,000 + $120,000) / $24

= 20,000

Sales required in dollars = (Fixed costs + Desired profit) / Contribution margin ratio

= ($360,000 + $120,000) / 0.4

= $1,200,000

d. Variable expenses = $36 - $3 = $33

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

= $60 - $33

= $27

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

= $27 / $60

= 0.45

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

= $360,000 / $27

= 13,333

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

= $360,000 / 0.45

= $800,000