Question

(​Break-even point and operating leverage​)​ Rockstar, Inc. manufactures a complete line of​ men's and​ women's casual shoes for independent merchants. The average selling price of its finished product is ​$90 per pair. The variable cost for this same pair of shoes is ​$45. Footwear Inc. incurs fixed costs of ​$160,000 per year.

a. What is the​ break-even point in pairs of shoes sold for the​ company?

b. What is the dollar sales volume the firm must achieve to reach the​ break-even point?

c. What would be the​ firm's operating profit or loss​ (that is, net operating​ income) at the following units of production​ sold: 5,000 pairs of​ shoes? 9,000 pairs of​ shoes? 17,000 pairs of​ shoes?

Answer 1

a.Break even point in pairs of shoes = Fixed costs/(Selling price per pair – variable costs per pair)
= 160,000/(90-45)

= 3,555.56 pairs

b.Contribution Margin ratio = (Sales – variable costs)/sales

= (90-45)/90

= 50%

Dollar sales volume required = Fixed costs/CM Ratio

= 160,000/50%

= $320,000

c.Net Operating Income = Sales – variable costs – fixed costs i.e. Contribution Margin – fixed costs

At 5000 pairs = 45*5000-160,000 = $65,000

At 9000 pairs = 45*9000-160,000 = $245,000

At 17000 pairs = 45*17000-160,000 = $605,000