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 ​$95 per pair. The variable cost for this same pair of shoes is ​$45. Footwear Inc. incurs fixed costs of ​$180,000 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: 7,000 pairs of​ shoes? 12,000 pairs of​ shoes? 18,000 pairs of​ shoes?

Answer 1

a.

Sale price per unit = $95

Variable cost per unit = $45

Contribution per unit = Sale price per unit - Variable cost per unit

Contribution per unit = $95 - $45 = $50

Fixed costs = $180,000

Break-even point (units) = Fixed costs / Contribution per unit

Break-even point (units) = $180,000 / $45 = 3,600 pairs

b.

Break even point ($) = Break-even point (units) * Sale price per unit

Break even point ($) = 3,600 * $95 = $342,000

c.

At 7,000 pairs of shoes

Contribution = 7,000 * $50 = $350,000

Fixed costs = $180,000

Operating profit = $170,000

At 12,000 pairs of shoes

Contribution = 12,000 * $50 = $600,000

Fixed costs = $180,000

Operating profit = $420,000

At 18,000 pairs of shoes

Contribution = 18,000 * $50 = $900,000

Fixed costs = $180,000

Operating profit = $720,000