Question

​(​Break-even

point and operating

leverage​)

Footwear Inc. manufactures a complete line of​ men's and​ women's dress shoes for independent merchants. The average selling price of its finished product is

​$75

per pair. The variable cost for this same pair of shoes is

​$65

.

Footwear Inc. incurs fixed costs of

​$170 comma 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 profit or loss at the following units of production​ sold:

5 comma 000

pairs of​ shoes?

11 comma 000

pairs of​ shoes?

17 comma 000

pairs of​ shoes?

Answer 1

Answer a)

Calculation of break–even point in pair of shoes

Break-even point (in units) = Total fixed cost/ Contribution margin per pair

                                                  = $ 170,000/ $ 10.00

                                                  = 17,000 units

Therefore the company must sell 17,000 pair of shoes to break-even.

Working note:

Contribution margin per unit = selling price per pair – variable cost per pari

                                                     = $ 75 - $ 65

                                                       = $ 10   

Answer b)

Calculation of Dollar Sales Volume to break-even

Break-even point (in dollars) = (Total fixed cost/ Contribution margin per pair) X Selling Price per pair

                                                     = ($ 170,000/ $ 10.00) X $ 75.00

                                                      = $ 1,275,000

Therefore break-even sales of the company is $ 1,275,000

Answer c)

Calculation of firm’s profit or loss when the company sells 5,000 units

Profit = (Contribution margin per unit X number of units sold) – Total fixed cost

           = ($ 10 X 5,000 units) - $ 170,000

           = $ 50,000 - $ 170,000

            = - $ 120,000

Therefore the company will incur total loss of $ 120,000 if the number of units sold is 5,000.

Calculation of firm’s profit or loss when the company sells 11,000 units

Profit = (Contribution margin per unit X number of units sold) – Total fixed cost

           = ($ 10 X 11,000 units) - $ 170,000

           = $ 110,000 - $ 170,000

           = - $ 60,000

Therefore the company will incur total loss of $ 60,000 if the number of units sold is 11,000.

Calculation of firm’s profit or loss when the company sells 17,000 units

Profit = (Contribution margin per unit X number of units sold) – Total fixed cost

           = ($ 10 X 17,000 units) - $ 170,000

           = $ 170,000 - $ 170,000

           = Nil

Therefore the company will break-even if it sells 17,000 units (i.e. it will neither earn any profit nor incur any loss)