Question

Piedmont Fasteners Corporation makes three different clothing fasteners in its manufacturing facility in North Carolina. Data concerning these products appear below:

Total fixed expenses are $400,000 per year.
All three products are sold in highly competitive markets, so the company is unable to raise its prices without losing unacceptable numbers of customers.
The company has an extremely effective lean production system, so there is no beginning or ending work in process or finished goods inventories.
Required:
1. What is the company's over-all break-even point in dollar sales?
2. Of the total fixed expenses of $400,000, $20,000 could be avoided if the Velcro product is dropped, $80,000 if the Metal product is dropped, and $60,000 if the Nylon product is dropped. The remaining fixed expenses of $240,000 consist of common fixed expenses such as administrative salaries and rent on the factory building that could be avoided only by going out of business entirely.
a. What is the break-even point in unit sales for each product?
b. If the company sells exactly the break-even quantity of each product, what will be the overall profit of the company?

Answer 1

Break-even sales in units:

 

Break-even point in units can be calculated using the below formula.

Break-even point = (Profit + Total fixed cost) / Contribution margin per unit

 

Contribution margin per unit can be calculated as follows;

Contribution margin per unit = Selling price - variable cost per unit

 

Velcro product:

 

Contribution margin per unit = 1.65 - 1.25

                                                    = 0.40

Metal product:

 

Contribution margin per unit  = 1.50 - 0.70

                                                      = 0.80

 

Nylon product:

Contribution margin per unit  = 0.85 - 0.25

                                                      = 0.60

Total fixed cost                           = $400,000

Profit at break-even point         = 0

 

Now we can calculate the break-even point using the above information;

 

Break-even point:

 

Velcro product:

 

 

Break-even point       = (Profit + total fixed cost) / Contribution margin per unit

                                     = (0 + 400,000) / 0.40

                                     = 1,000,000 units.

Metal product            = (0+ 400,000) / 0.80

                                     = 500,000 units

Nylon product           = (0 + 400,000) / 0.60 = 666,666 units