CASE 5–32 Break-Even Analysis for Individual Products in a Multiproduct Company LO5–5, LO5–9 Cheryl Montoya picked up the phone and called her boss, Wes Chan, the vice president of marketing at Piedmont Fasteners Corporation: “Wes, I’m not sure how to go about answering the questions
that came up at the meeting with the president yesterday.”
“What’s the problem?”
“The president wanted to know the break-even point for each of the company’s products, but I am having trouble figuring them out.”
“I’m sure you can handle it, Cheryl. And, by the way, I need your analysis on my desk tomorrow morning at 8:00 sharp in time for the follow-up meeting at 9:00.”
Piedmont Fasteners Corporation makes three different clothing fasteners in its manufacturing facility in North Carolina. Data concerning these products appear below:

Velcro Metal Nylon
Annual sales volume 100,000 200,000 400,000
Unit selling price $1.65 $1.50 $0.85
Variable expense per unit $1.25 $0.70 $0.25

Total fixed expenses are $400,000 per year.
All three products are sold in highly competitive markets, so the company is unable to raise prices without losing an unacceptable numbers of customers.
The company has an extremely effective lean production system, so there are 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? Explain this result.

Answer 1 :

              The break-even point in unit sales for each product

Formula :

Break-Even Point  = Total variable costs + Fixed Costs

 Break-Even Point= $365,000 + $400,000

Break-Even Point= $765,000

Answer 2:

a)  Break-even point in unit sales for each product :  

Break Even Point = Fixed cost for each product/Contribution per unit

                                  Velcro                Metal                  Nylon  

Fixed expenses        $20,000            $80,000            $60,000

Contribution per unit  $0.40               $0.80                $0.60

Break-even point    $20,000/$0.40  $80,000/$0.80   $60,000/$0.60

Total                          50,000 units       100,000 units     100,000 units

a) Working Notes :

                                         Velcro          Metal        Nylon            Total

Net Income                                                                               $40,000

Contribution per unit = $440,000/700,000 = $0.63

Answer 2 :

Part B)

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Piedmont Fasteners Corporation

1. Company's overall break-even point in dollar sales = Total variable costs + Fixed Costs

= $365,000 + $400,000

= $765,000

2. a) Break-even point in unit sales for each product:

= Fixed cost for each product/Contribution per unit

                                   Velcro                Metal                  Nylon  

Fixed expenses        $20,000            $80,000            $60,000

Contribution per unit  $0.40               $0.80                $0.60

Break-even point    $20,000/$0.40  $80,000/$0.80   $60,000/$0.60

=                              50,000 units       100,000 units     100,000 units

2b)   If the company sells exactly the break-even quantity of each product, the overall profit of the company will be a loss of $240,000.  This is due to the common fixed expenses.

Explanation:

a) Data and Calculations:

                                           Velcro          Metal        Nylon            Total

Annual sales volume        100,000     200,000    400,000      700,000

Unit selling price                  $1.65        $1.50        $0.85

Sales Revenue               $165,000   $300,000   $340,000 $805,000

Variable expense per unit  $1.25        $0.70        $0.25

Variable costs                $125,000   $140,000   $100,000   $365,000

Contribution per unit         $0.40        $0.80        $0.60

Contribution margin       $40,000   $160,000  $240,000   $440,000

Total fixed expenses                                                             $400,000

Net Income                                                                               $40,000

Contribution per unit (company-wide)  $440,000/700,000 = $0.63

                                           Velcro          Metal        Nylon            Total

Annual sales volume        100,000     200,000    400,000      700,000

Unit selling price                  $1.65        $1.50        $0.85

Sales Revenue               $165,000   $300,000   $340,000 $805,000

Variable expense per unit  $1.25        $0.70        $0.25

Variable costs                $125,000   $140,000   $100,000   $365,000

Contribution per unit         $0.40        $0.80        $0.60

Contribution margin       $40,000   $160,000  $240,000   $440,000

Total fixed expenses        20,000       80,000      60,000      160,000

Income                            $20,000     $80,000   $180,000   $280,000

Common Fixed expenses                                                        240,000

Net Income                                                                               $40,000