“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:

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 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 total sales dollars? 2. Of the total fixed costs of $400,000, $20,000 could be avoided if the Velcro product were dropped, $80,000 if the Metal product were dropped, and $60,000 if the Nylon product were dropped. The remaining fixed costs of $240,000 consist of common fixed costs 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 units 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.

SOLUTION:

Note: This is a problem that will challenge the very best students’ conceptual and analytical skills. However, working through this case will yield substantial dividends in terms of a much deeper understanding of critical management accounting concepts.

1.The overall break-even sales can be determined using the CM ratio.

VelcroMetalNylonTotal

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

Variable expenses 125,000 140,000 100,000 365,000

Contribution margin$ 40,000$160,000$240,000440,000

Fixed expenses 400,000

Net operating income$ 40,000

2.The issue is what to do with the common fixed cost when computing the break-evens for the individual products. The correct approach is to ignore the common fixed costs. If the common fixed costs are included in the computations, the break-even points will be overstated for individual products and managers may drop products that in fact are profitable.

a.The break-even points for each product can be computed using the contribution margin approach as follows:

VelcroMetalNylon

Unit selling price$1.65$1.50$0.85

Variable cost per unit 1.25 0.70 0.25

Unit contribution margin (a)$0.40$0.80$0.60

Product fixed expenses (b)$20,000$80,000$60,000

Unit sales to break even (b) ÷ (a)50,000100,000100,000

b.If the company were to sell exactly the break-even quantities computed above, the company would lose $240,000—the amount of the common fixed cost. This can be verified as follows:

At this point, many students conclude that something is wrong with their answer to part (a) because a result in which the company loses money operating at the break-evens for the individual products does not seem to make sense. They also worry that managers may be lulled into a false sense of security if they are given the break-evens computed in part (a). Total sales at the individual product break-evens is only $317,500 whereas the total sales at the overall break-even computed in part (1) is $732,000.

Many students (and managers, for that matter) attempt to resolve this apparent paradox by allocating the common fixed costs among the products prior to computing the break-evens for...

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