Question

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
Normal annual sales volume		112,000			212,000			287,000
Unit selling price	$	1.70		$	2.00		$	1.10
Variable expense per unit	$	1.00		$	1.40		$	.70

   

Total fixed expenses are $257,000 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 overall break-even point in dollar sales? (Round CM ratio to 4 decimal places and final answer to the nearest whole dollar.)

  

2. Of the total fixed expenses of $257,000, $17,500 could be avoided if the Velcro product is dropped, $103,200 if the Metal product is dropped, and $77,600 if the Nylon product is dropped. The remaining fixed expenses of $58,700 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? (Do not round intermediate calculations.)

   

b. If the company sells exactly the break-even quantity of each product, what will be the overall profit of the company? (Do not round intermediate calculations.)

Answer 1

1	Overall break-even point in dollars=Total fixed cost/Overall contribution margin ratio
	Contribution margin ratio=Total contribution margin/Total sales
						Velcro	Metal	Nylon	Total
	Normal annual sales volume				a	112000	212000	287000
	Unit selling price				b	1.7	2	1.1
	Sales				c=a*b	190400	424000	315700	930100
	Variable expenses per unit				d	1	1.4	0.7
	Variable expenses				e=a*d	112000	296800	200900	609700
	Contribution margin				f=c-e	78400	127200	114800	320400
	Contribution margin ratio=320400/930100=0.344479=34.479%
	Overall break-even point in dollars=257000/34.479%=$ 745381
2-a.	Break-even point in units=Fixed cost/Contribution margin per unit
						Velcro	Metal	Nylon
	Fixed cost				a	17500	103200	77600
	Unit selling price				b	1.7	2	1.1
	Variable expenses per unit				c	1	1.4	0.7
	Contribution margin per unit				d=b-c	0.7	0.6	0.4
	Break-even point in units				e=a/d	25000	172000	194000
2-b.	Overall profit:
						Velcro	Metal	Nylon	Total
	Sales volume				a	25000	172000	194000
	Unit selling price				b	1.7	2	1.1
	Sales				c=a*b	42500	344000	213400	599900
	Variable expenses per unit				d	1	1.4	0.7
	Variable expenses				e=a*d	25000	240800	135800	401600
	Contribution margin				f=c-e	17500	103200	77600	198300
	Less: Fixed cost					17500	103200	77600	198300
	Segment income/(loss)					0	0	0	0
	Less: Common fixed cost								58700
	Overall profit/(loss)								-58700