Question

National Co. manufactures and sells three products: red, white, and blue. Their unit sales prices are red, $46; white, $76; and blue, $101. The per unit variable costs to manufacture and sell these products are red, $31; white, $51; and blue, $71. Their sales mix is reflected in a ratio of 2:2:1 (red:white:blue). Annual fixed costs shared by all three products are $141,000. One type of raw material has been used to manufacture all three products. The company has developed a new material of equal quality for less cost. The new material would reduce variable costs per unit as follows: red, by $6; white, by $16; and blue, by $6. However, the new material requires new equipment, which will increase annual fixed costs by $11,000.

Required:
1.	Assume if the company continues to use the old material, determine its break-even point in both sales units and sales dollars of each individual product. (Round up your composite units to whole number. Omit the "$" sign in your response.)

Break-Even Points	Sales Units	Sales Dollars
Red at break-even		$
White at break-even		$
Blue at break-even		$

2.	Assume if the company uses the new material, determine its new break-even point in both sales units and sales dollars of each individual product. (Round up your composite units to whole number. Omit the "$" sign in your response.)

Break-Even Points	Sales Units	Sales Dollars
Red at break-even		$
White at break-even		$
Blue at break-even		$

Answer 1

Solution:

Part 1 – Old material

	Red	White	Blue
Unit Selling Price	$46	$76	$101
Less: Variable Costs	$31	$51	$71
Contribution Magin per unit	$15	$25	$30
x Sales Mix Ratio	40%	40%	20%
	$6.00	$10.00	$6.00
Weighted Avg Contribution Margin per unit	$22
Total Fixed Costs	$141,000
Break Even Poin in Units for the company (Total Fixed Cost / Weighted Avf CM per unit		6409
Break Even Point in Units for company	6409	6409	6409
x Sales Mix	40%	40%	20%
Break Even Point for each product	2564	2564	1282
Break Even Point in dollar sales (BEP in Units x Unit Sellling Price)	$117,944	$194,864	$129,482

	Sales Units	Sales Dollars
Red	2564	$117,944
White	2564	$194,864
Blue	1282	$129,482

Part 2 – New Materials

	Red	White	Blue
Unit Selling Price	$46	$76	$101
Less: Variable Costs	$25	$35	$65
Contribution Magin per unit	$21	$41	$36
x Sales Mix Ratio	40%	40%	20%
	$8.40	$16.40	$7.20
Weighted Avg Contribution Margin per unit	$32
Total Fixed Costs	$141,000
Break Even Poin in Units for the company (Total Fixed Cost / Weighted Avf CM per unit		4406
Break Even Point in Units for company	4406	4406	4406
x Sales Mix	40%	40%	20%
Break Even Point for each product	1762	1762	881
Break Even Point in dollar sales (BEP in Units x Unit Sellling Price)	$81,052	$133,912	$88,981
	Sales Units	Sales Dollars
Red	1762	81,052
White	1762	133,912
Blue	881	88,981

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