Question

Patriot Co. manufactures and sells three products: red, white, and blue. Their unit selling prices are red, $64; white, $94; and blue, $119. The per unit variable costs to manufacture and sell these products are red, $49; white, $69; and blue, $89. Their sales mix is reflected in a ratio of 5:4:2 (red:white:blue). Annual fixed costs shared by all three products are $159,000. 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 $29,000.

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.
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.

Answer 1

		Red	White	Blue
1]	Selling price per unit	$              64.00	$               94.00	$             119.00
	-Variable cost per unit	$              49.00	$               69.00	$               89.00
	Contribution margin per unit	$              15.00	$               25.00	$               30.00
	Sales mix	5	4	2
	Weighted average unit contribution margin	$              21.36
	[(15*5+25*4+30*2)/(5+4+2)]
	Break-even in sales units:				Total
	Break even in composite units = Annual fixed costs/Weighted average unit contribution margin = 159000/21.36 =	7444
	Product wise units at BEP	3384	2707	1353	7444
		[7444*5/11]	[7444*4/11]	[7444*2/11]
	Breakeven in sales dollars:
	Units at BEP*Selling price per unit =	$        2,16,553	$         2,54,449	$         1,61,061	$    6,32,063
2]		Red	White	Blue
	Selling price per unit	$              64.00	$               94.00	$             119.00
	-Variable cost per unit	$              43.00	$               53.00	$               83.00
	Contribution margin per unit	$              21.00	$               41.00	$               36.00
	Sales mix	5	4	2
	Weighted average unit contribution margin	$              31.00
	[(21*5+41*4+36*2)/(5+4+2)]
	Break-even in sales units:
	Break even in composite units = Annual fixed costs/Weighted average unit contribution margin = (159000+29000)/31 =	6065
	Product wise units at BEP	2757	2205	1103	6065
		[6065*5/11]	[6065*4/11]	[6065*2/11]
	Breakeven in sales dollars:
	Units at BEP*Selling price per unit =	$        1,76,436	$         2,07,313	$         1,31,225	$    5,14,974