Question

Patriot Co. manufactures and sells three products: red, white, and blue. Their unit selling prices are red, $50; white, $80; and blue, $105. The per unit variable costs to manufacture and sell these products are red, $35; white, $55; and blue, $75. Their sales mix is reflected in a ratio of 5:4:2 (red:white:blue). Annual fixed costs shared by all three products are $145,000. 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 $15; white, by $25; and blue, by $15. However, the new material requires new equipment, which will increase annual fixed costs by $15,000.

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

Calculation of weighted average contribution margin per unit
	Red	White	Blue	Total
Unit Selling price	50	80	105	235
Unit Variable cost	20	30	60
Unit Contribution Margin	30	50	45
Sales Mix	5	4	2	11
Contribution Margin	150	200	90	440
Weighted average contribution Margin				40	0.170213
Break even point in units sales = Fixed costs/Weighted average unit contribution margin
=(145000+15000)/40
4000	Units	or	940,000	Dollars
Red	1818.18	Units	427,272.73	Dollars
White	1454.55	Units	341,818.18	Dollars
Blue	727.27	Units	170,909.09	Dollars