Question

Patriot Co. manufactures and sells three products: red, white, and blue. Their unit selling prices are red, $59; white, $89; and blue, $114. The per unit variable costs to manufacture and sell these products are red, $44; white, $64; and blue, $83. Their sales mix is reflected in a ratio of 2:2:1 (red:white:blue). Annual fixed costs shared by all three products are $154,000. 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 $14; white, by $24; and blue, by $18. However, the new material requires new equipment, which will increase annual fixed costs by $24,000.
Required:

Part 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 composite units up to next whole number.)

2. Determine its break-even point in both sales units and sales dollars of each individual product. Determine the selling price per composite unit. Ratio Selling price per unit Total per composite unit Red 2 White 2 Blue 1 Determine the variable costs per composite unit. Ratio Variable cost per unit Total per composite unit Red White Blue Determine the break-even point in composite units. Choose Numerator: / Choose Denominator: = Break Even Units / = Break even units Determine its break-even point in units and sales dollars of each individual product. Number per composite unit Number of composite units to break even. Units sales at the break-even point Dollar sales at the break-even point Red White Blue

Part 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 composite units up to next whole number.)

Answer 1

Answer to part 1

Determination the selling price per composite unit
	Ratio	selling price per unit	Total per composite unit
Red	2	59	23.6
White	2	89	35.6
Blue	1	114	22.8
Total	5		82

Determination the variable costper composite unit
	Ratio	variable cost per unit	Total per composite unit
Red	2	44	17.6
White	2	64	25.6
Blue	1	83	16.6
Total	5		59.8

Determination of Break even point in composite units-

BEP = Total fixed cost / (selling price per composite unit - Variable cost per composite unit)

= 154000/(82-59.8)

= 154000/22.2

= 6937 units

BEP in sales dollars = 6937*selling price per composite units

= 6937*82

= $ 568834

Determination of the break even point in units and sales dollars of each individual product
	No. per composite unit	No. of composite units to break even	unit sale at the break even point	Dollar sale at the break even point
Red (6937*2/5)	2	6937	2774.8	163713.2
White (6937*2/5)	2	6937	2774.8	246957.2
Blue (6937*1/5)	1	6937	1387.4	158163.6
Total	5	20811	6937	568834

Answer to Part 2

Determination the selling price per composite unit
	Ratio	selling price per unit	Total per composite unit
Red	2	59	23.6
White	2	89	35.6
Blue	1	114	22.8
Total	5		82.00

Determination the variable costper composite unit
	Ratio	variable cost per unit	Total per composite unit
Red (44-14)	2	30	12
White (64-24)	2	40	16
Blue (83-18)	1	65	13
Total	5		41

BEP = (154000+24000)/(82-41)

= 178000/41

= 4341.5 or 4342 units

Determination of the break even point in units and sales dollars of each individual product
	No. per composite unit	No. of composite units to break even	unit sale at the break even point	Dollar sale at the break even point
Red (4342*2/5)	2	4342	1736.8	102471.2
White (4342*2/5)	2	4342	1736.8	154575.2
Blue (4342*1/5)	1	4342	868.4	98997.6
Total	5	13026	4342	356044

please check with your answer and let me know.