Patriot Co. manufactures and sells three products: red, white, and blue. Their unit selling prices are red, $20; white, $35; and blue, $65. The per unit variable costs to manufacture and sell these products are red, $12; white, $22; and blue, $50. Their sales mix is reflected in a ratio of 5:4:2 (red:white:blue). Annual fixed costs shared by all three products are $250,000. 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 $12; and blue, by $10. However, the new material requires new equipment, which will increase annual fixed costs by $50,000.

Required:
a. 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.)
b. If the company uses the new material, determine its new break-even point in both sales units and sales dollars of each individual product.
c. What insight does this analysis offer management for long term planning?

c. Management should start using the new material as soon as possible since it doesn't only decrease the break even point, if sales level remain the same, it will increase operating profits.

Explanation:

red's contribution margin = $8

white's contribution margin = $13

blue's contribution margin = $12

sales mix = 5:4:2

weighted contribution margin = ($8 x 5/11) + ($13 x 4/11) + ($12 x 2/11) = $3.6363 + $4.2727 + $2.1818 = $10.0908

new contribution margin:

red's contribution margin = $14

white's contribution margin = $25

blue's contribution margin = $22

sales mix = 5:4:2

weighted contribution margin = ($14 x 5/11) + ($25 x 4/11) + ($22 x 2/11) = $6.3636 + $9.0909 + $4 = $19.4545

abiolataiwo2015 abiolataiwo2015 · Answer 2 · 2022-03-22T15:48:14+01:00

The break-even point in both sales units and sales dollars of each individual product is:

Red 11,261.38 units; $225,240
White 9,009.11 units; $315,350
Blue 4,505 units ; $292,825

Break even

a. Break even number in units

Weighted contribution margin = ($8 x 5/11) + ($13 x 4/11) + ($12 x 2/11)

Weighted contribution margin = $3.6363 + $4.2727 + $2.1818

Weighted contribution margin = $10.0908

Break even number in units= $250,000 / $10.0908

Break even number in units = 24,775.04

Red

Break-even point sales units= 24,775.04 x 5/11

Break-even point sales units= 11,261.38 units

Break-even point sales dollars = 11,262 x $20

Break-even point sales dollars= $225,240

White

Break-even point sales units= 24,775.04 x 4/11

Break-even point sales units = 9,009.11 units

Break-even point sales dollars = 9,010 x $35

Break-even point sales dollars = $315,350

Blue

Break-even point sales units= 24,775.04 x 2/11

Break-even point sales units= 4,504.55

Break-even point sales units= 4,505 units (Approximately)

Break-even point sales dollars= 4,505 x $65

Break-even point sales dollars= $292,825

b. New break even number in units

Weighted contribution margin = ($14 x 5/11) + ($25 x 4/11) + ($22 x 2/11)

Weighted contribution margin = $6.3636 + $9.0909 + $4

Weighted contribution margin= $19.4545

New break even number in units= $300,000 / $19.4545

New break even number in units= 15,420.60

Red

New break even point in sales units = 15,420.60 x 5/11

New break even point in sales units = 7,009.36 units

New break even point in sales dollars = 7,010 x $20

New break even point in sales dollars= $140,200

White

New break even point in sales units = 15,420.60 x 4/11

New break even point in sales units = 5,607.49 units

New break even point in sales dollars = 5,608 x $35

New break even point in sales dollars= $196,280

Blue

New break even point in sales units = 15,420.60 x 2/11

New break even point in sales units = 2,803.75

New break even point in sales units =2,804 units (Approximately)

New break even point in sales dollars = 2,804 x $65

New break even point in sales dollars = $182,260

c. The insight does that this analysis offer management for long term planning is for that the management should use the new material.

Inconclusion the break-even point in both sales units and sales dollars of each individual product is: Red 11,261.38 units; $225,240.

Learn more about break-even here:https://brainly.com/question/9212451