Question

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?

Answer 1

Answer:

a. break even number in units = $250,000 / $10.0908 = 24,775.04

red units = 24,775.04 x 5/11 = 11,261.38 ≈ 11,262 units

total sales = 11,262 x $20 = $225,240

white units = 24,775.04 x 4/11 = 9,009.11 ≈ 9,010 units

total sales = 9,010 x $35 = $315,350

blue units = 24,775.04 x 2/11 = 4,504.55 ≈ 4,505 units

total sales = 4,505 x $65 = $292,825

total sales = $833,415

b. new break even number in units = $300,000 / $19.4545 = 15,420.60

red units = 15,420.60 x 5/11 = 7,009.36 ≈ 7,010 units

total sales = 7,010 x $20 = $140,200

white units = 15,420.60 x 4/11 = 5,607.49 ≈ 5,608 units

total sales = 5,608 x $35 = $196,280

blue units = 15,420.60 x 2/11 = 2,803.75 ≈ 2,804 units

total sales = 2,804 x $65 = $182,260

total sales = $518,740

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