Question

National Co. manufactures and sells three products: red, white, and blue. Their unit sales prices are red, $55; white, $85; and blue, $110. The per unit variable costs to manufacture and sell these products are red, $40; white, $60; and blue, $80. Their sales mix is reflected in a ratio of 5:4:2 (red:white:blue). Annual fixed costs shared by all three products are $150,000. 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 $10; white, by $20; and blue, by $10. However, the new material requires new equipment, which will increase annual fixed costs by $20,000.

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 up your composite units to whole number. Omit the "$" sign in your response.) 2. Assume if the company uses the new material, determine its new break-even point in both sales units and sales dollars of each individual product. (Round up your composite units to whole number. Omit the "$" sign in your response.)

Answer 1

Solution-1

Computation of Contribution

Particulars	Red	White	Blue
Sale price	55	85	110
(Variable cost)	40	60	80
Contribution	15	25	30

Weighted contribution

Red(15 x 5/11)	7
White(25 x 4/11)	9
Blue(30 x 2/11)	5
Weighted contribution	21

Break even point => Contribution - Fixed costs = 0

=> 21 x units = 150000

=> units = 150000/21 = 7143 nos

Sale composition in break even

Red = 7143 x 5/11 = 3247

White = 7143 x 4/11 = 2597

Blue = 7143 x 2/11 = 1299

Sales Value

Red = 3247 * 55 = 178585

white = 2597 * 85 = 220745

Blue = 1299 * 110 = 142890

Solution-2

Computation of Contribution
Particulars	Red	White	Blue
Sale price	55	85	110
(Variable cost)	30	40	70
Contribution	25	45	40

  

Weighted contribution
Red(25 x 5/11)	11
White(45 x 4/11)	16
Blue(40 x 2/11)	7
Weighted contribution	35

Break even point => Contribution - Fixed costs = 0

=> 35 x units = 170000

=> units = 170000/35 = 4857 nos

Sale composition in break even

Red = 4857 x 5/11 = 2207

White = 4857 x 4/11 = 1767

Blue = 4857 x 2/11 = 883

Sales Value

Red = 2207 * 55 = 121385

white = 1767 * 85 = 150195

Blue = 883 * 110 = 97130