Question

Clean Skin Company sells bottles of three face-wash products: Daily Wash, Mud Mask, and FaceCleanser.

The company has annual fixed costs of $300 000. Last year, the company sold 7 500 bottles of its face-wash products in the ratio of 2:1:2.

Clean Skin’s accounting department has compiled the following data related to the three face-wash products:

Selling price per unit of Daily Wash is $ 20; Mud Mask is $ 25 and Face Cleanser is $ 22

Variable cost per unit of Daily Wash is $ 12; Mud Mask is $ 16, and Face Cleanser is $ 12.

Calculate the number of bottles of Daily Wash, Mud Mask, and Face Cleanser that must be sold to break even. (

Answer 1

	Daily Wash	Mud Mask	Face Cleaner
Selling Price	20	25	22
Variable Cost	12	16	12
Contribution Margin	8	9	10
Selling Ratio	2	1	2

Contribution margin = Selling price - Variable cost

Break-even Point is the point where there is no profit or loss.

Solving the below equation will tell us how many units must be sold in each product to breakeven.

Ʃ (Ratio*C.M*No. of bottles) - Annual Fixed Cost = 0 (No profit/loss)

Let the No. of bottles be X

Therefore, the equation becomes,

2*8*X + 1*9*X + 2*10*X – 300000 = 0

16X + 9X + 20X = 300000

45X = 300000

X = 6666.66 ≈ 6667

No. of bottles to be sold:

Daily Wash = 2*6667 = 13,334 bottles

Mud Mask = 1*6667 = 6,667 bottles

Face cleaner = 2*6667 = 13,334 bottles