Question

A shift in the sales mix from products with a low contribution margin ratio towards products with a high contribution margin ratio will lower the break even point in the company as a whole.

The answer is True. But why? Can this be proven with a numerical example?

Answer 1

• Yes it is TRUE.
• A shift in sales mix in favour of product with higher contribution margin ratio will lower the break even point BECAUSE it will lead to an INCREASE in “Weighted average contribution margin ratio”.
• We know that ‘Weighted average contribution margin’ Is used as a ‘denominator’ value for computing Break Even level, as Break Even Sales = Fixed Cost / Weighted Average contribution margin ratio.
  When denominator increases (without any increase in numerator Fixed Cost), the break even will decrease.
• Example:

--Fixed Cost = $ 120,000

--Sales Mix in favour of lower CM ratio product

Working		A	B
A	Contribution margin ratio	10%	15%
B	Sales Mix	60%	40%
C = A x B	Weighted Average Contribution margin ratio	6%	6%
D	Fixed Cost		$120,000
E = 6% + 6%	Weighted Average Contribution margin ratio		12%
F = D/E	Break Even Sales $		$1,000,000

--Sales Mix in Favor of ‘B’, a higher CM ratio product.

Working		A	B
A	Contribution margin ratio	10%	15%
B	Sales Mix	40%	60%
C = A x B	Weighted Average Contribution margin ratio	4%	9%
D	Fixed Cost		$120,000
E = 4% + 9%	Weighted Average Contribution margin ratio		13%
F = D/E	Break Even Sales $		$923,077

--As you can see, the Break Even level has DECREASED to $ 923,077