By Yuriy Smirnov Ph.D.

A sales mix is a set of proportions of each product in total sales if a business sells multiple products. Furthermore, these products are not equally profitable for a business, so a contribution margin approach is usually used in break-even analysis with a sales mix or multiple products. Please note the additional assumption that the proportion of each product in total sales is constant during the accounting period.

Under the contribution margin approach, break-even analysis with a sales mix involves three steps.

__Step 1__. Calculate the per unit amount of contribution margin for each product.

Contribution Margin _{per Unit} = Sales Price _{per Unit} - Variable Cost _{per Unit}

__Step 2__. Calculate the weighted average contribution margin,

Weighted Average Contribution Margin = | N | CM_{i} × w_{i} |

Σ | ||

i = 1 |

where CM_{i} is the per unit amount of contribution margin of a relevant product, and w_{i} is a proportion of a relevant product in a sales mix.

__Step 3__. Calculate the break-even point for each product both in units and dollars.

BEP _{in Units} = |
Fixed Costs | × Percentage of Sales Mix |

Weighted Average Contribution Margin |

The dollar amount for each product can be calculated by multiplying the break-even sales in units by the sales price of a relevant product.

Alternatively, the break-even point in dollars for multiple products can be calculated as follows:

BEP _{in Dollars} = |
Fixed Costs |

Contribution Margin Ratio |

In turn, the formula to calculate the contribution margin ratio is as follows:

Contribution Margin Ratio = | Total Sales - Total Variable Costs |

Total Sales |

X-One Fashion LLC is selling three products: jeans, T-shirts, and sweaters. Information about expected sales price, variable costs, fixed costs, and the proportion in the sales mix for the second quarter is shown in the table below.

We should calculate the contribution margin per unit for each product as the first step in break-even analysis for the sales mix.

CM per Units _{Jeans} = $85 - $50 = $35

CM per Units _{T-Shirts} = $45 - $35 = $10

CM per Units _{Jeans} = $90 - $60 = $30

Calculation of the weighted average contribution margin is the second step in break-even analysis.

Weighted Average Contribution Margin = $35×0.40 + $10×0.45 + $30×0.15 = $23

As the third step, we should calculate the break-even point for each product.

BEP in Units _{Jeans} = ($690,000 ÷ $23) × 0.40 = 12,000

BEP in Units _{T-Shirts} = ($690,000 ÷ $23) × 0.45 = 13,500

BEP in Units _{Jeans} = ($690,000 ÷ $23) × 0.15 = 4,500

BEP in Dollars _{Jeans} = 12,000 × $85 = $1,020,000

BEP in Dollars _{T-Shirts} = 13,500 × $45 = $607,500

BEP in Dollars _{Jeans} = 4,500 × $90 = $405,000

BEP in Dollars _{Total} = $1,020,000 + $607,500 + $405,000 = $2,032,500

Assume that the actual performance of X-One Fashion LLC in the second quarter was as follows:

Let’s calculate the break-even point in dollars for the sales mix.

Sales _{Jeans} = $85 × 11,000 = $935,000

Sales _{T-Shirts} = $45 × 14,000 = $630,000

Sales _{Jeans} = $90 × 6,000 = $540,000

Total Sales = $935,000 + $630,000 + $540,000 = $2,105,000

Variable Costs _{Jeans} = $50 × 11,000 = $550,000

Variable Costs _{T-Shirts} = $35 × 14,000 = $490,000

Variable Costs _{Jeans} = $60 × 6,000 = $360,000

Total Variable Costs = $550,000 + $490,000 + $360,000 = $1,400,000

Contribution Margin Ratio = ($2,105,000 - $1,400,000) ÷ $2,105,000 = 0.335

BEP in Dollars _{Total} = $690,000 ÷ 0.335 = $2,059,701.49

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