By Yuriy Smirnov Ph.D.

Companies selling a single product are rare in business practice. More often companies sell many different products. The main objective of target profit analysis with a sales mix is determining the number of units of each product that a company needs to sell to earn a desirable profit.

Please note that target profit analysis involves two important assumption besides the assumptions of break-even analysis.

- The sales mix is predetermined. In other words, the proportion of each product in a sales mix is fixed.
- The sales mix remains constant during the accounting period.

Target profit analysis with a sales mix uses a contribution margin approach for different products that are not equally profitable for a company. Calculating target sales both in units and in dollars requires three steps.

__Step 1__. Calculate the contribution margin per unit for each product in the sales mix.

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

__Step 2__. Calculate the weighted average contribution margin for the sales mix,

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

Σ | ||

i = 1 |

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

__Step 3__. Calculate in units the number of target sales for each product.

Target Sales _{in Units} = |
Fixed Costs + Target Profit | × Percentage of Sales Mix |

Weighted Average Contribution Margin |

The dollar amount of target sales for a specific product can be calculated by multiplying the number of units by the sales price.

Assume that LWD Fashion LLC is selling three products as shown in the table below.

The company’s management expects to earn a profit of $450,000. Let’s perform target profit analysis if the proportion of jeans in the sales mix is 40%, T-shirts 20%, and sweaters 40%.

As the first step, we should calculate the contribution margin per unit for all products.

Contribution Margin per Unit _{Jeans} = $95 - $55 = $40

Contribution Margin per Unit _{T-Shirts} = $45 - $35 = $10

Contribution Margin per Unit _{Sweaters} = $90 - $60 = $30

The second step is to determine the weighted average contribution margin.

Weighted Average Contribution Margin = $40 × 0.40 + $10 × 0.20 + $30 × 0.40 = $30

Finally, we need to calculate target sales in units for all products.

Target Sales in Units _{Jeans} = ($600,000 + $450,000) ÷ $30 × 0.40 = 14,000 Units

Target Sales in Units _{T-Shirts} = ($600,000 + $450,000) ÷ $30 × 0.40 = 7,000 Units

Target Sales in Units _{Sweaters} = ($600,000 + $450,000) ÷ $30 × 0.40 = 14,000 Units

LWD Fashion LLC has to sell 14,000 pairs of jeans, 7,000 T-shirts, and 14,000 sweaters. To determine the dollar amount of target sales, we can simply multiply the number of units by the sales price per unit.

Target Sales in Dollars _{Jeans} = 14,000 × $95 = $1,330,000

Target Sales in Dollars _{T-Shirts} = 7,000 × $45 = $315,000

Target Sales in Dollars _{Sweaters} = 14,000 × $90 = $1,260,000

Total Target Sales = $1,330,000 + $315,000 + $1,260,000 = $2,905,000

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