### Economics Title

#### Weighted Ave Contribution Margin

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###### Recap: What is Contribution Margin?

In the previous page, we discussed that contribution margin is the amount of each product sold that goes towards fixed costs. In other words, it is like the gross profit, the amount of money you make after deducting all variable costs.

Hence the formula for contribution margin is: Contribution Margin Per Unit = Selling Price Per Unit - Variable Cost Per Unit OR Contribution Margin (Dollars) = Sales - Variable Cost

###### How Do You Calculate Contribution Margin for Multiple Product Lines?

When you have multiple product lines, you will need to calculate a weighted average to calculate the contribution margin. Weighted average simply refers to multiplying the contribution margin for each product by the percentage of sales they contribute to the business. The first step is to calculate a Sale Mix. A Sales Mix refers to the percentage of total sales that a product line makes up.

Therefore the formula is: Sales Mix = Product Line Sales (Units) / Total Sales (Units) After that, multiple the Sales Mix each respective product by the contribution margin of each Product Line to get the weighted average contribution margin of each product.

Afterwards, sum weighted average contribution margin of each product. In other words, for a company that produces three products, A, B and C.

The weighted average contribution margin is: Weighted Average Contribution Margin = Sales Mix (A)*Contribution Margin (A) + Sales Mix (B)*Contribution Margin (B) + Sales Mix (C)*Contribution Margin (C)

###### Worked Example: Weighted Average Contribution Margin

Dumbler Muffin is a Paper Company that sells three products, Printers, Paper and Ink. The expected sales and costs of each product are outlined below.

Printer: Sold for $300 each, variable costs per unit is $250. Expected sales for the year are 5,000 units.

Paper: Sold for $10 each, variable costs per unit is $5. Expected sales for the year are 30,000 units.

Ink: Sold for $30 each, variable costs per unit is $20. Expected sales for the year are 15,000 units.

Fixed Costs: $320,000 for the year.

What is the weighted average contribution margin of the business?

**Solution**

**Step 1: Calculate the Sales Mix of Each Product Line**

Sales Mix = Product Line Sales (Units) / Total Sales (Units)

Total Sales = 5,000 printer units + 30,000 paper units + 15,000 ink units = 50,000 units

Printer Sales Mix = 5,000/50,000 = 10% Paper Sales Mix = 30,000/50,000 = 60% Ink

Sales Mix = 15,000/50,000 = 30%

**Step 2: Calculate the Contribution Margin of Each Product**

Contribution Margin = Sale Price Per Unit - Variable Cost Per Unit

Printer Contribution Margin = $300 (SP) - $250 (VC) = $50 per unit

Paper Contribution Margin = $10 (SP) - $5 (VC) = $5 per unit

Ink Contribution Margin = $30 (SP) - $20 (VC) = $10 per unit

**Step 3: Multiply the Sales Mix by the Respective Contribution Margin of Each Product to Get the Weighted Average Contribution Margin **

Printer Weighted Ave Contribution Margin: 10% * $50 = $5

Paper Weighted Ave Contribution Margin: 60% * $5 = $3

Ink Weighted Ave Contribution Margin: 30% * $10 = $3

Therefore, the total Weighted Average Contribution Margin Per Unit: = $5 (Printer) + $3 (Paper) + $3 (Ink) = $11

On average, for every product sold, the business earns $11 towards fixed costs.

To calculate the Contribution Margin in Dollars: = Weighted Ave Contribution Margin * Total Units Sold = $11 * 50,000 = $550,000