# Weighted Average Unit Contribution Margin

The unit contribution margin for a product is the difference between the selling price and the cost price. So for example, if a business sells only one product with a selling price of 20.00 and a cost of 7.00, then the unit contribution margin for the product and the business is 20.00 – 7.00 = 13.00.

The problem becomes more complicated when a business sells multiple products. Each product will have a different contribution margin, and therefore to establish the overall unit contribution margin for the business, the contribution from each product must be weighted in proportion to the number of units of that product sold (sometimes referred to as the unit sales mix). The resultant unit contribution is known as the weighted average unit contribution margin.

Suppose, for example, that a business sells five products with contribution margins and unit sales mix percentages as follows:

Multiple products margin and unit sales mix
Product Margin Mix %
A 2.46 20%
B 5.90 19%
C 12.00 26%
D 18.90 14%
E 22.00 21%

While the individual contribution margins of each product are known, the overall unit contribution margin of the business needs to be calculated using the weighted average contribution margin per unit formula.

## Weighted Average Unit Contribution Margin Formula

The weighted average unit contribution margin formula takes each products unit contribution, and weights it in proportion to its unit sales mix percentage as follows:

```Weighted average unit contribution margin = Contribution A x Sales mix % A + Contribution B x Sales mix % B + ... Contribution E x Sales mix % E
Weighted average unit contribution margin = 2.46 x 20% + 5.90 x 19% + 12.00 x 26% + 18.90 x 14% + 22.00 x 21%
Weighted average unit contribution margin = 12.00
```

Providing the unit sales mix percentages remain constant, for every product sold by this business, on average it will receive a unit contribution margin of 12.00.

## Using the Weighted Average Unit Contribution Margin

The most important use for the weighted average unit contribution margin is in the calculation of the break even point for a multiple product business.

The break even formula is as follows:

`Break even units = Operating expenses / Contribution margin per unit`

For a multiple product business, the weighted average unit contribution margin is simply substituted into the formula. For our example above, if the fixed operating expenses were 96,000, then the break even units is given as follows:

```Break even units = Operating expenses / Weighted average unit contribution margin
Break even units = 96,000 / 12.00
Break even units = 8,000
```

The business needs to sell 8,000 units to break even. For this calculation to work, the unit sales mix percentages must remain constant, and the units must be sold in the correct proportions as follows:

Allocation of break even units
Product Mix % Units
A 20% 1,600
B 19% 1,520
C 26% 2,080
D 14% 1,120
E 21% 1,680
Total 100% 8,000

The total contribution margin from these products is as follows:

```Contribution = 2.46 x 1,600 + 5.90 x 1,520 + 12.00 x 2,080 + 18.90 x 1,120 + 22.00 x 1,680 Contribution = 95,992 rounded to 96,000
```

As the operating expenses were also 96,000 the business will break even at this level of unit sales for each of the five products.

Weighted Average Unit Contribution Margin November 6th, 2016

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