Weighted Average Unit Contribution Margin

The unit contribution margin for a production is the difference between the selling price and the cost price. So for example, if a business sells only i 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 concern is xx.00 – seven.00 = 13.00.

The problem becomes more complicated when a business sells multiple products. Each product will have a unlike contribution margin, and therefore to establish the overall unit of measurement contribution margin for the concern, 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 every bit the weighted boilerplate unit contribution margin.

Weighted Average Unit Contribution Margin Example

Suppose, for example, a business sells two products with contribution margins and unit sales mix percentages equally follows:

Multiple products margin and unit sales mix
Production	Margin	Mix %
A	3.00	80%
B	v.00	twenty%

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 of measurement formula.

Weighted Average Unit Contribution Margin Formula

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

Weighted boilerplate unit contribution margin = Contribution A 10 Sales mix % A + Contribution B x Sales mix % B + ... Contribution E ten Sales mix % E In this example there are only two products A and B Weighted average unit of measurement contribution margin = iii.00 x 80% + 5.00 x 20% = 3.40

Providing the unit of measurement sales mix percentages remain constant, for every product sold by this concern, on average it will receive a unit contribution margin of 3.40

Multiple Product Example

The calculation works with any number of products. Consider a concern which sells five products with contribution margins and unit sales mix percentages as follows:

Multiple products margin and unit sales mix
Production	Margin	Mix %
A	ii.46	20%
B	5.90	19%
C	12.00	26%
D	eighteen.xc	14%
E	22.00	21%

The weighted boilerplate contribution margin is calculated 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 ten 20% + 5.90 ten 19% + 12.00 x 26% + 18.90 ten 14% + 22.00 10 21% Weighted average unit contribution margin = 12.00

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

Using the Weighted Average Unit Contribution Margin

The most important utilise for the weighted boilerplate unit contribution margin is in the calculation of the break fifty-fifty point for a multiple product business concern.

The suspension even formula is every bit follows:

Break even units = Operating expenses / Contribution margin per unit

For a multiple product business, the weighted boilerplate unit contribution margin is simply substituted into the formula. For our example higher up, if the fixed operating expenses were 96,000, then the intermission even units is given equally follows:

Break even units = Operating expenses / Weighted average unit of measurement contribution margin Break even units = 96,000 / 12.00 Break even units = viii,000

The business organization needs to sell 8,000 units to suspension 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	xx%	1,600
B	19%	1,520
C	26%	2,080
D	fourteen%	1,120
Due east	21%	1,680
Total	100%	eight,000

The total contribution margin from these products is as follows:

Contribution = 2.46 x ane,600 + five.90 x 1,520 + 12.00 x ii,080 + 18.90 x ane,120 + 22.00 x ane,680 Contribution = 95,992 rounded to 96,000

As the operating expenses were also 96,000 the business concern will break even at this level of unit sales for each of the 5 products.

About the Author

Chartered accountant Michael Chocolate-brown is the founder and CEO of Double Entry Bookkeeping. He has worked as an accountant and consultant for more than 25 years and has built financial models for all types of industries. He has been the CFO or controller of both modest and medium sized companies and has run pocket-sized businesses of his own. He has been a manager and an auditor with Deloitte, a large 4 accountancy firm, and holds a degree from Loughborough Academy.

Dec half-dozen, 2019