# Break Even Analysis For Multiple Products

Calculating the the number of units which need to be sold for the business to reach break even is relatively straight forward when a business sells only one product.

As an example, suppose a business with operating expenses (fixed overhead) of 4,500, has only one product which has a unit selling price of 10.00, and a unit cost price of 4.00.

The break even units formula is used as follows:

```Unit contribution margin = Selling price - Cost price
Unit contribution margin = 10.00 - 4.00 = 6.00

Break even units = Operating expenses / Unit contribution margin
Break even units = 4,500 / 6.00
Break even units = 750 units
```

This can be summarized as follows:

Single product break even
Unit Total
Units 750
Revenue 10.00 7,500
Cost of sales 4.00 3,000
Contribution margin 6.00 4,500
Operating expenses 4,500
Net income 0

However, most businesses sell more than one product, and the calculation of the break even units needs to be amended to reflect this.

## Break Even Analysis for Multiple Products

In order to carry out a break even analysis for multiple product lines. Suppose for example, our business has the same operating expenses of 4,500, but this time is has two product lines. Product A is our low margin product with a selling price of 5.00 and a cost price of 4.00, and product B is our high margin product with a selling price of 20.00 and a cost price of 7.00. In addition, our financial projections show that our unit sales mix is 90% / 10%, meaning that 90% of our unit sales will be product A, and 10% will be product B.

The break even analysis for multiple products is carried out using the following steps:

### Step 1: Calculate the Weighted Average Contribution Margin

In the single product example we used the contribution margin of the product to work out the break even units. Because we now have two products, we need to find the average contribution margin of both products, however, because the products are not sold in equal numbers of units, we need to weight the contribution margin by the sales mix as follows:

```Product A unit contribution margin = 5.00 - 4.00 = 1.00
Product B unit contribution margin = 20.00 - 7.00 = 13.00
```

As the unit sales mix is 90% product A to 10% product B, the weighted average contribution margin (WACM) per unit is calculated using the sales mix formula as follows:

```WACM = Product A contribution x Product A sales mix % + Product B contribution x Product B sales mix %

WACM = 1.00 x 90% + 13.00 x 10% = 2.20
```

For these products, with a sales mix of 90%/10%, the weighted average contribution for every unit sold is 2.20 as shown in the diagram below. ### Step 2: Calculate the Break Even Units

The break even units are calculated as before except this time we use the weighted average contribution margin.

```
Weighted average contribution margin = 2.20

Break even units = Operating expenses / Unit contribution margin
Break even units = 4,500 / 2.20
Break even units = 2,046 units
```

### Step 3: Analyse the Break Even Units by Product

The break even units can now be split between the two products using the unit sales mix percentages as follows:

```Break even units = 2,046 units
Unit sales mix = 90% A / 10% B

Units of product A = 2,046 x 90% = 1,842
Units of product B = 2,046 x 10% = 205
```

It should be noted that as the business can’t sell a part of a product, the number of units is always rounded up.

This can be summarized as follows:

Break Even Analysis For Multiple Products
Unit A A Unit B B Total
Units 1,842 205 2047
Revenue 5.00 9,210 20.00 4,100 13,310
Cost of sales 4.00 7,368 7.00 1,435 8,803
Contribution margin 1.00 1,842 13.00 2,665 4,507
Operating expenses 4,500
Net income 7

The business breaks even when it sells 1,842 units of product A, and 205 units of product B. The small net income of 7 is due to rounding up to the nearest unit during the calculations.

## Multi Product Break Even Analysis

While this example uses a two product business, the calculations can be carried out for any number of products, the only change to the calculation is in step 1, where the weighted average contribution margin is calculated.

So for example, if the business had five products with contribution margins and sales mix percentages as follows:

Multiple Products Margin Mix
Product Margin Mix %
A 2.20 30%
B 4.90 10%
C 13.00 25%
D 22.00 15%
E 16.00 20%

The weighted average contribution margin is then calculated using the sales mix formula
as:

```WACM = Product A contribution x Product A sales mix % + Product B contribution x Product B sales mix % .........

WACM = 2.20 x 30% + 4.90 x 10% + 13.00 x 25% + 22.00 x 15% + 16.00 x 20%
WACM = 10.90
```

The weighted average contribution margin can now be used as before in steps 2 and 3 above.

It should be noted that this method of break even analysis for multiple products only works when the product sales mix remains constant. When preparing financial projections an estimate of the sales mix will be used and a break even position can be calculated. If as time passes the actual results reveal a different sales mix, then the financial projections would be revised and a new break even position must be determined using a revised sales mix calculation.