# Multi-Product Break-even Analysis

The Break-even point is the point where the business breaks even i.e., it experiences no profit no loss. At this point, the total costs of the business are covered by the total revenue the business generates. Another way of putting this is that the contribution earned by the business is just enough to cover the fixed costs.

## Multi-Product break-even analysis

The break-even point of a business is calculated using break-even analysis. Break-even analysis can be used for a single product or multiple products. However, we will consider multi-product break-even analysis in this article.

## Explanation

Multi-product break-even analysis is used when the business produces more than one product, and all products contribute to the overall revenue of the business in defined proportions. In this method, it is assumed that the products are sold in a constant sales mix that is pre-determined. This sales mix may be presented in the form of a ratio or percentage. For example, out of every 10 units sold by the business, 3 units are markers, 2 units are books, and 5 units are pencils. It can be presented as 3:2:5 or 30%, 20% and 50% for markers, books, and pencils respectively.

## Formula

The calculation of a multi-product break-even point is almost the same as a single-product break-even point. The only difference is that the denominator is the weighted average contribution per unit (for break-even point in units) or weighted average contribution to sales (C/S) ratio (for Break-even Revenue).

## Calculation – Breakeven Point

Let us take an example of Oak Wood Manufacturing Limited, a furniture manufacturing company. The company manufactures three products, chairs, tables, and sofas and these are sold in the proportion of 3:5:4. The following information is given:

Now that we have calculated the value of weighted average contribution per unit, we can put this into the multi-product break-even point formula to calculate the total number of units required to make it to the break-even point. However, to find how many units of each product we need to sell, this total figure needs to be multiplied by the respective proportion of each product in the sales mix. This is explained below:

Let’s say the total fixed costs were \$500,000.

## Summary – Break-even Point

Long story short, there are 3 steps to calculate the multi-product break-even point.

1. Calculate weighted average contribution per unit.
2. Calculate the break-even point using the multi-product break-even point formula (mentioned above).
3. Proportionate the total break-even point units into product types using sales mix proportion.

## Calculation – Break-even Revenue

The calculation of break-even revenue is rather simple. The denominator in the break-even revenue formula in the case of multiple products is the weighted average contribution to sales ratio. This is calculated as:

## Summary – Break-even Revenue

In conclusion, there are two steps to calculate the break-even revenue

1. Calculate the weighted average C/S ratio (as shown above)
2. Calculate the break-even revenue using the break-even revenue formula mentioned above.