The contribution margin for a single product is deducting the variable costs from the sales or revenue figure. The break-even point is the stage where the company makes no profit or losses. Estimating the break-even point for a multiple product facility can take different methods. One of such methods in calculating the weighted average contribution margin for the break-even analysis.
What Is The Weighted Average Contribution Margin?
For a multiple product facility, the contribution margin for each product weighed against the portion of sales is called the weighted average contribution margin. We can calculate the contribution per unit for each product and then take the average.
As we know, the formula to calculate the contribution margin for a single product is:
Contribution margin = Sales – Variable Costs
For multiple products, we can use the sales mix percentage for each product and calculate the weighted average contribution margin as,
Weighted Average Contribution margin = (Contribution of Product 1 × Sales mix %) + (Contribution of Product 2 × Sales mix %) + (Contribution of Product 3 × Sales mix %) ….
For break-even analysis, we intend to find the point where the profits are zero. As the total profit of a product unit is anything above the total costs (fixed + variable). Therefore,
Break-even point in units = Fixed Costs ÷ Contribution per unit
In multiple product scenarios, the formula can be rewritten as:
Break-even Revenue = total fixed costs ÷ weighted average contribution margin
The break-even point can be calculated for the unit’s bases as well,
Break-even Units = total fixed costs ÷ weighted average contribution margin per unit
Working Example
Let us suppose a company green Star produces 4 different products with the following data. The fixed costs for the company remain $ 300,000 for the production period.
| Product | Sales in Units | Sale Price per unit | Variable Cost per unit |
|---|---|---|---|
| P1 | 10,000 | 20 | 14 |
| P2 | 15,000 | 15 | 8 |
| P3 | 20,000 | 10 | 6 |
| P4 | 15,000 | 20 | 15 |
We can calculate the total sales, weighted average contribution margin, and the break-even point per unit or sales as below.
| Product | Sales in Units | Sale price per unit $ | Sales Mix | Variable Cost per unit $ | Contribution Margin per unit $ |
|---|---|---|---|---|---|
| P1 | 10,000 | 20 | 16.67% | 14 | 6 |
| P2 | 15,000 | 15 | 25% | 8 | 7 |
| P3 | 20,000 | 10 | 33.33% | 6 | 4 |
| P4 | 15,000 | 20 | 25% | 15 | 5 |
| Totals | 60,000 | 100% |
Weighted Average Contribution Margin = (6×16.67%) + (7×25%) + (4×33.33%) + (5×25%)
Weighted Average Contribution Margin = (1) + (1.75) + (1.33) + (1.25) = $ 5.33
Break-even Units = total fixed costs ÷ weighted average contribution margin per unit
Break-Even units = 300,000 / 5.33 = 56,285 units.
We can verify that by knowing the 56,285 multiplied with the average unit contribution $ 5.33 equals the fixed costs of $ 300,000.
Break-even units per sales mix for total 56,285 units:
| Product | P1 | P2 | P3 | P4 |
|---|---|---|---|---|
| Product | P1 | P2 | P3 | P4 |
| Sales Mix % | 16.67% | 25% | 33.33% | 25% |
| Product Break-Even Units | 9,382 | 14,071 | 18,760 | 14,071 |
Let us assume that the company wants a target profit of $100,000 with the current sales.
Revenue required = (fixed Costs + Target profit) ÷ (Contribution Margin %)
Contribution Margin % = (Fixed Costs ÷ Target profit) × 100 = 33.33%
Required Sales= (fixed Costs + Target profit) ÷ (Contribution Margin)
Required Sales = (300,000 + 100,000) ÷ 33.33%
Hence, Required Sales = $ 1,200,120 or $ 1,200,000 (rounded)
Analysis and Interpretation
The weighted average contribution margin analysis allows the company to anticipate its threshold production targets. For a single product, the calculations are straightforward. However, most companies produce tens and hundreds of products. The contribution margin essentially provides information on covering the variable costs. If the company can estimate the average of these variable costs, it can then add the fixed costs to ascertain the break-even point.
Further, if the company knows the number of units to reach the break-even point. It would then need to ascertain which number of units for each product it should produce to reach the optimum production levels.
Why Is the Weighted Average Contribution Margin Important In Break-Even Analysis?
Let us recall our example, Green Star produced 4 products with varying units and margins. The company’s fixed costs would remain at $ 300,000. Additionally, the company would need to make profits. The weighted average contribution used in the break-even analysis can produce the starting point for the company to know that must produce at least 56,282 units to cover its expenses.
Should the company produce more of the product P1, P2, or P3? Or equally, the proportion of all of the products at 25%? The sales mix percentage and the weighted average contribution provides the information on that. We saw the sales mix and the weighted average contribution margin gave varying required production levels for all four products.
Similarly, we saw that with a weighted average margin of 33.33%, the company would need to make $1.2 million in sales to receive a gross profit of $100,000. The analysis can provide useful forecasts for the company to examine the variable costs and increase its contribution.
Important Points
- It offers a starting point to forecast the minimum production units to cover the total costs
- The company can add the target profits to forecast the required sales
- The weighted average contribution margin can differentiate between the different product sales mix %
- The company can prioritize the production based on higher profit-generating products
However, we should remember as with any forecast plans, the break-even analyses also provide the estimated information only. The use of the weighted average contribution margin also carries some limitations.
- Weighted average contribution margin assumes the prices will remain unchanged during the production period
- It assumes the company will not incur additional fixed costs
- It does not offer any adjustments during the production levels
- The seasonal demand in lower contribution margin product can outweigh the contribution of other products
- It only calculated the requires volume production, practically many other factors can change the contribution margins
Conclusion
The weighted average contribution margin can provide useful forecast information on break-even sales and volume. The company can estimate the sales mix units and adjust the production of the most profitable products. However, it has some limitations such as the lack of flexibility during the production period for price changes and additional costs.
