Calculating the break-even point for a multi-product factory requires evaluating the overall production volume through a Weighted Average Contribution Margin (WACM). Because each product carries its own price tag, variable cost, and sales proportion, treating them as a combined "sales basket" provides an accurate overall facility threshold.
First, calculate the unit contribution margin ($CM_i$) for each product $i$ by subtracting its variable cost ($V_i$) from its selling price ($P_i$).
$$CM_i = P_i - V_i$$
2. Define the Sales Mix Ratio
Determine the sales mix weight ($W_i$) for each product based on its relative share of total unit sales volume. The sum of all weights must equal 1 ($100\%$).
$$W_i = \frac{\text{Sales Volume of Product } i}{\text{Total Combined Sales Volume of All Products}}$$
$$\sum W_i = 1$$
3. Compute the Weighted Average Contribution Margin (WACM)
Multiply each product's unit contribution margin by its sales mix weight, then sum these values to find the overall contribution per average unit.
$$\text{WACM} = \sum (CM_i \times W_i) = (CM_1 \times W_1) + (CM_2 \times W_2) + \dots + (CM_n \times W_n)$$
4. Calculate Total Facility Break-Even Volume
Divide the factory's total shared fixed costs ($FC_{total}$) by the $\text{WACM}$. This yields the total combined units the facility must produce and sell across all product lines.
$$\text{Total Break-Even Quantity (BEQ)} = \frac{FC_{total}}{\text{WACM}}$$
5. Allocate Break-Even Units Across Products
Finally, multiply the total facility break-even quantity by each individual product's sales mix weight to find the specific volume needed for each item.
$$\text{BEQ}_i = \text{Total BEQ} \times W_i$$
Illustrative Multi-Product Example
Consider a factory with $120,000 in total shared fixed costs manufacturing two products:
| Parameter | Product A | Product B |
| Selling Price ($P$) | $50 | $100 |
| Variable Cost ($V$) | $30 | $60 |
| Unit Contribution Margin ($CM$) | $20 | $40 |
| Expected Sales Mix ($W$) | 60% (0.60) | 40% (0.40) |
$$\text{WACM} = (\$20 \times 0.60) + (\$40 \times 0.40) = \$12 + \$16 = \$28$$
$$\text{Total BEQ} = \frac{\$120,000}{\$28} \approx 4,286 \text{ units (total)}$$
- Product A Target: $4,286 \times 0.60 = 2,572 \text{ units}$
- Product B Target: $4,286 \times 0.40 = 1,714 \text{ units}$
Weighted Contribution Margin Ratio (Revenue Method)
If product volumes are difficult to track or if the sales mix is driven by revenue proportions rather than physical units, use the Weighted Contribution Margin Ratio ($\text{CMR}_{overall}$).
$$\text{CMR}_i = \frac{P_i - V_i}{P_i}$$
$$\text{CMR}_{overall} = \sum (\text{CMR}_i \times R_i)$$
Where $R_i$ represents product $i$'s percentage share of total revenue (not unit volume). The total required facility revenue is then:
$$\text{Break-Even Revenue (BER)} = \frac{FC_{total}}{\text{CMR}_{overall}}$$