# Multi-Product Break-Even Analysis

The determination of the break-even point in CVP analysis is easy once the variable and fixed components of costs have been determined.

A problem arises when the company sells more than one type of product. Break-even analysis may be performed for each type of product if fixed costs are determined separeately for each product.

However, fixed costs are normally incurred for all the products hence a need to compute for the composite or multi-product break-even point.

## Multi-Product Break-Even Point Formula

In computing for the multi-product break-even point, the weighted average unit contribution margin and weighted average contribution margin ratio are used.

 BEP in units = Total fixed costs Weighted average CM per unit
 BEP in dollars = Total fixed costs Weighted average CM ratio

## Example

Belle Company manufactures and sells three products: Products A, B, and C. The following data has been provided the company.

 A B C Selling price \$100 \$120 \$50 Variable cost per unit 60 90 40 Contribution margin per unit 40 30 10 Contribution margin ratio 40% 25% 20%

The company sells 5 units of C for every unit of A and 2 units of B for every unit of A. Hence, the sales mix is 1:2:5. The company incurred in \$120,000 total fixed costs.

1. Multi-product break-even point in units

 BEP in units = Total fixed costs Weighted average CM per unit \$120,000 \$18.75 BEP in units = 6,400 units

a. Computation of weighted average CM per unit:

 ∑(CM per unit x Unit sales mix ratio) Product A (\$40 x 1/8) \$ 5.00 Product B (\$30 x 2/8) 7.50 Product C (\$10 x 5/8) 6.25 WA CM per unit \$18.75

The weighted average CM may also be computed by dividing the total CM by the total number of units.

 WA CM per unit = (40x1)+(30x2)+(10x5) = 18.75 8

b. Breakdown of the break-even sales in units:

 (B-E point x Unit sales mix ratio) Product A (6,400 units x 1/8) 800 units Product B (6,400 units x 2/8) 1,600 Product C (6,400 units x 5/8) 4,000 Total 6,400 units

The company must produce and sell 800 units of Product A, 1,600 units of Product B, and 4,000 units of Product C in order to break-even.

2. Multi-product break-even point in dollars

 BEP in dollars = Total fixed costs Weighted average CM ratio \$120,000 25.4237% BEP in dollars = \$472,000

a. Computation of weighted average CM ratio:

 ∑(CMR x Sales revenue ratio) Product A (40% x 100/590) 6.7797% Product B (25% x 240/590) 10.1695% Product C (20% x 250/590) 8.4745% WA CM per unit 25.4237%

Take note that this time, the ratio used is developed from the ratio of individual sales to total sales.

 Product A (100x1) 100 Product B (120x2) 240 Product C (50x5) 250 Total Sales 590

The weighted average CM may also be computed by dividing the total CM by the total sales.

 WA CM ratio = (40x1)+(30x2)+(10x5) (100x1)+(120x2)+(50x5) WA CM ratio = 25.4237%

b. Breakdown of the break-even sales revenue:

 (B-E point x Sales revenue ratio) Product A (\$472,000 x 100/590) \$  80,000 Product B (\$472,000 x 240/590) 192,000 Product C (\$472,000 x 250/590) 200,000 Total \$472,000

The company must generate sales of \$80,000 for Product A, \$192,000 for product B, and \$200,000 for Product C, in order to break-even. Alternatively, these can be computed by multiplying the individual break-even point in units for each product by their corresponding selling price, i.e. 800 units x \$100 for Product A = \$80,000, 1,600 units x \$120 for Product B = \$192,000, and 4,000 units x \$50 for Product C = \$200,000.

Online resource for all things accounting. more
Search this Site
Featured in the Blog
Feedback