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# Multi-Product Break-Even Analysis

## Introduction

The determination of the break-even point in CVP analysis is easy once variable and fixed costs are determined. A problem arises when the company sells more than one type of product.

In a Nutshell

Break-even analysis for multiple products is made possible by calculating weighted average contribution margins.

The break-even point in units is equal to total fixed costs divided by the weighted average contribution margin per unit (WACMU).

The break-even point can be computed as: total fixed costs divided by the weighted average contribution margin ratio (WACMR).

For companies that produce more than one product, break-even analysis may be performed for each type of product if fixed costs can be determined separately 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 = Total fixed costs in units Weighted average CM per unit
 BEP = Total fixed costs in dollars 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 individual sales to total sales amount.

 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 (computed earlier in #1) by their 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.

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