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.

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