Explain multiproduct breakeven analysis. What is the assumption on proportions among the quantities in multiproduct breakeven analysis? Provide a hypothetical example of multiproduct breakeven analysis. Provide in-text citations and explain your example in detail.
break even point refers to where the company's revenues and costs for the particular level of activity are equal and the company has no profit/loss at that given point.
However, most businesses sell more than one product, and the calculation of the break even units needs to be amended to reflect this.Hence a multi product break even analysis needs to be done.
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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