### Learning Outcomes

- Calculate multiple product break-even points

To calculate the break-even point for multiple product lines, first determine the **sales mix**, which is the percent of overall sales each of the two products represents.

Let’s say that BlankBooks, Inc. is considering adding a second product—a fancier version of the plain journal. Each product will have its own unit selling price and unit variable cost, as follows:

Plain | Fancy | |
---|---|---|

Sales price per unit | $ 10.00 | $ 14.00 |

Less: Variable cost per unit | 8.30 | 13.30 |

= Contribution margin per unit | Single Line$ 1.70 | Single Line$ 0.70 |

To calculate break-even, we’ll use a weighted average of the two contribution margins based on the expected product mix that the sales manager and production manager have initially agreed is possible.

Plain 2,320 units

Fancy 580 units

Plain | Fancy | Total | |
---|---|---|---|

Sales price per unit | $ 10.00 | $ 14.00 | |

Less: Variable cost per unit | 8.30 | 13.30 | |

= Contribution margin per unit | Single Line$ 1.70 | Single Line$ 0.70 | |

X Sales mix in units | 2,320.00 | 580.00 | 2,900.00 |

Contribution margin | Single Line$ 3,944.00Double line | Single Line$ 406.00Double line | Single Line$ 4,350.00Double line |

Weighted average contribution margin | $ 1.50Double line | ||

A **straight average** of the two contribution margins would be (1.70 + 0.70) / 2 = 1.20, but a simple average like that doesn’t take into account the fact that we are planning to sell four times as many plain journals as we do fancy (expressed as a ratio, it would be 4:1).

A **weighted average** takes the different volumes of each product into account by first extending the contribution margins to get the total contribution margin, and then dividing that amount by the total units.

The contribution margin for plain journals will be $1.70 X 2,320 = $3,944.00.

The contribution margin for fancy journals will be $0.70 X 580 = $406.00.

The total contribution margin will be $3,944.00 + $406.00 = $4,350.

Divide that by total units of 2,900 and we get a weighted average contribution margin of $1.50.

To get the break-even quantity then, we would divide total fixed costs that need to be covered by the weighted average contribution margin:

$3,400 / 1.50 = 2266.6666

This is a repeating decimal that is more accurately expressed as a fraction = 2,266 ⅔ units. Since we can’t make ⅔ of a unit, we round up to the next highest. This is a different rounding rule than normal because even if the fraction came out to be less than half a unit, we would still round up rather than round down.

For instance, if your calculation showed that you needed 999.25 units, you would still have to make 1,000 units in order to have a slight profit instead of a slight loss. In most real cases, none of your numbers will come out exactly even the way they do in the textbook.

So, we need 2,267 units in order to break-even. These units have to be split back out into plain and fancy. Our product mix is 80/20, which is the same as 4:1:

Unit Type | Total Units | Product Mix Percentage | Product Type Total Units |
---|---|---|---|

Sales Mix | |||

Classic | 2,267 | 80.00% | 1,813.6 |

Ultra | 2,267 | 20.00% | 453.4 |

Single Line2,267Double line | |||

Again, because these are books, we can’t make partial units, so we would have to round:

Unit Type | Total Units | Product Mix Percentage | Product Type Total Units |
---|---|---|---|

Sales Mix | |||

Classic | 2,267 | 80.00% | 1,814 |

Ultra | 2,267 | 20.00% | 453 |

Single Line2,267Double line | |||

Now let’s see how sound our calculation is by plugging this sales mix into our contribution margin model:

Units | $/Unit | Total | |
---|---|---|---|

Subcategory, Sales |
|||

Plain | 1,814 | $10.00 | $ 18,140.00 |

Fancy | 454 | $14.00 | $ 6,356.00 |

Total sales | Single Line$ 24,496.00 | ||

Subcategory, Variable costs |
Single Line | ||

Plain | 1,814 | $8.30 | $ 15,056.20 |

Fancy | 454 | $13.30 | $ 6,038.20 |

Total variable costs | Single Line$ 21,094.40 | ||

Contribution Margin | Single Line$ 3,401.60 | ||

Fixed costs | $ 3,400.00 | ||

Operating income | Single Line$ 1.60Double line | ||

The bottom line is not exactly zero because we rounded the number of units.

To calculate for a target profit, simply add the target profit to fixed costs and run the same calculations.

For instance, to get a target profit of $5,000 per month, fixed costs + target profit would be $8,400, and the total units needed would be:

$8,400 / 1.5 = 5,600 units

These units have to be split back out into plain and fancy. Our product mix is 80/20:

Unit Type | Total Units | Product Mix Percentage | Product Type Total Units |
---|---|---|---|

Sales Mix | |||

Classic | 5,600 | 80.00% | 4,480 |

Ultra | 5,600 | 20.00% | 1,120 |

Single Line5,600Double line | |||

And our contribution margin statement looks like this:

Units | $/Unit | Total | |
---|---|---|---|

Subcategory, Sales |
|||

Plain | 4,480 | $10.00 | $ 44,800.00 |

Fancy | 1,120 | $14.00 | $ 15,680.00 |

Total sales | Single Line$ 60,840.00 | ||

Subcategory, Variable costs |
Single Line | ||

Plain | 4,480 | $8.30 | $ 37,184.00 |

Fancy | 1,120 | $13.30 | $ 14,896.00 |

Total variable costs | Single Line$ 52,080.00 | ||

Contribution Margin | Single Line$ 8,400.00 | ||

Fixed costs | $ 3,400.00 | ||

Operating income | Single Line$ 5000.00Double line | ||

As you can see, once you have the model, especially once you have created it in a spreadsheet or other software program, you can expand it and use it for an incredible array of “what-if” analyses.

Here is a bit more involved example of calculating the break-even point for multiple product lines:

You can view the transcript for “acct 2102 Lofty Inc multi product break even CLASS ACTIVITY” here (opens in new window).

Now, let’s check your understanding of using the CVP model with multiple product lines.