# John has been asked to determine whether the $22.50 cost of tickets for the community dinner theaterExample of the Multiproduct Break-even Point

### Problem Data

It is required to find the **multiproduct break-even point** with the following data:

- Fixed Costs (F)
$35000

- Product 1
Selling Price per Unit (P): 22.5

Variable Cost per Unit (V): 10.5

Sales: 175 units

- Product 2
Selling Price per Unit (P): 5

Variable Cost per Unit (V): 1.75

Sales: 175 units

- Product 3
Selling Price per Unit (P): 5

Variable Cost per Unit (V): 2

Sales: 100 units

- Description
**John has been asked to determine whether the $22.50 cost of tickets for the community dinner theater**John has been asked to determine whether the $22.50 cost of tickets for the community dinner theater will allow the group to achieve break-even and whether the 175 seating capacity is adequate. The cost for each performance of a 10-performance run is $2,500. The facility rental cost for the entire 10 performances is $10,000. Drinks and parking are extra charges and have their own price and variable costs, as shown below: Tickets with dinner, SELLING PRICE=$22.50, VARIABLE COST=$10.50, ESTIMATED QUANTITY OF SALES UNITS=175. Drinks, SELLING PRICE=$5.00, VARIABLE COST=$1.75, ESTIMATED QUANTITY OF SALES UNITS=175. Parking, SELLING PRICE=$5.00, VARIABLE COST=$2.00, ESTIMATED QUANTITY OF SALES UNITS=100.

## Solution

The following are the detailed calculations to obtain the **multiproduct break-even point** according to the data provided. The calculation methods and formulas are based on the book Principles of Operations Management by Jay Heizer and Barry Render:

### Break-even Point in Sales Revenue ($)

**a) Break-even Point Formula in Sales Revenue ($):**

To calculate the break-even point in sales revenue ($), we will use the following formula

Where:

- BEP
_{$}: Break-even point in sales revenue ($) - F: Fixed Cost
- P
_{i}: Unit selling price of product i. - V
_{i}: Variable unit cost of product i. - W
_{i}: Percent each product is of total dollar sales.

*Note: The entire expression in the denominator of the formula is known as the weighted contribution.*

Likewise, to obtain the value of ** W_{i}**, we will apply the following expression:

Where ** Sales_{i}** indicates the sales revenue generated by product

**.**

*i***b) Table to determine the weighted contribution:**

Below is a table in which we will apply the formulas indicated:

1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 |
---|---|---|---|---|---|---|---|---|

Product 1 | 10.5 | 22.5 | 0.467 | 0.533 | 175 | 3937.5 | 0.741 | 0.395 |

Product 2 | 1.75 | 5 | 0.35 | 0.65 | 175 | 875 | 0.165 | 0.107 |

Product 3 | 2 | 5 | 0.4 | 0.6 | 100 | 500 | 0.094 | 0.056 |

Total | 5312.5 | 1 | 0.558 |

**c) Calculations Explained:**

The results shown in the table are explained below:

- Columns 2 and 3 are data entered to solve the problem.
- Column 4 is obtained by dividing the values in column 2 and 3.
- Column 5 is obtained by subtracting the value obtained in column 4 from 1.
- Column 6 shows the sales data in units that were entered in the problem. Since it is necessary to know the sales in monetary value ($), column 7 is calculated by multiplying column 3 by column 6.
- In column 8, the contribution to sales of each product was calculated by dividing each value in column 7 by the sum of the sales of all products: $5312.5. It is essential to mention that the sum of all values in column 8 must be 1.
- Finally, in column 9, multiplying the values of column 5 and column 8. The sum of all the values in column 9 gives us a result of
**0.558**. This value will be used to replace the formula.

Once we have obtained the value of the denominator of our formula, we will replace its value to calculate the break-even point:

For the company to break-even, it must have revenues of **$62724.014**

Based on current sales, the company has a **loss** of **$57411.514**

**d) Sales level by product for the Break-even point:**

To calculate the level of sales per product to cover the break-even point, multiply the sales contribution of each product by the calculated break-even point:

Products | Sales level for BEP_{$} |
---|---|

Product 1 | 0.741x62724.014 = $46478.494 |

Product 2 | 0.165x62724.014 = $10349.462 |

Product 3 | 0.094x62724.014 = $5896.057 |

### Break-even point in units for each product

To calculate the number of units that must be sold for each product to break even, divide the level of sales per product by its selling price:

Products | Units to be sold to cover BEP_{$} |
---|---|

Product 1 | 46478.494/22.5 = 2065.711 |

Product 2 | 10349.462/5 = 2069.892 |

Product 3 | 5896.057/5 = 1179.211 |

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