# Bagot Copy Shop has a volume of 125,000 black-and-white copies per month.Break-even Point Example - Cost Analysis

### Problem Data

It is necessary to find the alternative that generates **the lowest cost** using the **break-even analysis**:

- Alternative 1
Fixed Costs (F): 2000

Variable Cost per Unit (V): 0.03

- Alternative 2
Fixed Costs (F): 1500

Variable Cost per Unit (V): 0.035

- Description
**Bagot Copy Shop has a volume of 125,000 black-and-white copies per month.**Bagot Copy Shop has a volume of 125,000 black-and-white copies per month. Two salespeople have made presentations to Gordon Bagot for machines of equal quality and reliability. The Print Shop 5 has a cost of $2,000 per month and a variable cost of $.03. The other machine (a Speed Copy 100 ) will cost only $1,500 per month, but the toner is more expensive, driving the cost per copy up to $.035. If cost and volume are the only considerations, which machine should Bagot purchase?

## Solution

The following are the calculations and detailed graphs to obtain the **least cost alternative** based on the data provided:

### Break-even Analysis of Alternatives:

To perform the cost analysis, we will calculate the break-even point by comparing the alternatives two by 2, applying the following formula:

Where:

- BEP
_{m-b}: Break-even point in units of production between alternatives “m” and “b” - F
_{m}: Fixed cost of alternative “m” - CF
_{b}: Fixed cost of alternative “b” - CV
_{Um}: Variable cost per unit of alternative “m” - CV
_{Ub}: Variable cost per unit of alternative “b”

The result must be a positive value. In case we have a different result, we will analyze as follows:

- If the result is zero, it means that the fixed costs of both alternatives are equal, and the option with the lowest unit variable cost will always be the best alternative.
- If the result is negative, the alternatives do not intersect to form a break-even point. The alternative with the lowest unit variable cost and the lowest fixed cost simultaneously will be the best option.
- If the alternatives have the same unit variable cost, the break-even formula will not be applied, and the alternative with the lowest fixed cost will be the optimal one.

**a) Break-even Point between Alternatives 1 and 2:**

The **break-even point** in units of production of the **alternatives 1 and 2 is 100000**. When that amount is produced, **both alternatives have the same cost of $5000**.

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