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:

  • BEPm-b: Break-even point in units of production between alternatives “m” and “b”
  • Fm: Fixed cost of alternative “m”
  • CFb: Fixed cost of alternative “b”
  • CVUm: Variable cost per unit of alternative “m”
  • CVUb: 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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