# How to Complete a Break-Even Analysis in Production: Between Processes

Updated on December 11, 2018 Joshua has work experience in aerospace/aluminum manufacturing & distribution. He received his BBA in accounting from Kent State University.

## Breakeven Point Finding the breakeven point of a process can aid in understanding constraints, costs and production planning overall. Breakeven analysis can be used in various business applications making it worth learning.

## What is Breakeven Analysis?

Breakeven analysis calculates the point at which revenues equal expenses in many applications. For process analysis, I will be using breakeven analysis to compare processes in a production setting. In this sense we can compare costs of different processes to figure out what quantities need to be produced to make that process worth putting in place. Costs involved in a process must first be separate into variable and fixed costs. Fixed costs do not change with the quantity of output and will not zero when production is zero. For example, we stop producing the fixed cost remains. Fixed cost examples include rent, insurance and loan payments. In the example used here fixed cost will be the cost of equipment. Variable costs will change with the increase or decrease of output. Variable costs can be labor rates, shipping cost, direct materials cost and plenty more. For simplicity, variable cost will be the labor cost per hour and is transferred into a cost per unit of product.

## Breakeven Analysis Example

This example examines different processes within a pastry company. Suppose that there are different ways to produce pastries. The process 1 involves a worker cutting pastries by hand with a tool without the assistance of a machine. The worker can cut out 120 pastries per hour while being paid a rate of \$12 per hour. Another process used is a machine called the Demag 2000. This machine has a fixed cost of \$10,000 and can cut out 600 pastries per hour. The third process involves another machine called the Demag 3000. This equipment has a fixed cost of \$15,000 and can cut out 900 pastries per hour. If the bakery always meets its target of 200,000 pastries per year, let find out how long it will take to recoup costs associated with using a machine. Labor costs per pastry equals the pastry cutter's hourly wage rate divided by the output of that process.

## Step 1

The first thing we want to do is find intersect process 1 and process 2. To do so we must multiply each variable cost by Q, add fixed costs to each (process 1 has no cost since there is not capital investment), then let them equal each other. The equation is shown below:

p1=p2

\$.1 x Q = \$10,000 + \$.02 x Q

\$.1Q - \$.02Q = \$10,000

\$.08Q = \$10,000

Q =125,000

This breakeven point (BEP) shows the point at which both processes will be creating the same output at the same cost. So, if the company produces quantity a of 200,000 per year like they plan, then it will take the company 7.5 months 125,000/ 200,000 to recover the costs of purchasing a new machine (process 2). When comparing process 1 and 2 it is better to use process 1 when under 125,000 pastries need to be produced and process 2 if more than 125,000 pastries need to be produced.

## Step 2

Next, we can solve the breakeven point for process 2.

p2=p3

\$10,000 + \$.02 X Q = \$15,000 + \$.0133 x Q

\$10,000 + \$.02Q = \$15,000 + \$.0133333Q

\$.006667Q = \$15,000

\$.006667Q = \$5,000

Q=749,963 or about 750,000 pastries

When comparing the two automated processes we see that process is more useful with at if 750,000 pastries are produced.

## Create a Breakeven Graph

When completing a breakeven analysis is always nice to have a chart. A chart can be made easily in Microsoft Excel. While in excel make four columns. One for your X-Axis (Quantity) and three for your Y-Axes (Cost). For the quantity column start at zero and add 100,000, 200,000, 300,000... until you reach 1 million. Now for p1, plug 0 into the equation \$.10 X Q you will get zero. For p2 when you plug in o your get 10,000 (\$10,000 +\$.02 x Q) When plugging in for p3 you get 15,000 (\$15,000 + \$.0066 x Q). Continue to calculate for p1, p2 and p3 while plug in each 100,000 for Q. (hint: in excel if you complete a few rows you can highlight those rows and use the fill handle to complete the table). You should have a table like the one shown below.

## Creating The Graph

To create the graph, you must select all the data in the table click on the insert tab, then click on the scattered line selection that I circled in the photo. After creating the graph, I suggest adding a title and reducing the axis maximum quantity to show a better representation of the breakeven points. If you would like a copy of the table or graph you can download a link to the spreadsheet here.

## References

Boyer, K. & Verma, R. (2010). Operations & supply chain management for the 21st century. Mason, OH: South-Western.

© 2018 Joshua Crowder

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