Cost-Profit-Volume or Break-Even Analysis

Break-even analysis is a graphical and algebraic representation of the relationships among volume of output, costs and revenues. Costs can be classified into two types: fixed costs and variable costs. Fixed costs are the costs such as administration expenses, rents of the buildings, lighting, etc. And they do not vary with the volume of the output. Variable costs are the costs such as raw material cost, labor cost, etc. And they vary with the volume of the output.  The sum of the fixed and variable costs at a specific volume of output becomes the total cost at that volume of output.

Break-even analysis is one of the tools used for selection of a location. Since each and every location will have a different cost structure and sales volume, break-even analysis helps the manager identify the location where the profits are high. Figure shows the relationship of cost and volume in two different locations A and B.

Here, we assume that the revenues and costs are the linear functions of output volume. We also assume that the revenues for the two locations are the same, as there will not be much difference in the demand if the price of the product remains the same irrespective of the location it was produced at. From Figure, it is clear that if the volume of the output is less than V_o, location B is preferable as TC_B (total cost at location B) is less than TC_A (total cost at location A).  If the volume is more than V_o, location A is preferable as TC_A is less than TC_B.

Figure: Cost Volume Relationships of Two Locations

However, the lowest cost location may not always be the maximum profit location. This always depends on the price and volume of sales in a particular location. For instance, Figure 6.2 describes a situation where the company experiences a sales volume of V₂ in location B and a sales volume of V₁ in location A.  Here the higher cost location will result in a greater profit, and hence is preferred over the lower cost location.              

Figure: Higher Cost Locations Providing Higher Profits

Problem 

Godavari Electricals Ltd. wanted to set up a new plant for manufacturing industrial heaters. The management of Godavari Electricals identified Kakinada, Vijayawada, and Hyderabad as the potential areas to set up the plant. The fixed costs per year and the variable costs per heater at each of the three locations are given below.

The product is expected to be sold at Rs.1050 and the company hopes to sell 600 industrial heaters per year. Calculate the likely profit at each location and determine the most profitable location for the company.

Solution

We first calculate the total costs (sum of the fixed and variable costs) at each of the three locations when 600 units of goods are sold.

Total cost at Kakinada       = Rs. 2,00,000 + (325 × 600)

                                     = Rs. 3,95,000

Total cost at Vijayawada    = Rs. 2,50,000 + (285 × 600)

                                     = Rs. 4,21,000

Total cost at Hyderabad     = Rs. 3,00,000 + (265 × 600)

                                     = Rs. 4,59,000

Total revenue of the firm    = 1050 × 600 = Rs. 6,30,000.              

Therefore, the profits of the company if they were set up in the given locations would be as follows:

Profit at Kakinada               = Rs. 6,30,000 - Rs. 3,95,000

                                       = Rs. 2,35,000

Profit at Vijayawada            = Rs. 6,30,000 - Rs. 4,21,000

                                       = Rs. 2,09,000

Profit at Hyderabad             = Rs. 6,30,000 - 4,59,000

                                       = Rs. 1,71,000

From the above calculations, it is clear that Kakinada is the most profitable location to set up the new plant for producing 600 units per year.              

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