# Break-even Chart

A break-even chart is a graph which plots total sales and total cost curves of a company and shows that the firm’s breakeven point lies where these two curves intersect.

The break-even point is defined as the output/revenue level at which a company is neither making profit nor incurring loss. For a company to make zero profit, its total sales must equal its total costs. When sales are higher than total costs, it earns a profit but when total costs are higher than total sales, it loses money. A break-even chart visualizes the whole relationship and makes it easier to follow the break-even point.

A break-even chart is constructed such that units are plotted on the x-axis and revenue/cost on y-axis. It is useful only when the production is inside the relevant range i.e. output bracket in which fixed costs do not change.

## Example

Let’s consider a cab company which charges $5 per kilometer. Its fixed costs are$200,000 per cab per annum and its variable operating costs are \$3 per kilometer. Let’s find the minimum number of kilometers which the cabs must be plied or the company will suffer a loss.

Using the data above, we can write the following equations for total revenue and total costs:

$$\text{TR}\ =\ \text{\5}\ \times \text{Q}=\text{5Q}$$

$$\text{TC} \\ = \text{FC} + \text{VC} \\ = \text{\200,000} + \text{\3}\times \text{Q} \\ =\text{\200,000} + \text{3Q}$$

By plugging different Q values, we can create a table of total revenue and total costs, which may be bifurcated into total variable costs and total fixed costs.

An extract from the table is as follows:

Quantity Total Revenue Total Cost Total Variable Costs Total Fixed Costs
1 5 200,003 3 200,000
500 2,500 201,500 1,500 200,000
5,000 25,000 215,000 15,000 200,000
100,000 500,000 500,000 300,000 200,000
150,000 750,000 650,000 450,000 200,000
200,000 1,000,000 800,000 600,000 200,000

If we plot this table, we get the following graph:

The break-even point is this example is 100,000 units because it is the output level at which the total revenue and total cost curves intersect.

At any point below the break-even point, the company is incurring losses equal to the red-shaded area and at any point above 100,000 units, the company is making profit as represented by the blue-shaded area.