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.
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:
$$ TR\ =\ $5\ \times Q=5Q $$
$$ TC \\ = FC + VC \\ = $200,000 + $3\times Q \\ =$200,000 + 3Q $$
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|
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.
Written by Obaidullah Jan, ACA, CFA and last modified on