# Graphical representation of break-even analysis

Written by True Tamplin, BSc, CEPF®
Updated on June 22, 2021

## Break-even chart

Cost-Volume-Profit (or Break-Even) relationships can also be portrayed through the use of graphs. This method has the advantage of showing cost-volume-profit relationships over a range of sales. The graphic analysis permits managers to observe areas of profit or loss that would occur for a broad range of sales activity. The data from the earlier example are presented in a tabular form as below and are used to draw the break-even chart:

In plotting the graph it is. assumed that the selling price remains at \$25, variable cost remains at \$15 per unit and fixed cost at \$30,000 over the range of units sold. The units sold are plotted on the horizontal scale while total revenue is shown on the vertical scale. The total revenue line is plotted, running from \$0 at zero volume of sales to \$1,50,000 representing sales of 6,000 units at \$25 per unit. The total cost line is the sum total of fixed cost (\$3,000) and variable cost of \$15 per unit, plotted for various quantities of units to be sold.
The intersection of the two lines indicates the break-even point. Below and to the left of the break-even point, the difference between the total cost line and the total revenue line reflects the net loss for -the period. Conversely, the distance between these two lines to the right of the break-even point represents net profit for the period. The break-even graph conveys very clearly the role of contribution in the relationship of volume to profit by showing the net profit or loss at any volume. However, the graph can be interpreted only within the relevant range of operations, i.e. the level of activity over which fixed costs are assumed to remain fixed.

## The Profit-Volume Graph (P/V Graph)

A simpler version of the break-even chart known as the profit-volume graph (P/ V graph) is now discussed. The profit volume graph shows a direct relationship between sales and profits and is easy to understand. Break-even charts and P/ V graphs are often used together to obtain the advantages of both forms of presentation. The vertical scale (the y-axis) represents total profits or losses, while the horizontal scale (the x-axis) represents unit of product and sales revenue. An advantage of the P/ V graph is that profit and losses at any point can be read directly from the y-axis. The data used earlier for preparing the Break-Even chart have been used to draw up the P/ V graph given below.

The intersection of the profit line with the horizontal line gives the break-even point. Points above the line measure profits while points below the line measure losses.
The P/ V graph is a simple and convenient device of showing the extent to which profits are affected by changes in the factors that affect profit. For example, if unit selling prices, unit variable costs and total fixed costs remain constant, how many units are required to be sold so as to achieve a target profit or percentage return on sales. Or, if variable costs per unit can be reduced, what additional profits can be expected at any given volume of sales.
An advantage of the P/ V graph is that profits and losses at any point can be read directly from the vertical scale. A major disadvantage is that the graph does not clearly reveal how costs vary with changes in activity. Hence, as mentioned earlier, both the P/ V graph and Break-Even chart are used together by financial managers.