# Graphic approach, Charts "profit - sales volume", Analysis for...

## Graphical approach

Dependency costs-volume-profit can be represented graphically. Such graphs are very simplistic, but their main practical advantage is precisely the simplicity of construction and visibility. These graphs are essentially static; those or other changes in the initial data (including the sales price) require the construction of a new chart or series of graphs. It is also assumed linear dependence of costs and volumes of production (sales), which is a certain simplification. Graphs costs-volume-profit are constructed in the form that is best suited to illustrate a specific problem, from which it follows that there are different kinds of them.

## Graphs Profit - Sales Volume

### Analysis for the release of one type of product

Graph Profit - Sales Volume It is used to determine the possible profit (loss) at various levels of sales (production). The schedule is divided into two parts by a horizontal line of sales volumes, while the latter can be expressed in quantitative or cost terms, as well as in percentage. The vertical line represents the possible profit (loss). Above the horizontal line - profit, lower - losses.

Graph Profit - Sales Volume is a graph of the linear equation, which can be expressed as: where Пр - dependent variable; V is an independent variable.

Normally, the values ​​of the independent variable are plotted along the horizontal axis, and the values ​​of the dependent variable are plotted along the vertical axis. Let's consider the construction of the graph "profit - sales volume". applied to a single product.

EXAMPLE 10.3

We use the following data:

- fixed costs for the period - 100 den. units;

- variable costs per unit of output - 10 den. units/units;

- unit price - 20 den. units/units

Then the equation will look like this:

Pr = 20 V - 10 V - 100

or

Pr = 10 V - 100.

To construct a linear graph, two points are necessary; and usually choose those that correspond to zero sales and bullet profit. Equating V = 0, we get that Pr = -100. In other words, if the company has zero sales, its losses will be equal to constant costs. Equating Pr = 0, we obtain V = 10. The resulting two points determine the graph "profit - sales volume". (Figure 10.1). Fig. 10.1. Graph Profit - Sales Volume for one product

### Analysis for the release of several types of products

Graph Profit - Sales Volume can be used in the production of several types of products, but in such a situation the cost approach is more preferable. Since each product can be determined by sales revenue and variable costs, it is obvious that for each product, you can calculate the marginal revenue and the margin profit ratio. Consider an example.

EXAMPLE 10.4

The data for plotting are presented in Table. 10.10.

Table 10.10

Data for plotting

 Product Revenues from sales, den. units Variable costs, den. units Marginal revenue, den. units Marginal revenue ratio A 150 000 90 000 60 000 0.4 B 100 000 20 000 80 000 0.8 In 80 000 40 000 40 000 0.5 Г 50 000 40 000 10 000 0.2 Total 380 000 190 000 190 000 0.5 Constant costs, den. units (100,000) Profit, den. units 90 000

Data on revenue, marginal revenue and marginal revenue ratios are presented in Table. 10.10 as a whole for the company, and separately for each product. Therefore, you can plot the graph of "profit - sales" both for the entire volume of output, and separately for each product (Figure 10.2).

The total schedule is constructed similarly to the graph shown in the previous example, with the only difference being that in this case the sales volume is expressed not in units of output, but in monetary units. The breakeven point for the package in value terms will be 200,000 den. units (fixed costs: marginal revenue ratio or 100,000 den units: 0.5).

The chart begins at the point corresponding to the zero sales volume and the maximum loss (the sum of fixed costs in the amount of 100,000 den. units), crosses the abscissa axis at the breakeven point (200,000 den.) and ends at the point corresponding to the received profit of 90 000 den. units with sales of 380 000 den. units

Graphs Profit - Sales Volume for each product are constructed as follows. Profit lines are applied for each product as the marginal revenue ratio decreases, i.e. starting with product B, which has the highest marginal revenue ratio (0.8), and ending with the product G with the lowest marginal revenue ratio (0.2).

The profit line for product B starts at the same point as the sum chart, and runs to the point corresponding to the sales volume of 100,000 den. units and a loss of 20,000 den. units Since the marginal revenue from the sale of product B is 80,000 den. units, the graph shows that out of 100,000 den. units fixed costs (corresponding to the maximum loss) are covered by 80 000 den. units Consequently, after the sale of product B, the loss is 20,000 den. units (100,000 - 80,000).

The profit line for product B, which has a margin ratio of 0.5, starts at the point where the line for product B ends. After the sale of the product, the revenue will be 180,000 denominated. units (100 000 + 80 000), which will make a profit of 20 000 den. units Thus, the profit line for product B crosses the sales volume axis and ends at the point with coordinates 180,000, 20,000.

Accordingly, at the same point, the profit line for product A (marginal revenue coefficient 0.4) starts, and ends at the point with coordinates 330,000 (100,000 + 80,000 + 150,000), 80,000 (20,000 + 60 000).

The profit line for product D with the lowest margin ratio (0.2) is plotted on the schedule of the last. Product G adds another 10,000 den to profit. units, and the total is already 90 000 den. units, and 50,000 den. units to the sales volume equal to the amount of 380 000 den. units Fig. 10.2. Graph Profit - Sales Volume for several types of products

Graphical representation of the profit for each product visually reflects the fact that the steeper the slope of the line, the higher the margin profit ratio. If a product does not have marginal revenue, then the slope of the line will be downward. In addition, the size of the marginal revenue of each product in monetary units can be determined directly on the graph by measuring the vertical distance from the point where the profit line begins to the point where it ends. Such charts are also used to analyze the sales volume for different territories, sellers and types of consumers whose purchases provide the greatest profit for the company.

Note that for all the ease of construction and interpretation, the graph "profit - sales" does not reflect changes in costs when the volume of sales (production) changes. Such an opportunity is provided by the graphs "costs - volume - profit".

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