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# Graphical representations of CVP analysis

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Cost volume profit analysis (also called break-even analysis) is an extremely useful tool for managers because of its simplicity and because of its focus on essential business factors.

This material will cover the development of the break-even chart, the use of profit graphs (with illustrations of how cost and price changes impact profits), and a discussion of how you can develop a spreadsheet to generate profit graphs and compute break-even points.

Finally, the last section looks at how managers can use CVP to evaluate things like price changes and changes in marketing promotion expenditures.

## Development of a Break-Even Graph

The following graphs illustrate how one builds a break-even chart. This company has annual fixed costs of $40, a unit selling price of $10, and a unit variable cost of $6. Since it earns $4 from each unit that it sells for $10, the company has a margin percentage of 40% of sales.

First, one draws the fixed cost line on a graph. A flat line at the $40 level represents fixed costs.

Next, we show the variable cost line in this graph.

Adding the variable costs to the fixed costs provides the total costs. In break-even and cost-volume-profit analysis accountants assume all costs are either fixed or variable.

## Profit Graphs

Because the break-even chart has so many lines it can be confusing to read. Accordingly, accountants have developed the Profit Graph to show the same information but with fewer lines. The profit graph below shows the same information as the break-even chart.

Some points to note in this graph: The sloping line hits the vertical axis at a distance below the zero-profit line equal to the fixed costs. The slope of the line is equal to the margin percentage. The higher the percentage of margin to sales, the steeper the line.

## The Profit Impact of Variations in Critical Variables

The following graphs illustrate how price changes and cost changes impact the shape of the line in the profit graph. The base case (represented by the blue line) is the same case illustrated in the last graph. The red line represents the line for the change; in this first case, the price increases.

## Unit Sales Price Increases by $1

Notice the following changes in the graph. The break-even point has moved to the left. The slope of the line has increased because the margin percentage has risen.

## Unit Sales Price Drops by $1

Notice these changes in the graph: The new line (red line) has a flatter slope. The break-even point has moved to the right, i.e., it is higher.

## Variable Costs Decrease by $1

Although the variable cost decrease makes the line move in the same way as the price increase of $1, the new break-even is different from the one for the price increase. When the price increased to $11, the new margin percentage changed to 45.5% ($5 / $11), and this results in a break-even point of $88. With the variable cost drop, the new margin percentage is 50% ($5 / $10) for a break-even point of $80.

## Variable Costs Increase by $1

A variable cost increase increases the break-even point because the slope of the line flattens as you can see in this graph.

## Fixed Costs Increase by $10

Any change in fixed costs shifts the profit line up or down parallel to itself. In the case of a fixed cost increase, the line shifts downward by the amount of the fixed cost increase as in the following graph.

## Fixed Costs Decrease by $10

A decrease in the fixed costs causes the profit line to shift upward by the amount of the decrease. In the next graph the new line is parallel to the old one, but it is at a higher level. Naturally, this higher line results in a lower break-even point.

## Spreadsheet for doing profit graphs

For a copy of a spreadsheet that will allow you to change prices or costs and generate alternative profit graphs like those above. This spreadsheet generates profit graphs just like the ones illustrated here.

## Developing a Spreadsheet to Produce Profit Graphs

Use the following steps to create a spreadsheet for generating profit graphs and break-even points.

Column A–Use the FILL command to generate values from zero to 20 starting on row 6.

Column B–Multiply the Column A value by the value in D4

Column C–Multiply Column B by sales price in D1

Column D–Multiply variable cost in D2 by Column B value

Column E–Put a reference to fixed cost value in D3

Column F–Subtract the total of Columns D and E from Column C

The following spreadsheet illustrates these steps. The Multiplier value allows you to change the units sold to any value you want.

The next spreadsheet shows what happens as you reduce the value of the multiplier from 400 to 100. Notice how you can use this value to adjust where the break-even point appears on the graph.

We can develop a profit graph for a real company by simply putting its actual sales in the cell for the selling price and its variable costs in the cell for the unit variable cost. You then choose a multiplier value of something like .00001 (use trial and error to develop the right one) and generate the data for your profit graph.

# Numerical Analyses of Alternatives

Consider the following alternatives that a manager wants to evaluate. In this and the following examples the red lines and numbers represent the base case, and the blue represents the new alternative the manager is considering.

The company currently sells its product for $100 per unit, and the product has a unit variable cost of $60. Current expected sales are 3,000 units.

**SELF-CHECK ACTIVITY**

- Illustrate the graphical representation of CVP analysis?