04 - Cost Volume Profit Analysis

Question 1

What are the learning outcomes of the CVP (Cost-Volume-Profit) chapter?

Answer 1

• Explain the contribution concept and its use in cost-volume-profit (CVP) analysis.
• Calculate the break-even point, profit target, margin of safety and profit/volume ratio for a single product or service.
• Prepare break-even charts and profit/volume graphs for a single product or service.
• Calculate the profit maximising product sales mix using limiting factor analysis.

Question 2

What is Cost-Volume-Profit (CVP) analysis?

Answer 2

Definition

Cost-volume-profit (CVP) analysis is the study of the effect on future profit of changes in the fixed cost, variable cost, sales price, quantity and mix.

Other

• A common term used for this type of analysis is breakeven analysis.
• However, this is somewhat misleading since it implies that the focus of the analysis is the breakeven point—that is, the level of activity which produces neither profit nor loss.
• The scope of CVP analysis is much wider than this as indicated in the definition.
• However, the terms ‘breakeven analysis’ and ‘CVP analysis’ tend to be used interchangeably.

Question 3

What is Contribution?

Answer 3

Variable costs are those that vary with the level of activity. If we can identify the variable costs associated with producing and selling a product or service, we can highlight a very important measure: contribution.

Contribution = Sales value - Variable costs

Contribution is so called because it literally does contribute towards fixed costs and profit. Once the contribution from a product or service has been calculated, the fixed costs associated with the product or service can be deducted to determine the profit for the period.

As sales revenues grow from zero, the contribution also grows until it just covers the fixed costs. This is the breakeven point where neither profits nor losses are made.

Question 4

What is Break-Even?

Answer 4

It follows that to break even the amount of contribution must exactly match the amount of fixed costs.

Question 5

What is the Margin of Safety?

Answer 5

The margin of safety is the difference between the expected level of sales and the breakeven point.

Margin of safety = Projected sales - Breakeven point

The larger the margin of safety, the more likely it is that a profit will be made, that is, if sales start to fall there is more leeway before the organisation begins to incur losses. (Obviously, this statement is made on the assumption that projected sales volumes are above the breakeven point.)

The margin of safety can also be used as one route to a profit calculation. Contribution goes towards fixed costs and profit. Once breakeven point is reached, the fixed costs have been covered. After the breakeven point there are no more fixed costs to be covered and all of the contribution goes towards making profits grow.

Question 6

What is the Contribution to Sales (C/S) ratio?

How does it relate to the Breakeven point?

Answer 6

Contribution/Selling price * 100 = C/S %

You might sometimes see this ratio referred to as the profit-volume (P/V) ratio.

A higher contribution to sales ratio means that contribution grows more quickly as sales levels increase. Once the breakeven point has been passed, profits will accumulate more quickly than for a product with a lower contribution to sales ratio.

Breakeven point

Breakeven point in sales value = Fixed costs/ (C/S ratio)

Question 7

How do you calculate the level of sales required for a target profit?

Answer 7

Sales revenue required to achieve a profit of X =

(Fixed costs + X) / (C/S) ratio

Question 8

What can CVP analysis be used for?

Answer 8

The concepts of breakeven analysis and cost behaviour patterns can be used to evaluate proposals. Let’s consider this with the help of an example.

Question 9

What is a Basic Breakeven Chart?

Answer 9

A basic breakeven chart records costs and revenues on the vertical axis and the level of activity on the horizontal axis. Lines are drawn on the chart to represent costs and sales revenue. The breakeven point can be read off where the sales revenue line cuts the total cost line.

Question 10

What are Contribution Breakeven Charts?

Answer 10

One of the problems with the conventional or basic breakeven chart is that it is not possible to read contribution directly from the chart. A contribution breakeven chart is based on the same principles but it shows the variable cost line instead of the fixed cost line.

The same lines for total cost and sales revenue are shown so the breakeven point and profit can be read off in the same way as with a conventional chart. However, it is possible also to read the contribution for any level of activity.

The contribution can be read as the difference between the sales revenue line and the variable cost line.

This form of presentation might be used when it is desirable to highlight the importance of contribution and to focus attention on the variable costs.

Question 11

What are Profit-volume charts?

Answer 11

Another form of breakeven chart is the profit-volume chart. The profit-volume graph is also called a profit graph or a contribution-volume graph.

This chart plots a single line depicting the profit or loss at each level of activity.

The breakeven point is where this line cuts the horizontal axis. A profit-volume graph for the data of the earlier example is shown.

The vertical axis shows profits and losses and the horizontal axis is drawn at zero profit or loss.

Advantage

The main advantage of the profit-volume chart is that it is capable of depicting clearly the effect on profit and breakeven point of any changes in the variables.

Question 12

What are the assumptions of CVP analysis?

Answer 12

• Linear behaviour of costs
• Constant sales revenues
• Single factor affecting costs
• Single product or service
• Misleading profit forecast

Question 13

How does the assumption of Linear Behaviour of Costs limit the practical applicability of breakeven analysis?

Answer 13

Costs are assumed to behave in a linear fashion.

Unit variable costs are assumed to remain constant and fixed costs are assumed to be unaffected by changes in activity levels.

The charts can in fact be adjusted to cope with non-linear variable costs or steps in fixed costs but too many changes in behaviour patterns can make the charts very cluttered and difficult to use.

Question 14

How does the assumption of Constant Sales Revenue limit the practical applicability of breakeven analysis?

Answer 14

Sales revenues are assumed to be constant for each unit sold.

This may be unrealistic because of the necessity to reduce the selling price to achieve higher sales volumes.

Once again the analysis can be adapted for some changes in selling price but too many changes can make the charts unwieldy.

Question 15

How does the assumption of Single Factor affecting Costs limit the practical applicability of breakeven analysis?

Answer 15

It is assumed that activity is the only factor affecting costs and factors such as inflation are ignored.

This is one of the reasons why the analysis is limited to being essentially a short-term decision aid.

Question 16

How does the assumption of Single Product or Service limit the practical applicability of breakeven analysis?

Answer 16

Apart from the unrealistic situation of a constant product mix, the charts can only be applied to a single product or service.

Not many organisations have a single product or service and if there is more than one, the apportionment of fixed costs between them becomes arbitrary.

Question 17

How does the assumption of Misleading Profit Forecast limit the practical applicability of breakeven analysis?

Answer 17

The analysis seems to suggest that as long as the activity level is above the breakeven point, a profit will be achieved.

In reality, certain changes in the cost and revenue patterns may result in a second breakeven point after which losses are made.

Question 18

How would the economist graph the breakeven chart differently?

Answer 18

Total Cost Line

The total cost line is not a straight line which climbs steadily as in the accountant’s chart.

Instead it begins to reduce initially as output increases because of the effect of economies of scale.

Later it begins to climb upwards according to the law of diminishing returns.

Revenue Line

The revenue line is not a straight line as in the accountant’s chart. The line becomes less steep to depict the need to give discounts to achieve higher sales volumes.

However, within the middle range the economist’s chart does look very similar to the accountant’s breakeven chart. This area is marked as the ‘Relevant range’ in the chart.

Conclusion

For this reason, it is unreliable to assume that the cost-volume-profit relationships depicted in breakeven analysis are relevant across a wide range of activity.

In particular, the chart shows that the constant cost and price assumptions are likely to be unreliable at very high or very low levels of activity.

Managers should therefore ensure that they work within the relevant range, that is, within the range over which the depicted cost and revenue relationships are more reliable.