Chapter 3
Cost-volume-profit analysis
Cost and Management Accounting: Operations and Management – A southern African approach (3rd edition)
© Juta and Company Ltd 2021
ISBN 9781485131229
Learning objectives
After studying this chapter, you should be able to:
• Understand the importance of cost behaviour in costvolume-profit (CVP) analysis.
• Separate mixed costs into fixed and variable portions.
• Apply CVP techniques in both single-product and
multiple-product contexts.
• Apply sensitivity analysis to CVP analysis.
• Choose the most profitable cost structure for an
organisation using the change-over point.
• Recognise and describe the assumptions on which CVP
analysis is based.
Cost and Management Accounting: Operations and Management – A southern African approach (3rd edition)
© Juta and Company Ltd 2021
ISBN 9781485131229
Introduction
• It is also referred to as breakeven analysis.
• It is an important tool used to assist management in
planning and decision making.
• It looks speat the relationship between the following five
elements: product prices, product mix, variable cost per
unit, total fixed costs, and the level of activity.
• It aims to improve profitability by identifying the best
combination of the above five elements.
• It helps managers to answer some of the following
questions:
• What if we increase our fixed costs and sales volume?
• What impact would this have on our contribution and net profit?
Cost and Management Accounting: Operations and Management – A southern African approach (3rd edition)
© Juta and Company Ltd 2021
ISBN 9781485131229
Marginal costing statement
• This format is useful to managers when making
decisions regarding changes to profits, costs
and volume, since it groups costs according to
their behaviour.
Rand Totals
Sales
XXXXXX
Less: Total variable costs
XXXXXX
Contribution
XXXXXX
Less: Total fixed costs
XXXXXX
Net profit
XXXXXX
Cost and Management Accounting: Operations and Management – A southern African approach (3rd edition)
© Juta and Company Ltd 2021
ISBN 9781485131229
CVP analysis using formulae
Illustrative example 3.1
(single product)
Kirsty Ltd manufactures UPSs for desktop computers. Below is the marginal
costing statement of the company, for April:
Rand totals
Per unit
Percentage
Sales (1 650 power supplies)
825 000
?
100%
Less: Total Variable costs
495 000
?
?
Contribution
330 000
?
?
Less: Total Fixed costs
130 000
Net profit
200 000
Assume a tax rate of 30%.
Cost and Management Accounting: Operations and Management – A southern African approach (3rd edition)
© Juta and Company Ltd 2021
ISBN 9781485131229
CVP analysis using formulae
Illustrative example 3.1
(single product)
(cont.)
Required:
Calculate the following formulae and give a brief explanation of each
calculation:
1. Contribution per unit and as a percentage
2. Breakeven point (in units and rands)
3. Sales in units and Rands assuming that the company would like to
make a target profit of R250 000 before tax
4. Rands sales and sales in units, assuming that the company would
like to make a target profit of R175 000 after tax
5. Margin of safety (expressed in units, Rand totals and as a
percentage).
Round off final answers to the nearest whole number.
Cost and Management Accounting: Operations and Management – A southern African approach (3rd edition)
© Juta and Company Ltd 2021
ISBN 9781485131229
Breakeven analysis using formulae
1.
Contribution per unit
= Selling price per unit – Variable costs per unit
= R500 (R 825 000 ÷ 1650 units) – R300 (R495 000 ÷ 1650 units)
= R200
For every UPS sold, we generate a R200 contribution towards covering fixed
costs and making a profit. If we sell 5 UPSs, we generate a contribution of
R1 000 (5 x R200); and if we sell 10, we generate R2 000 (10 x R 200), and
so on.
Contribution as a percentage of sales (contribution margin ratio)
= Contribution ÷ Sales x 100
= R330 000 ÷ R825 000 x 100
= 40% or
= R200 ÷ R500 x 100
= 40%
For every Rand generated in sales, we generate 40 cents for contribution
towards fixed costs and profits.
Note: You can either use Rand per unit figures or total figures to calculate
the contribution ratio as indicated above.
Cost and Management Accounting: Operations and Management – A southern African approach (3rd edition)
© Juta and Company Ltd 2021
ISBN 9781485131229
2.
Breakeven point in units
= Fixed costs ÷ Contribution per unit
= R130 000 ÷ R200
= 650 units
The breakeven point in units indicates the number of units that must be
sold to cover all costs. Kirsty Ltd would have to sell 650 units in order to
break even.
Breakeven point in Rands
= Fixed costs ÷ Contribution margin ratio
=R130 000 ÷ 40%
=R325 000
OR
Breakeven point in units x Selling price per unit
= 650 x R500
=R325 000
The breakeven point in Rands is the total Rand sales that the company
must generate in order to cover all its costs.
Cost and Management Accounting: Operations and Management – A southern African approach (3rd edition)
© Juta and Company Ltd 2021
ISBN 9781485131229
Proof
Marginal costing income statement for April (indicating breakeven point)
Rand total
Per unit
Percentage
Sales (R 500 x 650 power supplies)
325 000
500
100%
Less: Variable costs (R300 x 650)
195 000
300
60%
Contribution
130 000
200
40%
Less: Fixed costs
130 000
Net profit
0
Cost and Management Accounting: Operations and Management – A southern African approach (3rd edition)
© Juta and Company Ltd 2021
ISBN 9781485131229
3.
Sales in units to make a target profit before tax
= (Fixed costs + Target profit) ÷ Contribution per unit
= (R130 000 + R 250 000) ÷ R200
= 1 900 units
Kirsty Ltd would have to sell 1 900 units in order to generate a net profit of
R250 000 before tax.
Sales in Rands to make a target profit
= (Fixed costs + Target profit) ÷ Contribution ratio
= (R130 000 + R250 000) ÷ 40%
= R950 000
Kirsty Ltd would have to generate Rand sales of R950 000 in order to
obtain the target profit of R250 000.
Cost and Management Accounting: Operations and Management – A southern African approach (3rd edition)
© Juta and Company Ltd 2021
ISBN 9781485131229
Proof
Marginal costing income statement (indicating target profit)
Total
Per unit
Percentage
Sales ( R500 x1 900 power supplies)
950 000
500
100%
Less: Variable costs (R300 x 1 900)
570 000
300
60%
Contribution
380 000
200
40%
Less: Fixed costs
130 000
Target net profit
250 000
Cost and Management Accounting: Operations and Management – A southern African approach (3rd edition)
© Juta and Company Ltd 2021
ISBN 9781485131229
4.
Sales in units to make a target profit after tax
The after-tax profit must first be converted to the net profit before tax. This can be
done by dividing the net profit after tax by 100% less the tax rate.
= [Fixed costs + Target profit after tax ÷ (100% – Tax rate)] ÷ Contribution per unit
= [R130 000 + (R175 000 ÷ 70%)] ÷ R200
= 1 900 units
Kirsty Ltd would have to sell 1 900 units in order to generate a net profit of
R175 000 after tax.
Sales in Rands to make a target profit after tax
= [Fixed costs + (Target profit after tax ÷ 70%)] ÷ Contribution margin ratio
= [R130 000 + (R175 000 ÷ 70%)] ÷ 40%
= R950 000
Kirsty Ltd would have to generate Rand sales of R950 000 in order to obtain a net
profit of R175 000 after tax.
Cost and Management Accounting: Operations and Management – A southern African approach (3rd edition)
© Juta and Company Ltd 2021
ISBN 9781485131229
5.
Margin of safety in units
= Budgeted sales in units – Breakeven sales in units
= 1 650 – 650
= 1 000 units
Margin of safety in Rands
= Budgeted sales in Rands – Breakeven sales in Rands
= R825 000 – R 325 000
= R500 000
(Margin of safety continues on next slide.)
Cost and Management Accounting: Operations and Management – A southern African approach (3rd edition)
© Juta and Company Ltd 2021
ISBN 9781485131229
Margin of safety as a percentage (margin of safety ratio)
The margin of safety as a percentage can be calculated by using either the
unit sales or Rand sales.
= (Budgeted sales in units – Breakeven sales in units) ÷ Budgeted sales in
units x 100
= (1 650- 650) ÷ 1 650 x 100
= 61%
OR
= (R825 000 – R325 000) ÷ 825 000 x 100
= 61%
The margin of safety indicates how close the business is operating to the breakeven
point. It tells the business by how much sales can decrease before the breakeven
point is reached. It can be expressed in units, Rands or as a percentage. Organisations
that have a high margin of safety are less likely to make a loss, while organisations that
have a low margin of safety, are more susceptible to losses.
Cost and Management Accounting: Operations and Management – A southern African approach (3rd edition)
© Juta and Company Ltd 2021
ISBN 9781485131229
CVP analysis using the algebraic
equation method
• The algebraic equation used is derived from the marginal costing
income statement.
Net profit = Sales – (Total variable costs + Total fixed costs)
• This equation can be rearranged as follows:
Sales = Total variable costs + Total fixed costs + Profit
Total variable costs = Sales – Total fixed costs – Profit
Total fixed costs = Sales – Total variable costs – Profit
Cost and Management Accounting: Operations and Management – A southern African approach (3rd edition)
© Juta and Company Ltd 2021
ISBN 9781485131229
Refer to illustrative example 3.1
Required:
Calculate the following using the algebraic equation method:
1. Breakeven point in units
2. Sales in units, assuming that the company would like to make a
target profit of R250 000 before tax
3. Sales in units assuming that the company would like to make a target
profit of R175 000 after tax
1.
The breakeven point in units can be calculated using the algebraic
equation method as follows:
Let Sales units = X. Note the profit is 0.
Sales
500x
200x
x
=
=
=
=
Total variable costs + Total Fixed costs + Profit
300x + R130 000 + 0
R130 000
650 units
Cost and Management Accounting: Operations and Management – A southern African approach (3rd edition)
© Juta and Company Ltd 2021
ISBN 9781485131229
2.
Target profit in units
Let Sales units = 5x. Note that the target profit is R 250 000.
Sales
500x
200x
x
3.
=
=
=
=
Total variable costs + Total Fixed costs + Profit
300x + R130 000 + R250 000
R380 000
1 900 units
Let Sales units = 5x. Note that the target profit is R175 000 after tax.
Sales
500x
200x
x
=
=
=
=
Total variable costs + Total fixed costs + Profit
[300x + R130 000 + (R175 000 ÷ 70%)]
R380 000
1 900 units
Cost and Management Accounting: Operations and Management – A southern African approach (3rd edition)
© Juta and Company Ltd 2021
ISBN 9781485131229
What-if analysis
(sensitivity analysis)
• What-if analysis (sensitivity analysis) investigates the sensitivity of a
product to changes in price, mix, variable cost per unit, total fixed
costs, and level of activity. It looks at the impact that these changes
have on the breakeven point, margin of safety and profits.
Refer to illustrative example 3.1.
What impact would an increase in fixed costs and sales volume have
on contribution and profit?
• Assume that Kirsty Ltd is trying to increase their market share and
has embarked on an advertising campaign which would cost the
company R10 000. This increased advertising will increase sales
volume by 10%. Advise Kirsty Ltd regarding the implementation of
the advertising campaign. This question can be answered in one of
three ways:
Cost and Management Accounting: Operations and Management – A southern African approach (3rd edition)
© Juta and Company Ltd 2021
ISBN 9781485131229
Method 1 (redraft the marginal income statement)
Marginal costing income statement (indicating changes in fixed costs and sales
volume)
Original
Change in fixed
Difference
% of
costs and sales
(R)
sales
volume (R)
(R)
Sales (@ R 500 UPS)
825 000
907 500*
82 500
100%
Less: Total variable costs (@ R300)
495 000
544 500
49 500
60%
Contribution
330 000
363 000
33 000
40%
Less: Total fixed costs
130 000
140 000*
10 000
Net profit
200 000
223 000
23 000
If we implement the change in the fixed cost and sales volume, the profit would
increase by R23 000.
Cost and Management Accounting: Operations and Management – A southern African approach (3rd edition)
© Juta and Company Ltd 2021
ISBN 9781485131229
Method 2 (incremental analysis)
Incremental analysis only takes into account the differences, i.e. the changes.
The contribution per unit will remain the same since there is no change in the
selling price per unit and variable cost per unit, only the fixed costs increase.
Incremental approach:
R
Expected total contribution (R907 500 x 0.40)
363 000
Present total contribution (R825 000 x 0.40)
330 000
Incremental contribution
33 000
Change in fixed costs
Less: Incremental advertising expense
10 000
Increase in net profit
23 000
Cost and Management Accounting: Operations and Management – A southern African approach (3rd edition)
© Juta and Company Ltd 2021
ISBN 9781485131229
Method 3 (algebraic equation)
The algebraic equation will be rearranged in order to calculate the net profit.
Let Net profit = x
Net Profit =
x =
=
Sales – (Total variable costs + Total fixed costs)
[(1 650+ 10%) x R 500] – {[(1 650 + 10%) x R 300] + [130 000 + 10 000]}
223 000
Decision:
The advice to Kirsty Ltd is to undertake the advertising campaign since it would result in
an increase of R23 000 in net profit.
Note the incremental approach is a shorter approach.
Cost and Management Accounting: Operations and Management – A southern African approach (3rd edition)
© Juta and Company Ltd 2021
ISBN 9781485131229
What impact would an increase in variable costs and sales
volume have on contribution and profit?
Kirsty Ltd is having a problem with the suppliers of one of the components for
the UPS, i.e. the cooling fans, and has managed to source another supplier for
the component. This new supplier however charges more for the component,
because it is of a higher quality, resulting in an increase in the variable cost of
R25 per component. This high quality component ultimately will increase the
overall quality of the UPS and result in an increase in sales by 180 UPSs per
month. Advise Kirsty Ltd on whether or not the higher quality component should
be used.
Cost and Management Accounting: Operations and Management – A southern African approach (3rd edition)
© Juta and Company Ltd 2021
ISBN 9781485131229
Incremental approach:
R
Expected total contribution (1 830* x R 175*)
Present total contribution (1 650 x R 200)
320 250
330 000
Incremental contribution
(9 750)
Change in fixed costs
0
Decrease in net profit
(9 750)
Decision:
Kirsty Ltd should not purchase the high quality component, since profits would
decrease by R9 750.
Cost and Management Accounting: Operations and Management – A southern African approach (3rd edition)
© Juta and Company Ltd 2021
ISBN 9781485131229
What impact would a change in fixed cost, selling price and
sales volume have on our contribution and profits?
The marketing manager has done extensive market research and estimates that
a decrease in the selling price of R50 per unit would result in an increase in sales
of 40%. However, to make customers aware of the price decrease, the
advertising budget would have to be increased by R15 000 for the month. Advise
Kirsty Ltd on whether or not to implement these changes.
Cost and Management Accounting: Operations and Management – A southern African approach (3rd edition)
© Juta and Company Ltd 2021
ISBN 9781485131229
Algebraic approach:
Net Profit = Sales – (Total variable costs + Total fixed costs)
x = [(1 650 + 40%) x (R 500 – R50)] – {[(1 650 + 40%) x R300] + [130 000 +
15 000]}
= R1 039 500 – (R693 000 + 145 000)
= R201 500
The decrease in the selling price per unit will cause the contribution per unit to decrease,
but the overall profit would increase.
Decision:
Kirsty Ltd should implement the above changes since profits would increase by R1 500
(R201 500 – R200 000).
Cost and Management Accounting: Operations and Management – A southern African approach (3rd edition)
© Juta and Company Ltd 2021
ISBN 9781485131229
What impact would a change in variable cost, fixed cost
and sales volume have on our contribution and profits?
The marketing manager believes that because the sales representatives earn a
fixed salary of R7 000 per month, they are not motivated to sell as many UPSs
as possible. After extensive negotiations with the HR department, they have
agreed to change the sales representatives from a fixed salary to a commission
basis of R10 for every UPS sold. This change is expected to increase sales by
15% per month. Advise Kirsty Ltd on whether or not to implement the above
changes.
Cost and Management Accounting: Operations and Management – A southern African approach (3rd edition)
© Juta and Company Ltd 2021
ISBN 9781485131229
Incremental approach:
R
Expected total contribution (1 898*x R190**)
Present total contribution (1 650 x R200)
360 620
330 000
Incremental contribution
30 620
Add: Change in fixed costs salaries avoided
7 000
Increase in net profit
37 620
Decision:
Kirsty Ltd should implement the above changes since profits would increase by
R37 620.
Cost and Management Accounting: Operations and Management – A southern African approach (3rd edition)
© Juta and Company Ltd 2021
ISBN 9781485131229
Cost-volume-profit analysis
and graphs
• Graphs are useful for decision making since they summarise important
information in a diagram.
• They are also easier to understand, especially for individuals with no
accounting background.
• CVP analysis uses line graphs to show information such as breakeven
point, margin of safety, etc.
Cost and Management Accounting: Operations and Management – A southern African approach (3rd edition)
© Juta and Company Ltd 2021
ISBN 9781485131229
Breakeven graph
Illustrative example 3.5
A company produced a product called Widgets, which it sells to various
manufacturing concerns. Widgets are used in the manufacturing of
electrical equipment.
Selling price per unit
Variable cost per unit
Total fixed costs
Budgeted sales
R100
R50
R50 000
2 000 units
Cost and Management Accounting: Operations and Management – A southern African approach (3rd edition)
© Juta and Company Ltd 2021
ISBN 9781485131229
Steps involved in drawing
a breakeven line graph
Step 1
Determine the scale.
The x-axis is the horizontal axis where we record the units (activity level).
The y-axis is the vertical axis where we record the Rand totals.
Scale:
x-axis (units)
y-axis (Rands)
2cm = 200 units
1cm = R25 000
Step 2
Plot the points and draw in the lines to join the points.
There are three lines to be drawn. The first line is the fixed cost line. Plot the
fixed cost point on the y-axis, i.e. R50 000, and then draw in a straight line
parallel to the x-axis (because fixed costs do not change with the level of
activity).
Cost and Management Accounting: Operations and Management – A southern African approach (3rd edition)
© Juta and Company Ltd 2021
ISBN 9781485131229
Cost and Management Accounting: Operations and Management – A southern African approach (3rd edition)
© Juta and Company Ltd 2021
ISBN 9781485131229
The second line to be drawn in is the total cost line.
Plot the total cost point. The total cost that would be incurred, is as follows:
Variable costs
+ Fixed costs
= Total cost
(2 000 x R50)
R100 000
R50 000
R150 000
Plot R150 000 on the y-axis and 2 000 units on the x-axis. From the x-axis
follow the 2 000 units with your ruler upwards and from the y-axis follow
the R150 000 with your ruler across and plot the point where the two meet
on the graph. Draw in the total cost line starting from R50 000, to where the
Rands and units point meet on the graph.
Cost and Management Accounting: Operations and Management – A southern African approach (3rd edition)
© Juta and Company Ltd 2021
ISBN 9781485131229
Cost and Management Accounting: Operations and Management – A southern African approach (3rd edition)
© Juta and Company Ltd 2021
ISBN 9781485131229
The third line to be drawn is the sales revenue line. Plot the sales revenue
points. The total Rand sales that would be generated, is R200 000 (2 000 x
R100).
Plot R200 000 on the y-axis and 2 000 units on the x-axis. From the x-axis,
follow the 2 000 units with your ruler upwards and from the y-axis follow
the R200 000 with your ruler across and plot the point where the two
meet on the graph.
Draw in the sales revenue line starting from 0 to where the Rands and
units point meet on the graph.
Cost and Management Accounting: Operations and Management – A southern African approach (3rd edition)
© Juta and Company Ltd 2021
ISBN 9781485131229
Cost and Management Accounting: Operations and Management – A southern African approach (3rd edition)
© Juta and Company Ltd 2021
ISBN 9781485131229
Step 3
Label all the lines that you have drawn in on the graph.
Cost and Management Accounting: Operations and Management – A southern African approach (3rd edition)
© Juta and Company Ltd 2021
ISBN 9781485131229
Interpretation of the graph
The point where the sales revenue line and the total cost line intersect each other is
known as the breakeven point. If we follow the point of intersection down to the xaxis, this represents the breakeven point in units, i.e. 1 000 units. If we follow the point
of intersection back across to the y-axis, this represents the breakeven point in Rands,
i.e. R100 000. If our Rand sales are below the breakeven point, we are making a loss
and if the Rand sales are above the breakeven point, we are making a profit. The
margin of safety is reflected on the graph as well, i.e. the difference between the
budgeted sales and the breakeven sales. We can check the accuracy of the graph by
using the breakeven formulae.
Breakeven point in units:
= Fixed costs ÷ Contribution per unit
= R50 000 ÷ (R100 – R50)
= 1 000 units
Breakeven point in Rands:
= BEP units x Selling price
= 1 000 x R 100
= R100 000
Cost and Management Accounting: Operations and Management – A southern African approach (3rd edition)
© Juta and Company Ltd 2021
ISBN 9781485131229
Contribution graph
Essentially the contribution graph is very similar to the breakeven graph. The
main purpose of the contribution graph is to show contribution at various
levels of activity. There are three lines drawn in on the graph, i.e. the variable
cost line (this line replaces the fixed cost line), total cost line and sales
revenue line.
Refer to illustrative example 3.5.
The total cost line and the sales revenue line will be drawn in on the graph as
above.
The variable cost line can be drawn as follows:
Plot the variable cost points. The variable costs that would be incurred are
R100 000 (2 000 x R50). Plot the R100 000 on the y-axis and then plot the
2 000 units on the x-axis. From the x-axis follow the 2 000 units upwards and
from the y-axis follow the R100 000 across and plot the point where the two
meet on the graph. Draw in the variable cost line starting from 0 to where
the Rands and units point meet on the graph.
Cost and Management Accounting: Operations and Management – A southern African approach (3rd edition)
© Juta and Company Ltd 2021
ISBN 9781485131229
Cost and Management Accounting: Operations and Management – A southern African approach (3rd edition)
© Juta and Company Ltd 2021
ISBN 9781485131229
Profit-volume graph
The profit-volume graph looks at profit generated at various levels of activity.
This graph consists of only one line, i.e. the profit line.
Refer to illustrative example 3.5.
The x-axis (horizontal axis) records the activity level in units. The y-axis
(vertical axis) which records the Rand totals, extends above zero to indicate
profits and below zero to indicate losses.
The profit line can be drawn in as follows:
If our activity level is zero, then our loss equals our fixed costs, since we still
have to cover our fixed costs whether or not we produce any units. The first
point plotted is therefore the fixed cost of -R50 000 at zero activity level. The
second point plotted is the breakeven point of 1 000 units on the x-axis. The
profit line is then drawn joining these two points.
Cost and Management Accounting: Operations and Management – A southern African approach (3rd edition)
© Juta and Company Ltd 2021
ISBN 9781485131229
Cost and Management Accounting: Operations and Management – A southern African approach (3rd edition)
© Juta and Company Ltd 2021
ISBN 9781485131229
Problems associated
with the graphs
• There are various limitations associated with the graphs and
these need to be taken into account since they affect the
reliability of graphs for planning and decision making.
• It must be noted that graphs are not 100% accurate since they
only indicate possible performance within the relevant range,
i.e. the expected range of activity. Outside this range they are
more than likely to be inaccurate. The relevant range looks at
both the minimum and maximum activity levels within which
the company expects to operate, i.e. the operating capacity of
the company.
• Fixed costs are more than likely to be stepped and not a
straight line, since fixed cost may change if the activity level
rises beyond the maximum expected range.
Cost and Management Accounting: Operations and Management – A southern African approach (3rd edition)
© Juta and Company Ltd 2021
ISBN 9781485131229
Problems associated
with the graphs
• Variable costs and sales are more than likely to take on a curved shape
instead of a straight line. This takes into account possible discounts on
sales, payments for overtime, charges for delivery, etc.
• The graphs only indicate the relationships in the short term and are
therefore not reliable for long-term planning.
• All variable cost will vary or change with only either production level or
sales level.
Cost and Management Accounting: Operations and Management – A southern African approach (3rd edition)
© Juta and Company Ltd 2021
ISBN 9781485131229
Economist’s view of
breakeven graph
• The economist graph has a smooth curved shape in comparison to the
accountant’s line graphs. The total cost line decreases initially as the
output increases indicating economies of scale, i.e. the more units we
produce the lower the fixed cost per unit, since there are more units to
share the fixed cost. Then it increases upwards indicating diminishing
returns.
• The revenue line curves downward indicating the need to reduce the
selling price, i.e. discounts in order to increase sales volume.
• Interpretation of the graph: It shows the point of profit maximisation. It
has two breakeven points. The first breakeven point is very similar to the
accountant’s graph and falls within the relevant range whereas the second
breakeven point falls outside the relevant range.
• The economist’s graphs highlight the fact that the revenue and cost
assumptions at the extremes, high and low point levels of activity, are
unreliable. Within the relevant range however, the differences between
the economist’s and accountant’s graphs are minimal.
Cost and Management Accounting: Operations and Management – A southern African approach (3rd edition)
© Juta and Company Ltd 2021
ISBN 9781485131229
Cost and Management Accounting: Operations and Management – A southern African approach (3rd edition)
© Juta and Company Ltd 2021
ISBN 9781485131229
Multiple-product
breakeven analysis
• The main assumption of CVP analysis for multiple products is that the
organisation sells their products according to a specified mix (sales mix).
Sales mix is how much of each of the products are sold in proportion to
total sales. It can be expressed as a ratio, e.g. 2:2:1 or as a percentage, e.g.
40%, 40%, and 20%.
• Different products have different profit margins, i.e. there are high-margin
products and low-margin products. If the organisation increases the sales
on their products that have a high margin, and decreases sales on their
products with a low margin, then profits increase and vice versa.
• Consequently, managers strive to sell a combination of products that will
maximise profits. Changes in the sales mix cause profits to change.
Cost and Management Accounting: Operations and Management – A southern African approach (3rd edition)
© Juta and Company Ltd 2021
ISBN 9781485131229
Illustrative example 3.8
(multiple products)
Kirsty Ltd currently manufactures and sells UPSs (Uninterrupted Power
Supplies) for desktop computers. Due to the current electricity shortages,
power cuts have resulted in many companies losing valuable data. After
extensive market research, the company has decided to extend its
product range to include UPSs for data centres as well. These UPSs are
emergency power generators that are instantaneous or near
instantaneous allowing time for equipment to shut down properly and
therefore ensure that valuable data is not lost.
Currently fixed costs are R130 000. With the production of the UPSs for
the data centre, the fixed costs would increase by a further R260 000. This
includes additional supervisory salaries, additional equipment leased, etc.
Cost and Management Accounting: Operations and Management – A southern African approach (3rd edition)
© Juta and Company Ltd 2021
ISBN 9781485131229
Illustrative example 3.8
(multiple products)
The UPSs for desktop computers sell for R500 per unit and have a total
variable cost per unit of R300, while the UPSs for data centres sell for
R1 250 per unit and have a variable cost per unit of R625. For every one
UPS for desktops sold, the company sells two UPSs for data centres. The
budgeted sales revenue for the next period is R5 637 500.
Required:
Calculate the following:
1. Breakeven point in units
2. Breakeven point in rands
3. Sales in units and rands, assuming the company wants to make a
profit of R3 million before tax
4. The margin of safety in rands and as a percentage.
Round off final answers to the nearest whole number.
Cost and Management Accounting: Operations and Management – A southern African approach (3rd edition)
© Juta and Company Ltd 2021
ISBN 9781485131229
Solution
1. Steps involved in calculating the breakeven point in units for multiple
products:
Step 1: Calculate the contribution per unit
UPSs for desktops
(R)
UPSs for data
centres
(R)
Selling price
Less: Variable cost
500
300
1 250
625
Contribution per
unit
200
625
Cost and Management Accounting: Operations and Management – A southern African approach (3rd edition)
© Juta and Company Ltd 2021
ISBN 9781485131229
Step 2: Calculate the contribution per mix (weighted average contribution per unit)
= (200 × 1) + (625 × 2)
= R1 450
Step 3: Calculate the breakeven point in terms of the number of mixes
= Fixed costs ÷ Contribution per mix (weighted average contribution)
= R390 000 ÷ R1 450
= 269 mixes (rounded)
Step 4: Calculate the breakeven point in units for each product
= Breakeven point in terms of the number of mixes × Sales mix per product
(269 × 1) = 269 units of UPSs for desktops
(269 × 2) = 538 units of UPSs for data centres
Cost and Management Accounting: Operations and Management – A southern African approach (3rd edition)
© Juta and Company Ltd 2021
ISBN 9781485131229
2. The breakeven point in rands for multiple products can be calculated in two ways,
that is, using the breakeven point based on the number of units of the product or
using the weighted average contribution margin ratio.
Breakeven point based on the number of units of the product:
Breakeven point in units for each product × Selling price per unit
269 units of UPS for desktops
× R500 = R134 500
538 units of UPS for data centres
× R1 250 = R672 500
Total revenue
= R807 000
Or
Breakeven point based on weighted average contribution margin ratio:
Contribution per mix (weighted average contribution per unit) ÷ Revenue per mix ×
100
= R1 450 ÷ [(500 × 1) + (1 250 × 2)] × 100
= R1 450 ÷ R3 000 × 100
= 48% rounded
Cost and Management Accounting: Operations and Management – A southern African approach (3rd edition)
© Juta and Company Ltd 2021
ISBN 9781485131229
Breakeven point in rands (total)
= Fixed costs ÷ Weighted average contribution margin ratio
= R390 000 ÷ 0.48
= R812 500 represents the total rand sales that must be generated to cover costs
and make no profit
To calculate the breakeven point in rands for each product, the revenue ratio mix
must be calculated first
UPSs for desktops
(1 × 500)
= R500
UPSs for data centres
(2 × 1 250)
= R2 500
Revenue ratio mix
500:2 500
Breakeven point in rands for each product:
UPSs for desktops
R812 500 × (500 ÷ R3 000) = R135 417
UPSs for data centres
R812 500 × (2 500 ÷ R3 000) = R677 083
Note: The answers in both methods for calculating the breakeven point in rands would
differ slightly due to rounding.
Cost and Management Accounting: Operations and Management – A southern African approach (3rd edition)
© Juta and Company Ltd 2021
ISBN 9781485131229
The breakeven point is dependent upon the sales mix. If the sales mix changes, the
breakeven point in rands would also change. Market share and customer preferences
can cause the sales mix to change.
3. Sales in units to earn a target profit
= (Fixed costs + Target profit) ÷ Weighted average contribution per unit
= (R390 000 + R3 000 000) ÷ R1 450
= 2 338 mixes
Sales in units per product to earn the target profit
(2 338 × 1) = 2 338 units of UPSs for desktops
(2 338 × 2) = 4 676 units of UPSs for data centres
Sales in Rands to earn a target profit
= (Fixed costs + Target profit) ÷ Weighted average contribution margin ratio
= (R390 000 + R3 000 000) ÷ 0.48
= R7 062 500 represents the total Rand sales that must be generated to earn the
required target profit of 3 million.
Cost and Management Accounting: Operations and Management – A southern African approach (3rd edition)
© Juta and Company Ltd 2021
ISBN 9781485131229
The target profit required per product can be
calculated as follows:
Target profit in rands for each product:
UPSs for desktops
R7 062 500 × (500 ÷ R3 000) = R1 177 083
UPSs for data centres
R7 062 500 × (2 500 ÷ R3 000) = R5 885 417
4. Margin of safety in rands
= Budgeted sales – Breakeven sales
= R5 637 500 – R812 500
= R4 825 000
Margin of safety as a percentage
= (Budgeted sales – Breakeven sales) ÷ Budgeted sales × 100
= [(R5 637 500 – R812 500) ÷ R5 637 500] × 100
= 86%
Note: The margin of safety is calculated in the same way for both single and multiple
products.
.
Cost and Management Accounting: Operations and Management – A southern African approach (3rd edition)
© Juta and Company Ltd 2021
ISBN 9781485131229
Profit-volume graph for
multiple products
• The profit-volume graph for multiple products consists of two lines: a
straight line and a bent line.
• The straight line is the profit line where we assume that the products are
sold in a specified mix.
• The bent line is where we assume that the organisation sells the product
with the highest contribution ratio first and so on.
Cost and Management Accounting: Operations and Management – A southern African approach (3rd edition)
© Juta and Company Ltd 2021
ISBN 9781485131229
Illustrative example 3.9
(profit volume graph for multiple products)
A company produces three products: Widgets, Gadgets and Fidgets. Fixed costs
amount to R100 000 for the year. Information relating to the three products is as
follows:
Widgets (R)
Gadgets (R)
Sales
300 000
120 000
80 000
500 000
Less: Variable costs
200 000
70 000
30 000
300 000
Contribution
100 000
50 000
50 000
200 000
33%
42%
63%
Contribution ratio
Fidgets (R)
Total (R)
Required:
Draft a multiple-product profit-volume graph indicating the breakeven
sales.
Cost and Management Accounting: Operations and Management – A southern African approach (3rd edition)
© Juta and Company Ltd 2021
ISBN 9781485131229
Step 1
Determine the scale.
The x-axis (horizontal axis) records the Rand sales. The y-axis (vertical axis)
records Rand totals and extends above zero to indicate profits and below zero
to indicate losses.
Scale:
x-axis (Rand totals indicating either profit or loss)
y-axis (total Rand sales)
1cm = R50 000
1cm = R50 000
Cost and Management Accounting: Operations and Management – A southern African approach (3rd edition)
© Juta and Company Ltd 2021
ISBN 9781485131229
Step 2
Plot the points and draw in the profit line.
The profit line can be drawn in as follows:
The fixed cost point is plotted on the y-axis at -R 100 000. The breakeven Rand
sales is plotted in on the x-axis at R250 000 and the profit point is plotted at
+R100 000 above the x-axis. The straight line is drawn from the -R100 000 and
passes through the breakeven point in Rands on the x-axis and is extends
towards the profit point of R100 000. The breakeven point in Rands of
R250 000 is derived as follows:
= Fixed costs ÷ Weighted average contribution ratio
= R100 000 ÷ 40%*
= R100 000 ÷ 0.40
= R250 000
*(0.33 x 0.60) + (0.42 x 0.24) + ( 0.63 x 0.16)
= 0.3996 or 40% rounded
And profit of R100 000 is derived as follows:
= Contribution – Fixed costs
= R200 000 – R100 000
= R100 000
Cost and Management Accounting: Operations and Management – A southern African approach (3rd edition)
© Juta and Company Ltd 2021
ISBN 9781485131229
Step 3
Plot the points and draw in the bent line.
Rank the products in order of which product has the highest contribution
margin ratio, i.e. Fidget 63%, Gadget 42% and Widget 33%. The products
must be produced in this order.
We plot in the points for product Fridget first. The first point plotted is the
Rand sales of R80 000 for product Fidget on the x-axis and the second point
plotted is the contribution of -R50 000 (fixed costs R100 000 – R50 000
contribution from Fridget) on the y-axis.
Note the -R50 000 is derived as follows:
This R50 000 represents the fixed costs that are still to be covered, before
profits are generated. Draw in the bent line starting from the fixed costs of
-R100 000, extending to where the R80 000 contribution and -R50 000 meet.
This is the first part of the bent line.
Cost and Management Accounting: Operations and Management – A southern African approach (3rd edition)
© Juta and Company Ltd 2021
ISBN 9781485131229
We plot in the points for product Gadget next. The first point plotted is the
Rand sales of R200 000 (R80 000 + R 120 000 Fidget and Gadget sales) on
the x-axis and the second point plotted is the contribution of R0 on the
y-axis (R50 000 contribution from Gadget less fixed costs of R50 000 still to
be covered). Fixed costs have been covered, so the company can begin to
generate profits. The two points are joined to form the second part of the
bent line.
Lastly we plot in the points for product Widget. The first point plotted is the
Rand sales of R500 000 (R80 000 + R120 000 + R300 000 Fidget, Gadget and
Widget sales) on the x-axis and the second point plotted is the contribution
of R100 000 on the y-axis. R100 000 is the profit generated since fixed costs
have already been covered in full. The two points are joined to form the last
part of the bent line.
Cost and Management Accounting: Operations and Management – A southern African approach (3rd edition)
© Juta and Company Ltd 2021
ISBN 9781485131229
Cost and Management Accounting: Operations and Management – A southern African approach (3rd edition)
© Juta and Company Ltd 2021
ISBN 9781485131229
Interpretation of the graph
The dotted straight line indicates the profit generated from the
specified sales mix, while the solid bent line assumes that the
organisation sells the most profitable product first and so on. As
indicated on the graph, the breakeven point in Rands is R250 000.
Cost and Management Accounting: Operations and Management – A southern African approach (3rd edition)
© Juta and Company Ltd 2021
ISBN 9781485131229
Cost structure
• The cost structure of an organisation is the ratio of fixed and
variable costs that exist within the organisation. It can be
changed for example if the organisation changes from being
labour intensive to capital intensive. The chosen cost
structure has a direct impact on profits.
• What is the best cost structure for an organisation? There is
no clear-cut answer since there are various factors that
influence this decision, for example the long-term trends in
sales, changes in the level of sales and the attitude of the
owners towards risk. A cost structure decision is essentially a
trade-off between risk and return.
Cost and Management Accounting: Operations and Management – A southern African approach (3rd edition)
© Juta and Company Ltd 2021
ISBN 9781485131229
Types of cost structures
• Organisations with higher fixed costs and lower variable
costs will experience greater changes in profits. If sales
increase, then profits will increase dramatically and if sales
decrease, profits will decrease dramatically.
• Organisations with lower fixed costs and higher variable
costs will experience greater stability in profits. They will
generate less income in the good years, but are protected
from losses in bad years.
Cost and Management Accounting: Operations and Management – A southern African approach (3rd edition)
© Juta and Company Ltd 2021
ISBN 9781485131229
Operating leverage
• The degree of operating leverage can be used to forecast changes in
profits. It measures how the net income is affected by changes in
sales. A company with a higher proportion of fixed costs in their
cost structure will have a higher operating leverage. It is calculated
as: Contribution ÷ Net income
• High operating leverage
When the operating leverage is high, a small percentage increase in
sales can yield a large percentage increase in net income.
• Low operating leverage
When the operating leverage is low, a large percentage increase in
sales can yield a small percentage increase in net income.
Cost and Management Accounting: Operations and Management – A southern African approach (3rd edition)
© Juta and Company Ltd 2021
ISBN 9781485131229
Change over point
Organisations would be faced with the option of choosing a cost
structure, i.e. either higher fixed costs with lower variable costs or
lower fixed costs with higher variable costs.
The output volume will help determine the best cost structure. The
changeover point indicates the output volume where the total costs
of each option are equal. At this volume of output, it does not matter
which cost structure you choose. However, if the output volume is
below the changeover point, then the option of lower fixed costs with
higher variable costs will generate a higher net income. If the output
volume is above the changeover point, then the option of higher fixed
costs with lower variable costs will generate a higher net income.
Cost and Management Accounting: Operations and Management – A southern African approach (3rd edition)
© Juta and Company Ltd 2021
ISBN 9781485131229
Changeover point = (F2 – F1) ÷ (V1 – V2)
Where:
F2 = total fixed cost of option with the higher fixed costs
F1 = total fixed cost of option with the lower fixed costs
V1 = variable cost per unit of option with the lower fixed costs
V2 = variable cost per unit of option with the higher fixed costs
Cost and Management Accounting: Operations and Management – A southern African approach (3rd edition)
© Juta and Company Ltd 2021
ISBN 9781485131229
Illustrative example 3.10
(cost structure)
Two companies within the same industry have two different cost structures.
One company is highly automated and capital intensive, while the other is
labour intensive. Last year both companies generated the same Rand sales
and net profit.
Sales (R200 per unit)
Less : Total variable costs
Company A
labour
intensive
(R)
150 000
(R)90 000
Contribution
Less: Total fixed costs
60 000
45 000
Net profit
15 000
%
Company B
capital
intensive
(R)
100
150 000
60
45 000
%
40
70
105 000
90 000
100
30
15 000
Cost and Management Accounting: Operations and Management – A southern African approach (3rd edition)
© Juta and Company Ltd 2021
ISBN 9781485131229
Required:
Calculate the following and comment on each:
1. Operating leverage for both companies
2. The changeover point
3. Net income before tax for both companies assuming that there is a 10%
increase in sales, with no change in fixed costs
4. Net income before tax for both companies assuming that there is a 10%
decline in sales, fixed costs remain unchanged.
Cost and Management Accounting: Operations and Management – A southern African approach (3rd edition)
© Juta and Company Ltd 2021
ISBN 9781485131229
Solution
1.
Operating leverage = Contribution ÷ Net income
Company A
R60 000 ÷ R15 000 = 4
Company B
R105 000 ÷ R15 000 =7
Company A’s net income grows four times faster than its sales while
Company B’s net income grows seven times faster than its sales. This is due
to the fact that Company B has a higher proportion of fixed costs in their
cost structure.
2.
Changeover point = (F2 – F1) ÷ (V1 – V2)
= (R90 000 – R 45 000) ÷ (R120 – R60)
= R45 000 ÷ R60
= 750 units
(V1 = 200 × 0.60 and V2 = 200 × 0.30)
Choice of cost structure:
If the output volume is below 750 units, then Company A’s cost structure
will generate a higher net income.
If the output volume is above 750 units, then Company B’s cost structure
will generate a higher net income.
Cost and Management Accounting: Operations and Management – A southern African approach (3rd edition)
© Juta and Company Ltd 2021
ISBN 9781485131229
3.
Company A
Company B
% increase
in sales
x
10%
10%
Degree of
operating
leverage
4
7
= % increase in
net income
40%
70%
With an increase of 10% in sales, Company A’s net income will increase
by 40%, R15 000 x 40% = R6 000 increase, so new net income will be
R21 000.
With an increase of 10% in sales, Company B’s net income will increase
by 70%, R15 000 x 70% = R10 500 increase, so new net income will be
R25 500.
Cost and Management Accounting: Operations and Management – A southern African approach (3rd edition)
© Juta and Company Ltd 2021
ISBN 9781485131229
Proof
Sales
Less: Total variable costs
Contribution
Less: Total fixed costs
Net profit
Company A
% Company B
labour
capital
intensive
intensive
(R)
(R)
165 000 100
165 000
99 000 60
49 500
66 000 40
115 500
45 000
90 000
21 000
25 500
%
100
30
70
In line with the changeover point, if sales increase by 10%, Company B’s
cost structure would be preferable.
Cost and Management Accounting: Operations and Management – A southern African approach (3rd edition)
© Juta and Company Ltd 2021
ISBN 9781485131229
4.
With a decrease of 10% in sales, Company A’s net income will decrease by
40%, 15 000 x 40% = R 6000 decrease, new net income will be R 9 000.
With a decrease of 10% in sales, Company B’s net income will decrease by
70%, R15 000 x 70% = R 10 500 decrease, so new net income will be R
4 500.
Proof
Sales
Less: Total variable costs
Contribution
Less: Total fixed costs
Net profit
Company A
Labour
intensive (R)
135 000
81 000
54 000
45 000
9 000
%
100
60
40
Company B
Capital
intensive (R)
135 000
40 500
94 500
90 000
4 500
%
100
30
70
In line with the changeover point, if sales decrease by 10%, Company A’s
cost structure would be preferable.
Cost and Management Accounting: Operations and Management – A southern African approach (3rd edition)
© Juta and Company Ltd 2021
ISBN 9781485131229
Assumptions of
cost-volume-profit analysis
There are various assumptions associated with the CVP context and these need to be
taken into account since they affect their reliability for planning and decision making.
• As the activity level changes, the price of a product or service will remain the same
within the relevant range.
• Within the relevant range, costs are linear and can all be accurately divided into
their fixed or variable elements. The variable costs are constant per unit and the
fixed cost remains fixed within the relevant range.
• All variable cost will vary or change with only either production level or sales level.
• In organisations that sell various products, the sales mix is constant.
• The cost structure of an organisation is constant within the relevant range.
• In manufacturing organisations there is no stock; the number of units produced
equals the number of units sold.
Taking cognisance of the above assumptions, the risk or danger lies in a manager
considering a change in activity level outside of the relevant range.
Cost and Management Accounting: Operations and Management – A southern African approach (3rd edition)
© Juta and Company Ltd 2021
ISBN 9781485131229