COST-VOLUME-PROFIT ANALYSIS

Study unit 6
Learning outcomes
• After completion of this study unit you should
be able to:
• Define and calculate each of the following:
• Break-even point
• Contribution (Marginal revenue)
• Contribution ratio
• Margin of safety
• Margin of safety ratio
• Degree of operating leverage
Learning outcomes
• Discuss the criticisms relating to break-even
analysis.
• To make adjustments when one of the assumptions
of cost-volume-profit analysis is not met.
• Discuss how cost-volume-profit analysis in
management accounting used.
Learning outcomes
• After completion of this study unit you should be
able to:
• Discuss the assumptions of break even analysis and
consider the implications thereof.
• Calculate the expected turnover (sales) to achieve a
specified target profit before and after tax.
• Apply cost-volume-profit analysis to organizations.
Learning outcomes
• After completion of this study unit you should be
able to:
• Figures calculated on the basis of the following graphs:
• Conventional break-even point graph(cost-volume-profit graph)
• Contribution graph
• Profit-volume graph
1. Introduction
 Decision making is a very important factor in any
organization and a study of the relationship between
cost, volume and profit contribution can assist us in
this regard.
 Examples of problems that can be solved are:
◦ Determination of selling price (SP) at breakeven point (BEP)
◦ Determination of SP to yield specific % return on capital
◦ Determination of sales volume that will yield a certain return
◦ Impact of increase in sales on profit
2. Terminology
• Contribution (marginal revenue)
Sales less variable costs; remaining amount available to
cover fixed costs, and afterwards contribute to profit
• Contribution ratio
Contribution expressed as a percentage of sales
• Break-even point
Point where no profit or loss occurs
THEREFORE THE CONTRIBUTION = FIXED COSTS
2. Terminology
• Margin of safety
Measure the extent to which sales may decline before a
loss is made
• Margin of safety ratio
Margin of safety expressed as a percentage of total sales -
indicates allowable % decline in sales before a loss is made
• Sales mix
Combination of products that a company sells
3. Break-even analysis:
Assumptions
 Selling price of a product / service is constant
 Variable cost per unit is constant
 Total fixed costs are constant
 Sales mix is constant at a company with multiple
products
3. Break-even analysis:
Assumptions
 Production and sales are synchronized - no change
in inventories (Prod = Sales)
 Productivity remains constant
 Efficiency remains constant
 Distinction between fixed and variable costs can be
accurately performed
4. Break-even point
• The break-even point is the level of sales where the
profit is zero (Rand or units)
• Three methods:
• Mathematical equation-method
• Contribution-method
• Graph-method
4. Break-even point
Mathematical equation method
Sales = variable costs + fixed cost + profit

So at the break-even point, profit is zero and the

equation as follows:
Sales = variable costs + fixed costs + 0
4. Break-even point
To calculate units:
SP X = VC X + FC + 0
(SP X – VC X) = FC
X(SP – VC) = FC
X = FC / (SP – VC)
4. Break-even point
• Contribution method
• Derived from the mathematical method – NB!
Break-even point (units)
= Fixed cost
Contribution/unit
Break-even point (R)
= Fixed cost
Contribution ratio
4. Break-even point
The graphical method
 When compiling the graph, the following lines
should be drawn:
1. The fixed cost line
2. The total cost line that represents the total cost as
well as the slope of the variable cost.
3. The total sales line that represents sales and the
slope indicates sales price per unit.
4. The point where the total cost and the total sales
lines intersect is the break-even point.
C-V-P graph-First, draw the fixed cost line

K-V-W grafiek / C-V-P graph

70
60
50
Rand
R'000

40
30
20
10
0
0 10 20 30 40 50
Volume
Second, draw the total cost line on
the fixed cost line

70
K-V-W Grafiek / C-V-P Graph
60
50
Rand

40
R'000

30
20
10
0
0 10 20 30 40 50
Volume
Read the break-even point from the
graph

70 K-V-W Grafiek / C-V-P Graph

60
50
Rand
R'000

40
30
20
10
0
0 10 20 30 40 50
Volume
Lastly, draw the total sales line

70 C-V-P Graph
60
50
Rand
R'000

40
30
20
10
0
0 10 20 30 40 50
Volume
Firstly, draw the variable cost line

70
Contribution graph
60
50
Rand
R'000

40
30
20
10
0
0 10 20 30 40 50
Volume
Draw the total cost line on top of the
variable cost line

70 Contribution graph
60
50
Rand

40
R'000

30
20
10
0
0 10 20 30 40 50
Volume
Draw the sales line

70 Contribution graph
60
50
Rand
R'000

40
30
20
10
0
0 10 20 30 40 50
Volume
Read the break-even point from the
graph

70 Bydrae grafiek / Contribution graph

60
50
Rand
R'000

40
30
20
10
0
0 10 20 30 40 50
Volume
Draw a profit line, the fixed cost on the y-axis
and the profit at a specific sales quantity

Profit-Volume graph
15
Rand

10
R'000

5
0
-20 -10 0 10 20 30 40 50
-5 Volume
-10
-15
-20
5. Margin of safety
• The margin of safety is the profitable portion of
sales in units or Rand that is safe .
It is calculated as follows:
Margin of safety =
Total sales less break-even sales
5. Margin of safety
• The margin of safety ratio or percentage represents
the portion that is safe and shows the percentage
by which sales can drop before a loss is made
• Formula:
Margin of safety ratio
= Margin of safety (rand / units)
Total sales (rand / units)
5. Margin of safety
• Example
A lab provides the following information:
Income per test R40.00
Material per test R8.00
Commission per test R5.00
Overhead per test R2.00
Salary – fixed R10 000
Rent R5 000
800 tests were performed in January
Required - calculate:
• Contribution
• Contribution ratio
• Break- even point
• Margin of safety ratio
5. Margin of safety

1) Contribution calculation:
Sales R32 000 R40
Variable cost (R12 000) (R15)
Material (R6 400) (R8)
Commission (R4 000) (R5)
Overhead (R1 600) (R2)
Contribution R20 000 R25
5. Margin of safety
2) Contribution ratio:

Contribution ÷ Sales
= R25 ÷ R40
= 62.5%
3) Break-even point

Fixed cost ÷ Contribution per unit

= R15 000 ÷ R25 per test
= 600 units
Fixed cost ÷ Contribution ratio
= R15 000 ÷ 62.5%
= R24 000
5. Margin of safety
4) Margin of safety ratio
Margin of safety
= Sales less break-even sales
= R32 000 – R24 000
= R8 000

Margin of safety %
= Margin of safety ÷ Sales
= R8 000 ÷ R32 000
= 25%
6. Target profit
• The same principle applies as with break-even point

• Instead of only using fixed cost in the formulae, the

target profit is added to the fixed cost

• Always use operating profit (before tax)

6. Target profit
Formulae
•Sales = variable cost + fixed cost + profit

•Target sales = Fixed cost + profit

(units) Contribution per unit

•Target sales = Fixed cost + profit

(Rand) Contribution ratio
COST-VOLUME-PROFIT:
• Study formulae on p 54 – 55 of the study guide and
use in the homework questions
7. Impact of taxation
• Only has an influence if a profit is made
• If tax is applicable, then the target profit after tax
must be converted to a target profit before tax.
• Operating profit before tax = Net profit after tax ÷ (1 – tax rate)
• 100,000 = 72,000 ÷ (1 – 0.28) or
• 72,000 = 100,000 x (1 – 0.28)
8. Changes in price, cost and
volume
• By using the contribution format income statement, the
impact on profit of the following changes can be predicted:
• Fixed cost and sales volume
• Variable cost and sales volume
• Fixed cost , sales price and sales volume
• Variable cost , sales price and sales volume
• Changes in normal selling price
Example:
Total Per unit
• Sales (20,000 units) 300 000 15
• Less variable cost (180 000) (9)
• Contribution 120 000 6
• Less fixed cost (70 000)
• Operating profit 50 000
Example: Sales volume increases by
15%.
Total Per unit
• Sales (23,000 units) 345 000 15
• Less variable cost (207 000) (9)
• Contribution 138 000 6
• Less fixed cost (70 000)
• Operating profit 68 000
Example: Sales price decreases by R1.50
per unit and volume increases by 25%.
• Total Per unit

• Sales (25,000 units) 337 500 13.50

• Less variable cost (225 000) (9)
• Contribution 112 500 4.50
• Less fixed cost (70 000)
• Operating profit 42 500
Example: Sales price increases by R1.50, fixed
cost increases by R20 000 and volume
decreases by 5%.
Total Per unit
• Sales (19,000 units) 313 500 16.50
• Less variable cost (171 000) (9)
• Contribution 142 500 7.50
• Less fixed cost (90 000)
• Operating profit 52 500
Example: Sales price increases by 12%, variable
cost increases by R0.60 per unit and volume
decreases by 10%.
Total Per unit
• Sales (18,000 units) 302 400 16.80
• Less variable cost (172 800) (9.60)
• Contribution 129 600 7.20
• Less fixed cost (70 000)
• Operating profit 59 600
10. Critical evaluation of break-
even analysis
• All the assumptions as discussed earlier, are
limitations.
• It is unlikely that sales and production will be the
same.
• Break-even analysis is, however, a very important
technique for decision making purposes.
11. C-V-P analysis and managerial
accounting
• Management accountants use cost-volume-profit
analysis for:
• Profit planning
• Decision making
• Performance evaluation
12 Operating leverage
• Operating leverage is the degree to which net profit
is sensitive to a percentage change in sales.
• If operating leverage is high, a small percentage
increase in sales will have a larger increase in net
profit.
12. Operating leverage
• Is calculated as follows:
Degree of = Contribution
operating leverage Net profit
12. Operating leverage
• A degree of operating leverage of five means that
net profit will grow five times as fast as sales.
• Therefore, if sales increases with 10%, net profit will
increase with five times as much, thus with 50%
(i.e. 50% of net profit, not sales).
12. Operating leverage
Actual Increased
Sales sales
(500) (550)
Verkope / Sales 250,000 275,000
Ver. koste / Var. cost 150,000 165,000
Bydrae / Contribution 100,000 110,000
Vaste koste / Fixed cost 80,000 80,000
Netto wins / Net profit 20,000 30,000

10% increase in sales from R250 000 to R275 000. . .

. . . causes a 50% increase in profit from R20 000 to R30 000.

12. Operating leverage
• The degree of operating leverage is determined by
the cost structure of the company, in other words
the relationship between fixed and variable cost.
• If a company has a high proportion of fixed cost,
will it have a high or low degree of operating
leverage?
• High, because a small change in sales has a large
effect on contribution (because variable cost is low)
and therefore has a large effect on profit.
Conclusion
• Cost-Volume-Profit analysis is a very important
concept in organisations for decision making
purposes.
• Break-even analysis is an important concept flowing
from C-V-P analysis.
• With the help of CVP analysis, a couple of types of
questions can be answerde.
Homework
• Moo Ltd
• Lipton
Thank You