Question 3 : Cost Volume Profit
(CVP) Analysis
Kumpanart Kavalee
Reclassification of Expense
CVP Analysis in this lecture is based on variable costing approach
CVP Formula
CVP Analysis : Illustration 1
CVP Analysis : Illustration 1
CVP Chart
CVP Formula with Tax Application
Before tax CVP formula :
(P-VC)Q – TFE = EBT
With tax consideration :
[(P-VC)Q – TFE] – [((P-VC)Q – TFE)T] = NP
[(P-VC)Q – TFE].[1 – T] = NP
CVP Analysis : Illustration 2
CVP Analysis : Illustration 2
CVP Chart
What is Cost-Volume-Profit Analysis?

Cost-Volume-Profit (CVP) Analysis

CVP analysis is a sensitivity analysis of interrelationships of selling
price, costs, quantity sold and profit (“CVP interrelationships”) for
short-term profit planning

Basic applications of CVP
(1) Determination of Break-Even and Target Profit
(2) Sensitivity Analysis of Profit Planning (Pricing Decision,
Cost Reduction, and Sales Mix Strategies)
(3) Determination of Margin of Safety
(4) Risk management (Operating leverage)
Types of CVP Analysis
There are generally 2 broad types of CVP analysis
1) Non-linear CVP analysis
2) Linear CVP analysis
Non-Linear CVP Analysis

Non-linear CVP analysis is mostly used in economics because
economics are based on many economic principles such as law of
diminishing returns, productivity, etc.. which are more realistic and
applicable to long-term perspective

However, economic (non-linear) based CVP comes up with
(1) Difficult and unreliable to estimate input parameters
(2) Calculation difficulty (use of complicated mathematics
like calculus to solve a non-linear equation)
(3) Impractical and unrealistic approach for short-term
profit planning because many variables are remain
unchange in short-term
Linear CVP Analysis

Based on economic principles “costs of input normally remain unchanged in short-run”;
therefore linear CVP analysis becomes more realistic, more applicable and more
practicable for short-term analysis

To make linear CVP become realistic, applicable and practicable to short-term analysis,
we need 2 things
(1) Holding 5 assumptions for doing analysis

Constant sales price

Constant variable cost per unit

Constant total fixed costs

Constant sales mix (for multi-products analysis)

Units sold equal units produced
(2) Need to revise sales price, variable cost per unit, total fixed costs, sales
mix proportion regularly and constantly
Illustration 3 : Break-Even, Margin of
Safety, and Target Profit Analysis
Illustration : Break-Even, Margin of Safety,
and Target Profit Analysis
Behavioural P/L (Answer to Question 1)
Unit cost Ratio and Percentage
(Answer to Question 2 – 5)
Contribution Margin VS Fixed Costs
Total contribution margin = total
sales revenue – total variable
costs or profit before tax + total
fixed costs
Total Contribution margin is an
amount of profit available to
absorb fixed costs
The more fixed costs incurred,
the more contribution margin is
used to absorb the fixed costs
incurred, and the less profit is a
result. On the other hand, the
less fixed costs incurred, the less
contribution margin is used to
absorb the fixed costs incurred,
and the more contribution margin
is turned to profit.
Figure Out Break-Even Point
(Answer to Question 6 -7)
Margin of Safety (Answer to Question 8)
Margin of Safety
Target Profit (Answer to Question 9 – 10)
Target Profit (Answer to Question 11 – 12)
Derivations of CVP Formula
Without Tax
Consideration
Unit variable
cost or selling
price are
Known
(Solve for Q)
Unit variable
cost or selling
price are
unknown
(Solve for S)
With Tax
Consideration
Analysis of Operating Risk
(Operating Leverage)
Operating Leverage
= The use of fixed operating cost (TFC) to alter the
relative percent changes in sales to percent change in EBIT or EBT.
The more TFC use, the more profit fluctuation, the more operating risk
Effect of Gearing (Leverage)
Measurement of Operating Leverage


How much the extent of operating risk as being measured by operating
leverage?
We can calculate numeric expression to show the extent of operating
leverage by
Measurement of Operating Leverage
DOL (TCM / EBT)
DOL (% Change)
1.42
1.25
1.18
1.25
The greater the ratio  the greater TFC and the greater operating risk
(potential profit fluctuation)
Operating Leverage in Decision Making

As variable costs and fixed costs sometimes can be use
interchangeably

For example : Company X uses more
workers
(more
variable costs) whereas company Y uses more machines (more
fixed costs)

Therefore, the company management normally use different
mix of variable costs and fixed costs to earn different amount
of profit and also borne different level of operating risk.
Operating Leverage in Decision Making
Illustration
Total fixed costs
375,000
100,000
Operating Leverage in Decision Making
Behavioural format profit and loss statement at 10,000 units sold
Operating Leverage in Decision Making
CVP Application on Operating Leverage
Q : Which alternative of system should management
select?
A : It is depend on whether which alternative will result
in higher expected profit after taking possibility and
magnitude of potential loss into consideration
CVP Application on Operating Leverage
CVP Application on Operating Leverage
If an average annual sales volume during life of automated system is 10,000 units per
year and there is very rare possibility that sales volume will drop below 9,167 units
(Margin of Safety Ratio = 8.33%)  Management should select Automate System
CVP Application on Operating Leverage
Illustration
Operating Leverage in Decision Making
High leverage
Choice
Low leverage
Choice
Basic Features
Unit variable cost
Relative lower
Relative higher
Total fixed expense
Relative higher
Relative lower
Contribution margin
Relative higher
Relative lower
Break-even point
Relative higher
Relative lower
Margin of safety
Relative lower
Relative higher
Degree of operating
leverage (DOL)
Relative higher
Relative lower
Risk / Return Profiles
Down-side risk
Relative higher
Relative lower
Up-side potential
Relative higher
Relative lower
CVP Application on Sale Mix Strategy
CVP analysis on sale mix strategy is mostly used by the
company when the company has two or more complementary
products that normally sell in bundle e.g. coffee and creamy powder
Basic Application :
Figure out breakeven or target profit of two or more
assorted products sold in bundle with a constant mix (e.g.
1 coffee : 3 creamy powers)
 Finding new mixture of assorted products that will result in
lower breakeven or higher target profit

CVP Application on Sale Mix Strategy
Formula for find out Composite Break-Even or Target Profit
in Unit
CVP Application on Sale Mix Strategy
Illustration :
Baubles and Trinkets are complementary products. The company’s sale mix
analysis shows that every 3 units of Bauble sold 1 units of Trinkets could be sold.
The unit information of Baubles and Trinkets are as follows :
Now, the company management wants to increase sale of Trinket. Consequently
the management arrives at a decision to avail a strong demand of Bauble for
increasing sale of Trinkets by wrapping 3 units of Bauble and 2 units of Trinket in a
single bundle for sale. Assuming that the company management does not change a
package’s selling price, how much is the company’s breakeven for a bundle sale
CVP Application on Sale Mix Strategy
Solution
Numerator : Total fixed costs + Target profit before tax = $7600 + $0 = $ 7,600
Denominator : The composite (or weighted average) unit contribution margin is ($0.40)(.6)
+ ($0.875)(.4) = $0.59.
The break-even point for both products combined is $7600 / $0.59 = 12,881 units.
Breakeven in units sold of Baubles = (12,881)(60%) = 7,729 units
Breakeven in units sold of Trinkets = (12,881)(40%) = 5,152 units
CVP Application on Sale Mix Strategy
Determination of feasible mix
After conducting marketing research  Maximum units of Baubles and Trinkets
could be sold are 7,729 and 5,961 units respectively. Therefore, the feasible mix of
Baubles and Trinkets that make the company’s profit is at break-even are 50% :
50% or 60% : 40%
CVP Application on Sale Mix Strategy
Illustration
CVP Application on Combined Capacity
CVP Application on Combined Capacity
Profit – Volume Ratio (PVR)
Profit – Volume Ratio (PVR)
Cash Break Even Point
BEP in case of Opening Stock
CVP Analysis with Relevant Range
BEP in case of Relevant Range of Variable
Cost
BEP in case of Relevant Range of Fixed Cost
BEP in case of Semi-Variable Cost