Cvp

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 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 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

With Tax

Consideration

Unit variable

cost or selling

price are

Known

(Solve for Q)

Unit variable

cost or selling

price are

unknown

(Solve for S)

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

The greater the ratio the greater TFC and the greater operating risk

(potential profit fluctuation)

DOL (TCM / EBT) 1.42 1.25 1.18

DOL (% Change) 1.25

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.


Illustration

Total fixed costs 375,000 100,000


Behavioural format profit and loss statement at 10,000 units sold


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



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


Illustration


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


Formula for find out Composite Break-Even or Target Profit

in Unit


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


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

Solution


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%


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

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