ACCT 404
MANAGEMENT ACCOUNTING
LESSON 1
Cost-Volume-Profit (CVP) Analysis
Course Instructor
Teddy Ossei Kwakye, PhD
Senior Lecturer in Accounting
Department of Accounting
tokwakye@ug.edu.gh
Learning outcomes
•
Define cost-volume-profit (CVP) analysis, identify and explain the different approaches to
CVP analysis, and explain how organisations use CVP information in decision making.
•
Calculate break-even point sales units and revenue for companies selling one product or
service.
•
Determine the sales volume and revenue to achieve desired profit of firms selling one
product or service and include taxes in CVP analysis.
•
Determine the break-even point sales and revenue of firms selling more than one
product or service.
•
Explain the concept and importance of margin of safety and degree of operating
leverage to organisations and identify the assumptions and limitations of CVP analysis.
LO1
LO2
LO3
LO4
LO5
Slide 2
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Learning Outcome 1
Define cost-volume-profit (CVP) analysis, identify and explain the
different approaches to CVP analysis, and explain how organisations use
CVP information in decision making.
Slide 3
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CVP analysis
[slide 1 of 2]
CVP
analysis
LO1
A method for analyzing how operating decisions and
marketing decisions affect profit based on an
understanding of the relationship between variable costs,
fixed costs, unit selling price, and the output level.
It is based on an explicit model of the relationships among
the three factors – costs, sales, and profits – and how they
change in a predictable way as the volume of activity
changes.
It uses cost behaviour theory and variable (or marginal)
costing
Slide 4
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CVP analysis
[slide 2 of 2]
Applications
(or uses) of
CVP analysis
LO1
Ascertaining the break-even point sales units and revenue for firms.
Determining the level of sales units and revenue to achieve a target profit.
Setting the selling prices of products and services.
Determining the amount of revenue required to avoid losses.
Establishing whether fixed costs expose firms to an unacceptable level of risk.
Performing strategic ‘what if’ analysis to influence current operations and
predict future operations.
It helps managers to respond to changing market factors from an informed
background.
Slide 5
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Approaches to CVP analysis
[slide 1 of 7]
LO1
This approach is
premised on the basic
profit equation.
CVP
model or
equation
approach
SP(Q) = TFC + VC(Q) + P
• SP - Selling price; Q - Units of
output sold; TFC - Total fixed
cost; VC - Variable cost per
unit; P - Profit
Slide 6
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Approaches to CVP analysis
[slide 2 of 7]
LO1
Contribution margin
• the excess of sales over all variable cost
associated with sales output, to cover
fixed costs and add to profit i.e., the
profit before fixed cost.
• Contribution margin = Total sales – Total
variable cost
Contribution
margin
approach
Contribution margin per unit
• the difference between per unit selling
price and per unit variable cost.
• It measures the increase in profit for a
unit increase in sales revenue.
• Contribution margin per unit = Selling
price – Variable cost per unit
Slide 7
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Approaches to CVP analysis
[slide 3 of 7]
LO1
Contribution margin ratio or
percentage
•the ratio of contribution margin to sales revenue
or the ratio of unit contribution margin per unit to
selling price, expressed as ratio or percentage.
•It shows the proportion of sales or selling price
that contributes to the recovery of fixed cost
•it is a measure of the profit contribution per sales
cedis.
Contribution
margin
approach
Uses of contribution margin ratio or
percentage
•identifies the amount of increase (or decrease) in
profits caused by a given increase (or decrease) in
sales revenue.
•may be used to determine the contribution
margin associated with a particular sales revenue.
•Variable cost to sales ratio can be deduced from
contribution margin ratio or percentage.
Slide 8
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Approaches to CVP analysis
[slide 4 of 7]
LO1
This approach substitutes
contribution margin into
the CVP equation
Contribution
margin
approach
CM(Q) – TFC = P
• CM – Contribution margin per
unit; Q – Units of output sold;
TFC – Total fixed cost; P – profit
TCM – TFC = P
• TCM – Total contribution
margin; TFC – Total fixed cost; P
- Profit
Slide 9
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Approaches to CVP analysis
[slide 5 of 7]
LO1
Graphical approach: CVP
graph
• Shows how the levels of revenues
and total costs change over
different levels of output.
• Where revenue line falls below
(above) the cost line, losses
(profits) results.
Slide 10
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Approaches to CVP analysis
[slide 6 of 7]
LO1
Graphical approach:
Contribution margin
graph
• It is like the traditional CVP
graph except that it makes it
possible to read contribution
at different levels of activity
Slide 11
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Approaches to CVP analysis
[slide 7 of 7]
LO1
Graphical approach: Profitvolume graph
• It illustrates how the level of profits
changes over different levels of
output or volume of sales.
• It highlights the total amount of
profit or loss at different sales
volumes.
Slide 12
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Learning Outcome 2
Calculate break-even point sales units and revenue for companies selling
one product or service.
Slide 13
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Break-even point analysis
[slide 1 of 2]
LO2
Break-even point (BEP)
• The volume of sales at which the total revenues and costs are
equal, and the firms’ operations breaks even.
• The organisation makes no profit or loss, i.e., profit is zero.
• The firm’s total contribution margin from sales is equal to the
total fixed cost.
• BEP can be expressed in both sales units and sales amount (value).
• BEP sales increases when:
• fixed costs increases.
• variable costs increases.
• sales price decreases.
Slide 14
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Break-even point analysis
[slide 2 of 2]
Using CVP model
BEP sales in units
(QBE)
QBE = TFC ÷ (SP – VC)
LO2
Using contribution margin
BEP sales in
amount or value
(TSBE)
BEP sales in units
(QBE)
Multiply BEP sales
in unit (QBE) by the
selling price (SP)
per unit
QBE = TFC ÷ CM
BEP sales in
amount or value
(TSBE)
Multiply BEP (QBE) sales
in units by the selling
price per unit, or
Determine the
contribution margin
ratio or percentage
(CMR)
TSBE = QBE * SP
•TSBE = TFC ÷ CMR
Slide 15
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Example: Break-even point analysis
[slide 1 of 2]
LO2
Studio Emerald Enterprise is a photo-finishing store and
has provided the following data for the month of March
in 2022. They charge GHS0.60 per unit for developing
prints. During March, they developed 12,000 prints at a
variable cost of goods sold of GHS0.30 per unit. Their
variable selling cost was GHS0.06 per print. The total
fixed cost of Studio Emerald Enterprise in the month of
March was GHS1,500 and they desire a before tax
profit of GHS1,800.
Slide 16
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Example: Break-even point analysis
[slide 2 of 2]
Solution
CVP model
• QBE = TFC ÷ (SP – VC)
Contribution margin
• CM = SP – VC
= 1,500 ÷ [0.60 – (0.30 + 0.06)]
= 6,250 prints
• TSBE = QBE * SP
LO2
= 0.60 – (0.30+0.06)
= 0.24
• QBE = TFC ÷ CM
= 6,250 * 0.60
= GHS3,750
= 1,500 ÷ 0.24
= 6,250 prints
• TSBE = TFC ÷ CMR
= 1,500 ÷ 0.4
= GHS3,750
Slide 17
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Learning Outcome 3
Determine the sales volume and revenue to achieve desired profit of
firms selling one product or service and include taxes in CVP analysis
Slide 18
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Profit planning
[slide 1 of 2]
LO3
Profit planning
• Involves the determination of sales volume or output level
by managers to achieve a targeted profit assuming
operating costs remain constant.
• It entails revenue planning, cost planning, and accounting
for the effect of income taxes (when planning for the
desired profit after tax).
• When planning for a targeted profit, before tax profit must
be used,
• after-tax profit must be grossed up as:
• Before-tax profit = After-tax profit ÷ (1 – tax rate)
Slide 19
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Profit planning
[slide 2 of 2]
LO3
Using CVP model
Using contribution margin
Sales in units to
achieve desired
profit (QDP)
Sales in units to
achieve desired
profit (QDP)
QDP = (TFC + DP) ÷
(SP – VC)
Sales revenue to
achieve desired
profit (TSDP)
Multiply QDP by
the selling price
(SP) per unit
TSDP = QDP * SP
QDP = (TFC + DP) ÷ CM
Sales revenue to
achieve desired
profit (TSDP)
Multiply QDP sales in
units by the selling
price per unit, or
Determine the
contribution margin
ratio or percentage
(CMR)
•TSDP = (TFC + DP) ÷ CMR
Slide 20
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Example: Profit planning
[slide 1 of 2]
LO3
Studio Emerald Enterprise is a photo-finishing store and has
provided the following data for the month of March in 2022.
They charge GHS0.60 per unit for developing prints. During
March, they developed 12,000 prints at a variable cost of
goods sold of GHS0.30 per unit. Their variable selling cost was
GHS0.06 per print. The total fixed cost of Studio Emerald
Enterprise in the month of March was GHS1,500 and they
desire:
(a) a before tax profit of GHS1,800, and
(b) an after-tax profit of GHS1,800 (tax rate is 25%)
Slide 21
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Example: Profit planning
[slide 2 of 3]
LO3
Solution
CVP model
• QDP = (TFC + PP) ÷ (SP – VC)
Contribution margin
• QDP = (TFC + DP) ÷ CM
= (1,500 + 1,800) ÷ (0.60 – 0.36)
= 13,750 prints
• TSDP = QPP * SP
= (1,500 + 1,800) ÷ 0.24
= 13,750 prints
• TSDP = (TFC + DP) ÷ CMR
= 13,750 * GH¢0.60
= GH¢8,250
= (1,500 + 1,800) ÷ 0.4
= GH¢8,250
Slide 22
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Example: Profit planning
[slide 3 of 3]
LO3
Solution
Before-tax profit = after-tax profit ÷ (1 – tax rate)
= 1,800 ÷ (1 – 0.25)
= GH¢2,400
CVP model
Contribution approach
QDP = (1,500 + 2,400) ÷ (0.60 – 0.36) QDP = (1,500 + 2,400) ÷ 0.24
= 16,250 prints
= 16,250 prints
TSDP
TSDP
= 16,250 * GH¢0.60
= GH¢9,750
Slide 23
= (1,500 + 2,400) ÷ 0.4
= GH¢9,750
acct404_CVPAnalysis_teddyok_BSc
Learning Outcome 4
Determine the break-even point sales and revenue of firms selling more
than one product or service
Slide 24
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CVP analysis for multiple products
[slide 1 of 2]
LO4
Best approached using
the contribution margin
approach
Assume a constant sales
mix for the products or
services.
Sales mix is the relative
proportion of the
different products sold or
services provided that
constitutes the total
revenue or sales of firms.
The contribution margin
used is weighted on the
quantities of each
product or service
included in the ‘bag’ of
products or services
the weighted average
contribution margin per
unit (WACM) is used if it
is assumed that the sales
mix will remain constant
in units
Slide 25
the weighted average
contribution margin ratio
(WACMR) is used if it is
assumed that sales mix
will remain constant in
amount or value
acct404_CVPAnalysis_teddyok_BSc
CVP analysis for multiple products
[slide 2 of 2]
LO4
Weighted average contribution margin
• Sum of the total contribution margin for each of the products or services (ΣTCM) divided
by the sum of sales units for each of the products or services (ΣQ), i.e., ΣTCM ÷ ΣQ or
• Sum of the product of sales mix of each product or service (Smix) and the corresponding
contribution margin per unit (CM) of all the product, i.e., Σ(Smix * CM)
Weighted average contribution margin ratio
• Weighted average contribution margin per unit (WACM) divided by weighted average
revenue (WAR), where WAR = Sum of the product of the sales mix of each product or
service (Smix) and the corresponding selling price per unit (SP) of all the products. i.e.,
WACM ÷ Σ(Smix * SP) or
• Sum of the product of the sales mix of each product or service (Smix) and the
corresponding contribution margin ratio (CMR) of all the products, or i.e., Σ(Smix * CMR)
Slide 26
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Break even point for multiple products
[slide 1 of 2]
LO4
Calculate the BEP for all the
products or services in total
as:
BEP sales
for
multiple
products
• In sales units: QBE = TFC ÷ WACM
• In sales value or amount: TSBE =
TFC ÷ WACMR
Determine the BEP for each
product or service based on
the sales mix by multiplying
the sales mix by total BEP
calculated i.e., Smix * QBE or
Smix * TSBE
Slide 27
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Break even point for multiple Products
[slide 2 of 2]
LO4
Graphical approach
• It is similar to the profit-volume
graph for single products
• Profit/loss and cumulative sales
from each of the products are
plotted on the graph
• Cumulative sales are
determined in order of
contribution margin to sales
ratio
• Profit/loss of each product is
determined by deducting fixed
cost from the cumulative
contributions of each product
Slide 28
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Example: BEP for multiple products
[slide 1 of 2]
LO4
Unilever (Ghana) Ltd sells three types of soap – Sunlight, Lux and
Geisha – and planning their operations for the quarter ended 30th
June 2021. Unilever expects to sell the products for GHS30,
GHS32 and GHS40 per bar respectively, with a variable costs per
bar of GHS24, GHS24 and GHS36 respectively. During the quarter
ended 31st March 2021, sales revenue from Sunlight was
GHS750,000, Lux was GHS600,000 and Geisha was GHS150,000.
The total fixed costs for the period are expected to be
GHS168,000, and it is assumed that Unilever’s sales will remain
constant in sales amount for the three products.
Slide 29
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Example: BEP for multiple products
[slide 2 of 2]
LO4
Solution
• Sales mix (Smix)
Sunlight : Lux : Geisha = 0.5 : 0.4 : 0.1 (the ratio of the products sales values)
• WACMR
CM for Sunlight = GH¢6
CM of Lux = GH¢8 CM of Geisha = GH¢4
CMR for Sunlight = 0.2
CMR of Lux = 0.25
CMR of Geisha = 0.1
WACMR = (0.5 * 0.2) + (0.4 * 0.25) + (0.1 * 0.1) = 0.21
• Total break-even sales revenue (TSBE)
TSBE = GH¢168,000 ÷ 0.21 = GH¢800,000
• Break-even sales revenue of each soap
Sunlight = 0.5 * GH¢800,000 = GH¢400,000
Lux = 0.4 * GH¢800,000 = GH¢320,000
Geisha = 0.1 * GH¢800,000 = GH¢80,000
Slide 30
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Profit planning for multiple products
[slide 1 of 1]
LO4
Calculate the sales for all the
products or services in total to
achieve the desired profit as:
Profit
planning
for multiple
products
• In sales units: QDP = (TFC + DP) ÷ WACM
• In sales value or amount: TSDP = (TFC + DP) ÷
WACMR
Determine the sales for each
product or service based on the
sales mix by multiplying the sales
mix by total sales to achieve the
desired profit calculated i.e., Smix
* QDP or Smix * TSDP
Slide 31
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Example: Profit planning for multiple products
[slide 1 of 2]
LO4
Unilever (Ghana) Ltd sells three types of soap – Sunlight, Lux and
Geisha – and planning their operations for the quarter ended 30th June
2018. Unilever expects to sell the products for GHS30, GHS32 and
GHS40 per bar respectively, with a variable costs per bar of GHS24,
GHS24 and GHS36 respectively. During the quarter ended 31st March
2018, sales revenue from Sunlight was GHS750,000, Lux was
GHS600,000 and Geisha was GHS150,000. The total fixed costs for the
period are expected to be GHS168,000, and it is assumed that
Unilever’s sales will remain constant in sales amount for the three
products. Assuming that Unilever wants to achieve a desired before-tax
profit of GHS25,200. Determine the sales revenue for each of the soaps
for Unilever to achieve the desired profit.
Slide 32
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Example: Profit planning for multiple products
[slide 2 of 2]
LO4
Solution
• Sales mix (Smix)
Sunlight : Lux : Geisha = 0.5 : 0.4 : 0.1
• WACMR
WACMR = (0.5 * 0.2) + (0.4 * 0.25) + (0.1 * 0.1) = 0.21
• Sales revenue to achieve the desired profit (TSDP)
TSDP = (GH¢168,000 + GH¢25,200) ÷ 0.21 = GH¢920,000
• Sales revenue for each soap to achieve the desired profit
Sunlight = 0.5 * GH¢920,000 = GH¢460,000
Lux = 0.4 * GH¢920,000 = GH¢368,000
Geisha = 0.1 * GH¢920,000 = GH¢92,000
Slide 33
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Learning Outcome 5
Explain the concept and importance of margin of safety and degree of
operating leverage to organisations and identify the assumptions and
limitations of CVP analysis
Slide 34
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Margin of safety
[slide 1 of 1]
LO5
It shows how far a company is operating from its break-even point and
indicates the amount by which sales revenue can drop before reaching
break-even point and losses begin to be incurred by an organization
The value or amount of sales above the break even point
Planned (or actual) sales − breakeven sales (in units or in value)
It is a useful measure for comparing the risk of two or more alternative as
it measures the amount of ‘cushion’ against losses
A higher margin of safety serves as a good cushion and indicates lesser
risk for losses.
Slide 35
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Degree of operating leverage
[slide 1 of 1]
The extent of fixed
costs in the cost
structure of an
organisation
The greater the
operating leverage, the
greater the operating
risk
Slide 36
DOL = Total
contribution margin ÷
operating profit
or
DOL = (total fixed cost
÷ profit) + 1
LO5
DOL has an inverse
relationship
with
margin of safety i.e.,
the smaller the margin
of safety, the larger the
degree of operating
leverage and vice versa
acct404_CVPAnalysis_teddyok_BSc
Assumptions of CVP analysis
[slide 1 of 1]
Assumption
of CVP
analysis
LO5
The behaviour of total cost and revenue is linear over the relevant range
Costs can be accurately categorised into fixed and variable components.
Selling price per unit of the product variable and fixed costs will not change as sales
volume varies within the relevant range. The sales volume is the only cost driver.
Labour productivity, production technology and market conditions do not change.
There are no capacity additions during the period under consideration.
In multiproduct organisations, the sales mix remains constant over the relevant range.
In manufacturing firms, the levels of all inventory at the beginning and end of the period
are the same.
Total contribution margin increases proportionately with increases in sales volume.
Slide 37
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End of Lesson