Chapter 2 CVP Analysis
Chapter 2 CVP Analysis
Chapter 2 CVP Analysis
PROFIT ANALYSIS
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INTRODUCTION
Today we will focus on gaining an
understanding of how . . .
Costs
Volume, and
Profits
Interact
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LECTURE OUTLINE
Cost behavior
Cost-Volume-Profit (CVP)analysis
Contribution margin and its measures
Break-event point analysis
Computing sales for target income
Multiple-product analysis
With risk and uncertainty
Assumptions in CVP analysis
Using sensitivity analysis
Ethical consideration
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IMPORTANT OF COST BEHAVIOR IN
BUSINESS
Understanding cost behavior help
managers to:
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COST BEHAVIOR
Cost behavior is the way a cost changes
when the level of output changes.
Cost behavior patterns:
Fixed costs
Variable costs
Mixed costs (Semi-variable costs)
Step costs (Step-fixed costs)
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FIXED AND VARIABLE COSTS
Fixed costs
Remains unchanged in total within a relevant
range as the level of output varies
As activity increases, total fixed costs do not
change, but unit fixed cost declines
Variable costs
Change in total in direct proportion to a change in
output
As activity increases, total variable costs increase,
but unit variable cost do not change
Notes: The relevant range is the limit of output level within which
a specific relationship between costs and the cost driver is
valid.
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FIXED COSTS & RELEVANT RANGE
1 $30 $30
10 $30 $300
100 $30 $3,000
200 $30 $6,000
1 $9,000 $9,000
10 $9,000 $900
100 $9,000 $90
200 $9,000 $45 8
FIXED COST
FIXED AND VARIABLE COSTS
$
$
Volume Volume
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MIXED COSTS (SEMI-VARIABLE COSTS)
Mixed cost includes both fixed and variable cost
components (compensation for sales
representatives)
The formula for mixed costs is:
Total cost = total fixed cost + total variable cost
Y = a + bX
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MIXED-COSTS
Linearity Assumption
Total Costs
$
Fixed Costs
Variable
Costs
Volume
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STEP-FIXED COSTS (STEP COSTS)
But different
between ranges
of activity
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Volume
SEPARATING MIXED COSTS
Why we need to separate mixed costs into fixed
and variable components?
Accounting records typically show the total costs and
the associated amount of output of a mixed cost item.
E.g. the total cost of maintenance and the number of
maintenance hours provided during a given period of
time.
Methods for Separating Mixed Costs
The High-Low Method
The Scatterplot Method
The Method of Least Squares 14
SEPARATING MIXED COSTS
A scatter plot can be useful in allowing us to plot the
data points to visualise the relationship between cost
and the level of output
The high-low method involves taking the two
observations with the highest and lowest level of
output to calculate the cost function
Regression analysis is a statistical technique that
uses all observations to determine the cost function
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COST VOLUME PROFIT (CVP) ANALYSIS
A technique used to determine the effects of
changes in an organisation’s sales volume on its
costs, revenue and profit
Can be used in profit-seeking and not-for profit
organisations
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INCOME STATEMENTS . . .
Traditional Contribution Format
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CONTRIBUTION MARGIN AND ITS
MEASURES
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CONTRIBUTION MARGIN AND ITS
MEASURES
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THE CONTRIBUTION APPROACH
For each additional unit Wind sells, $200
more in contribution margin will help to
cover fixed expenses and profit.
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THE CONTRIBUTION APPROACH
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BEP: CONTRIBUTION MARGIN METHOD
The contribution margin method is a variation of the
equation method.
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BEP: COST VOLUME PROFIT (CVP) GRAPH
Shows how costs, revenue and profits change as
sales volume changes
Four steps
1. Draw the fixed expense line
2. Draw the total expense line
3. Draw the total revenue line
4. Break-even point—where the total revenue and
total expense lines intersect
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CVP GRAPH
450,000
400,000
350,000
300,000
Total Expenses
250,000
200,000
50,000
-
- 100 200 300 400 500 600 700 800
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Units
CVP GRAPH
450,000
400,000
350,000
300,000
Total Sales
250,000
200,000
150,000
100,000
50,000
-
- 100 200 300 400 500 600 700 800 28
Units
CVP GRAPH
450,000
400,000
350,000
300,000
250,000
200,000
150,000
Break-even point
100,000
50,000
-
- 100 200 300 400 500 600 700 800
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Units
UNITS & SALES NEEDED TO ACHIEVE A
TARGET INCOME
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INCLUDING INCOME TAXES
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CVP ANALYSIS & RISK AND CERTAINTY:
SAFETY MARGIN
Gives a feel for how close projected operations are
to the break-even point.
There are 3 measures: in dollars, in percentage
and in units
Break-even
sales Actual sales
400 units 500 units
Sales $ 200,000 $ 250,000
Less: variable expenses 120,000 150,000
Contribution margin 80,000 100,000
Less: fixed expenses 80,000 80,000
Net operating income $ - $ 20,000
THE MARGIN OF SAFETY
PERCENTAGE
RBC’s margin of safety can be expressed as 20% of
sales. ($50,000 ÷ $250,000)
Break-even
sales Actual sales
400 units 500 units
Sales $ 200,000 $ 250,000
Less: variable expenses 120,000 150,000
Contribution margin 80,000 100,000
Less: fixed expenses 80,000 80,000
Net operating income $ - $ 20,000
THE MARGIN OF SAFETY IN UNITS
The margin of safety can be expressed in terms of the
number of units sold. The margin of safety at RBC is
$50,000, and each bike sells for $500; hence, RBC’s
margin of safety is 100 bikes.
Margin of $50,000
= = 100 bikes
Safety in units $500
CVP ANALYSIS: OPERATING LEVERAGE
Operating leverage is the use of fixed costs to
multiple the impact of sales changes on income.
Degree of operating leverage (DOL) for a given level of sales
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OPERATING LEVERAGE
Operating leverage is a measure of how sensitive
net operating income is to percentage changes in
sales. It is a measure, at any given level of sales, of
how a percentage change in sales volume will
affect profits.
Contributi on Margin
DOL Degree of Operating Leverage
Net Operating Income * *
Degree of
Operating = $100,000 = 5
Leverage $20,000
OPERATING LEVERAGE
With an operating leverage of 5, if RBC increases its sales by
10%, net operating income would increase by 50%.
1
DOL
MoS%
CVP ANALYSIS WITH MULTIPLE PRODUCTS
Sales mix
The relative proportions of each type of product
(units) sold by the organisation
Package unit contribution margin
The unit contribution margins of a package in
according with sales mix
Fixed costs
Break - even package =
Package unit contribution margin
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THE CONCEPT OF SALES MIX
Sales mix is the relative proportion in which a
company’s products are sold.
Different products have different selling prices, cost
structures, and contribution margins.
When a company sells more than one product,
break-even analysis becomes more complex as
the following example illustrates.
Sales $ 250,000
$300,000 x Contributi on Margin 1
DOL
BE% = Net Operating Income MoS%
64.15% Net Operating Income
MoS%
Breakeven sales $160,375 Contributi on Margin
$192,450 95,000
Total breakeven sales = MoS% 35.85%
265,000
$352,825
MoS% 1 BE%
BE% 1 MoS% 1 35.85 64.15%
MULTI-PRODUCT BREAKEVEN ANALYSIS
(THE BE% METHOD)
Bicycle Carts Total
160,37 100 192,45 100 100.0
Sales 5 % 0 % 352,825 %
Contribution 105,84
margin 64,150 40% 7 55% 169,997 48.2%
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TREATING CVP ANALYSIS WITH CAUTION
CVP analysis is merely a simplified model
The usefulness of CVP analysis may be greater in
less complex smaller firms, or stand-alone
projects
For larger firms, CVP analysis can be valuable as
a decision tool for the planning stages of new
projects and ventures
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KEY ASSUMPTIONS OF CVP
ANALYSIS
Selling price is constant.
Costs are linear and can be accurately divided into
variable (constant per unit) and fixed (constant in total)
elements.
In multiproduct companies, the sales mix is constant.
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CVP ANALYSIS AND MANAGERIAL ETHICS
Ethical judgment
Make sure to have the best
information possible when making
decisions
Not let personal factors affect the use
of cost information
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