Transcript Presentation Outline

Chapter 4
Cost-Volume-Profit Analysis
Revenues
Costs
Presentation Outline
I.
Common Cost Behavior Patterns
II. Cost Estimation Methods
III. The Relevant Range
IV. Cost-Volume Profit Analysis
V. Degree of Operating Leverage
VI. Excel and Regression Analysis
I. Common Cost Behavior Patterns
A. Variable Costs
B. Fixed Costs
C. Discretionary versus Committed Fixed
Costs
D. Mixed Costs
E. Step Costs
A. Variable Costs
Although variable cost per unit remain
constant, total variable cost increases
and decreases in proportion to changes
in the activity level.
$
Variable cost
in total
Level of Activity
B. Fixed Cost in Total
Although fixed cost per unit decreases with increases
in activity levels, total fixed cost is not affected by
changes in the activity level within the relevant
range (i.e., total fixed cost remains constant even if
the activity level changes.
$
Total fixed
cost
Level of Activity
C. Discretionary versus Committed Fixed Costs
Committed Fixed Costs
Examples include rent,
depreciation, insurance.
Two key factors are:
1. Long term in nature
2. Can’t be reduced to
zero even for short
periods of time without
seriously impairing the
organization.
Discretionary Fixed
Costs
Arise from annual decisions
by management to
spend in certain fixed
cost areas (i.e.,
advertising, research and
development,
maintenance).
D. Mixed Cost
A mixed cost has both a variable and a
fixed component.
$
Total cost line
Variable
component
Fixed
component
Level of Activity
E. Step Costs
Step costs are those costs that are fixed for a range of
volume but increase to a higher level when the upper
bound of the range is exceeded. At that point the costs
again remain fixed until another upper bound is
exceeded.
$
Level of Activity
II. Cost Estimation Methods
A. High-Low Method
1. The Variable Cost Element
2. The Fixed Cost Element
B. Scattergraphs
1. Outliers
C. Regression Analysis
A. The High-Low Method
The high-low method determines the fixed and
variable portions of a mixed cost by using only
the highest and lowest levels of activity and
related costs within the relevant range.
1. The Variable Cost Element
$
Total Cost
Line
Variable Cost
Fixed Cost
Activity Level
The variable cost element b is computed as follows:
b = (Cost at high activity level) – (Cost at low activity level)
(High activity level) – (Low activity level)
2. The Fixed Cost Element
Variable cost
per unit
y=a+bx
Total cost
Fixed
cost
Number of units
of activity
The fixed portion of a
mixed cost is found by
subtracting total
variable cost from total
cost (high or low level).
See Illustration on Page 120
B. Scattergraph
Cost of Receiving
Report
Scattergraph
250
200
150
100
50
0
-
50
100
150
Number of Shipments Received
A scattergraph is a graph that plots all known activity
observations and the associated costs. A regression
line is the line of “best fit” which is the least squares
regression line. In a scattergraph, the line is
estimated.
1. Outliers
Outliers are abnormal
or nonrepresentative
observations within
a data set that may
be inadvertently
used in the
application of the
high-low method.
C. Regression Analysis
Regression analysis is a statistical
technique that analyzes the association
between dependent and independent
variables.
An independent variable is a variable
that, when changed, will cause
consistent and observable changes in
the dependent variable.
1. Illustration Using Microsoft Excel
Cost of Receiving
Report
Least Squares Regression
y = 1.2369x + 54.657
250
200
150
100
50
0
-
50
100
Number of Shipments Received
150
2. Simple Regression v. Multiple Regression
Simple Regression
Only one independent
variable is used to
predict the
dependent variable.
y=a+bx
Multiple Regression
Two or more
independent
variables are used to
predict the
dependent variable.
y = a + b1x1 + b2x2
III. The Relevant Range
The assumed range of activity is referred to a
the relevant range, which reflects the
company’s normal operating range. The
relevant range is the range over which cost
behavior assumptions are valid.
A. The Relevant Range and Total Variable Cost
B. The Relevant Range and Total Fixed Cost
A. The Relevant Range and Total Variable Cost
Although total variable cost increases when activity
increases, the rate is only constant within the relevant
range.
$
Relevant
range
Level of Activity
Total
variable cost
B. The Relevant Range and Total Fixed Cost
Total fixed cost can behave in a step-cost
manner when outside the relevant range..
$
Relevant
range
Level of Activity
Total fixed
cost
IV. Cost-Volume-Profit Analysis
A. Contribution Margin Concepts
B. The Profit Equation
C. Contribution Margin Method
D. Multiproduct Analysis
E. Constraints
F. Cost-Volume-Profit Assumptions
G. Margin of Safety
A. Contribution Margin Concepts
Sales – Variable
Expenses =
Contribution Margin
Contributes toward
covering fixed
expenses and then
toward providing a
profit.
May be computed
per unit or in total
(see page 235).
Contribution margin
ratio is the
contribution margin
divided by sales (see
page 240)
B. The Profit Equation
Total
Variable
+
Sales =
costs
Unit selling
x=
price
Fixed
costs
Target pretax
+
profit
Unit variable
Fixed
Target pretax
x + costs +
cost
profit
Note: x = Number of units sold
Solve for x to determine units that must be sold to reach a certain
target pretax profit. Target pretax profit equals zero to compute
breakeven.
C. Contribution Margin Method
Unit Sales Needed to Reach a Target Pretax Profit
Fixed costs + Target pretax profit
Unit contribution margin
=
Target
units
Sales Dollars Needed to Reach a Target Pretax Profit
Fixed costs + Target pretax profit
Contribution margin ratio
=
Target
sales $
Target pretax profit equals zero to compute breakeven.
D. Multiproduct Analysis
Contribution Margin Approach (See
example on pages 127-128)
Contribution Margin Ratio Approach
(See example on pages 128-131)
E. Constraints
When there are constraints on how many
items can be provided, the focus shifts
from the contribution margin per unit to
the contribution margin per unit of
constraint. See illustration on page
135.
F. Cost-Volume-Profit
Assumptions
Selling price remains constant
Cost can be accurately separated into
fixed and variable components
Variable and fixed cost behavior
assumptions hold
Sales mix is constant
G. Margin of Safety
Actual unit sales
- Breakeven unit sales
= Margin of Safety in
Units
How much can
sales drop
before we
incur a loss?
Actual sales dollars
- Breakeven sales dollars
= Margin of Safety in
Dollars
V. Degree of Operating Leverage
Operating leverage is a measure of the
mix of variable and fixed costs in a firm.
Degree of
operating
leverage
=
Total contribution margin
Pretax profit
The degree of operating leverage can be used to predict the impact
on profit before tax of a given percentage increase in sales. For
example, if the degree of operating leverage is 2.5 and there is a
10% increase in sales, then pretax profit should increase by 25%.
VI. Excel and Regression
Analysis
An Illustration of
Regression Analysis
Using Microsoft
Excel
Dependent variable
Independent variable
Prediction
equation
Variable
Cost per
Unit
y = $3,998.25 + 2.09x
Fixed Cost
Number
of Units
Slope of regression line
$3,998.25
Fixed
Cost
Coefficient of Correlation
The multiple R (called the coefficient of correlation) is a
measure of the proximity of the data points to the regression
line. In addition, the sign of the statistic (+ or -) tells us the
direction of the correlation. In this case, there is a positive
correlation between the number of pizzas produced
(independent variable) and the total overhead costs
(dependent variable). A coefficient of correlation may range
from zero (no relationship, to 1 (perfect relationship).
A coefficient of correlation of 1 would indicate that
all data observations fall on the regression line.
Coefficient of Determination
The R Square (often represented R2 and called the coefficient
of determination) is a measure of goodness of fit (how well
the regression line “fits” the data). R2 can be interpreted as
the proportion of variation in the dependent variable
(overhead costs) that is explained by changes in the
dependent variable (the number of pizzas). The R2 may range
from zero to one. An R2 of less than one indicates that other
independent variable might have an impact on the dependent
variable.
Summary
Cost behavior
Separating mixed costs
The relevant range
Target net profit and breakeven analysis
Degree of operating leverage