Chapter 4 Cost-Volume-Profit Analysis

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Chapter 4Cost-Volume-Profit Analysis
Revenues
Costs
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Presentation Outline

1. Common Cost Behavior Patterns
2. Cost Estimation Methods
3. The Relevant Range
4. Cost-Volume Profit Analysis
5. Degree of Operating Leverage
6. Excel and Regression Analysis

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I. Common Cost Behavior Patterns

1. Variable Costs
2. Fixed Costs
3. Discretionary versus Committed Fixed Costs
4. Mixed Costs
5. Step Costs

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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
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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
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C. Discretionary versus Committed Fixed Costs

• Committed Fixed Costs
• Examples include rent, depreciation, insurance.
  Two key factors are
• Long term in nature
• Cant 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).

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D. Mixed Cost

• A mixed cost has both a variable and a fixed
  component.

Total cost line
Variable component
Fixed component
Level of Activity
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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
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II. Cost Estimation Methods

• High-Low Method
• The Variable Cost Element
• The Fixed Cost Element
• Scattergraphs
• Outliers
• Regression Analysis

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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.

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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)
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2. The Fixed Cost Element
Variable cost per unit
Number of units of activity
y a b x

• The fixed portion of a mixed cost is found by
  subtracting total variable cost from total cost
  (high or low level).

Total cost
Fixed cost
See Illustration on Page 120
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B. Scattergraph

• 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.

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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.

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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.

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1. Illustration Using Microsoft Excel
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2. Simple Regression v. Multiple Regression

• Simple Regression
• Only one independent variable is used to predict
  the dependent variable.
• y a b x

• Multiple Regression
• Two or more independent variables are used to
  predict the dependent variable.
• y a b1x1 b2x2

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III. The Relevant Range

• The assumed range of activity is referred to a
  the relevant range, which reflects the companys
  normal operating range. The relevant range is
  the range over which cost behavior assumptions
  are valid.
• The Relevant Range and Total Variable Cost
• The Relevant Range and Total Fixed Cost

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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.

Total variable cost
Relevant range
Level of Activity
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B. The Relevant Range and Total Fixed Cost

• Total fixed cost can behave in a step-cost manner
  when outside the relevant range..

Total fixed cost
Relevant range
Level of Activity
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IV. Cost-Volume-Profit Analysis

1. Contribution Margin Concepts
2. The Profit Equation
3. Contribution Margin Method
4. Multiproduct Analysis
5. Constraints
6. Cost-Volume-Profit Assumptions
7. Margin of Safety

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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)

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B. The Profit Equation
Total Sales
Variable costs
Fixed costs
Target pretax profit



or
Unit selling price
Unit variable cost
Fixed costs
Target pretax profit
x

x


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.
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C. Contribution Margin Method
Unit Sales Needed to Reach a Target Pretax Profit
Fixed costs Target pretax profit
Target units

Unit contribution margin
Sales Dollars Needed to Reach a Target Pretax
Profit
Fixed costs Target pretax profit
Target sales

Contribution margin ratio
Target pretax profit equals zero to compute
breakeven.
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D. Multiproduct Analysis

• Contribution Margin Approach (See example on
  pages 127-128)
• Contribution Margin Ratio Approach (See example
  on pages 128-131)

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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.

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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

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G. Margin of Safety
How much can sales drop before we incur a loss?

• Actual sales dollars
• - Breakeven sales dollars
• Margin of Safety in Dollars

Actual unit sales - Breakeven unit sales
Margin of Safety in Units
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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.
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VI. Excel and Regression Analysis
An Illustration of Regression Analysis Using
Microsoft Excel
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Dependent variable
Independent variable
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y 3,998.25 2.09x
Variable Cost per Unit
Prediction equation
Number of Units
Fixed Cost
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Slope of regression line
Fixed Cost
3,998.25
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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).
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A coefficient of correlation of 1 would indicate
that all data observations fall on the
regression line.
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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.
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Summary

• Cost behavior
• Separating mixed costs
• The relevant range
• Target net profit and breakeven analysis
• Degree of operating leverage