chapter 4 cost-volume-profit analysis
DESCRIPTION
Chapter 4 Cost-Volume-Profit Analysis. Revenues. Costs. Presentation Outline. Common Cost Behavior Patterns Cost Estimation Methods The Relevant Range Cost-Volume Profit Analysis Degree of Operating Leverage Excel and Regression Analysis. I. Common Cost Behavior Patterns. Variable Costs - PowerPoint PPT PresentationTRANSCRIPT
Chapter 4Cost-Volume-Profit Analysis
Revenues
Costs
Presentation OutlineI. Common Cost Behavior Patterns
II. Cost Estimation MethodsIII. The Relevant Range
IV. Cost-Volume Profit AnalysisV. Degree of Operating LeverageVI. Excel and Regression Analysis
I. Common Cost Behavior Patterns
A. Variable CostsB. Fixed Costs
C. Discretionary versus Committed Fixed Costs
D. Mixed CostsE. Step Costs
A. Variable CostsAlthough variable cost per unit remain constant, total variable cost increases
and decreases in proportion to changes in the activity level.
$
Level of Activity
Variable cost in total
B. Fixed Cost in TotalAlthough 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.$
Level of Activity
Total fixed cost
C. Discretionary versus Committed Fixed Costs
Committed Fixed CostsExamples include rent,
depreciation, insurance. Two key
factors are:1. Long term in nature2. 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 CostA mixed cost has both a variable and
a fixed component.
$
Level of Activity
Fixed component
Variable component
Total cost line
E. Step CostsStep 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 Method1. The Variable Cost Element
2. The Fixed Cost Element
B. Scattergraphs1. 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
Fixed Cost
Variable Cost
Total Cost Line$
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
The fixed portion of a mixed cost is found by
subtracting total variable cost from total cost (high or low level).
y = a + b x
Total cost Fixed cost
Variable cost per unit
Number of units of activity
See Illustration on Page 120
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.
Scattergraph
050
100150200250
- 50 100 150
Number of Shipments Received
Co
st
of
Re
ce
ivin
g
Re
po
rt
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 AnalysisRegression 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
Least Squares Regression
y = 1.2369x + 54.657
050
100150200250
- 50 100 150
Number of Shipments Received
Cos
t of R
ecei
ving
R
epor
t
2. Simple Regression v. Multiple Regression
Simple RegressionOnly one
independent variable is used to predict the
dependent variable.
y = a + b x
Multiple RegressionTwo 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.
$
Level of Activity
Total variable cost
Relevant range
B. The Relevant Range and Total Fixed Cost
Total fixed cost can behave in a step-cost manner when outside the relevant range..
$
Level of Activity
Total fixed costRelevant
range
IV. Cost-Volume-Profit Analysis
A. Contribution Margin ConceptsB. The Profit Equation
C. Contribution Margin MethodD. Multiproduct Analysis
E. ConstraintsF. Cost-Volume-Profit Assumptions
G. Margin of Safety
A. Contribution Margin Concepts
Sales – Variable Expenses = Contribution MarginContributes 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 EquationTotal Sales =
Variable costs +
Fixed costs +
Target pretax profit
Unit selling price x =
Unit variable cost x +
Fixed costs +
Target pretax 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 MethodUnit 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 componentsVariable and fixed cost behavior
assumptions holdSales mix is constant
G. Margin of Safety
Actual sales dollars- Breakeven sales
dollars= Margin of Safety in
Dollars
How much can sales drop before we
incur a loss?
Actual unit sales- Breakeven unit sales= Margin of Safety in
Units
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 impacton profit before tax of a given percentage increase in sales. Forexample, if the degree of operating leverage is 2.5 and there is a
10% increase in sales, then pretax profit should increase by 25%.
An Illustration of Regression Analysis
Using Microsoft Excel
VI. Excel and Regression Analysis
Dependent variable
Independent variable
y = $3,998.25 + 2.09x
Fixed Cost
Variable Cost per
Unit
Number of Units
Prediction equation
$3,998.25
Fixed Cost
Slope of regression line
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 behaviorSeparating mixed costs
The relevant rangeTarget net profit and breakeven
analysisDegree of operating leverage