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

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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.

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

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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