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Chapter 4 Cost-Volume-Profit Analysis

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Revenues

Costs

- Common Cost Behavior Patterns
- Cost Estimation Methods
- The Relevant Range
- Cost-Volume Profit Analysis
- Degree of Operating Leverage
- Excel and Regression Analysis

- Variable Costs
- Fixed Costs
- Discretionary versus Committed Fixed Costs
- Mixed Costs
- Step 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

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

Committed Fixed Costs

Examples include rent, depreciation, insurance. Two key factors are:

Long term in nature

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).

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

$

Total cost line

Variable component

Fixed component

Level of Activity

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

- High-Low Method
- The Variable Cost Element
- The Fixed Cost Element

- Scattergraphs
- Outliers

- Regression Analysis

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.

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)

Variable cost per unit

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

Number of units of activity

y = a + b x

Total cost

Fixed cost

See Illustration on Page 120

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.

Outliers are abnormal or nonrepresentative observations within a data set that may be inadvertently used in the application of the high-low method.

- 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.

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

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.

- The Relevant Range and Total Variable Cost
- The Relevant Range and Total Fixed 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

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

$

Total fixed cost

Relevant range

Level of Activity

- Contribution Margin Concepts
- The Profit Equation
- Contribution Margin Method
- Multiproduct Analysis
- Constraints
- Cost-Volume-Profit Assumptions
- Margin of Safety

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)

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.

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.

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

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.

- 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

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

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

y = $3,998.25 + 2.09x

Prediction equation

Variable Cost per Unit

Number of Units

Fixed Cost

Slope of regression line

Fixed Cost

$3,998.25

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.

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