Chapter 5

Cost Behavior PowerPoint Authors: Susan Coomer Galbreath, Ph.D., CPA Charles W. Caldwell, D.B.A., CMA Jon A. Booker, Ph.D., CPA, CIA Cynthia J. Rooney, Ph.D., CPA

McGraw-Hill/Irwin Copyright © 2014 by The McGraw-Hill Companies, Inc. All rights reserved.

Cost Behavior Patterns

Cost behavior describes the way total cost behaves, or changes, when some measure of activity changes.

The range of activity within which assumptions about cost behavior hold true is the relevant range . Unit variable costs remain unchanged.

Total fixed costs remain unchanged.

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Learning Objective 5-1

Identify costs as variable, fixed, step, or mixed.

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Variable Costs

Total variable costs increase as activity increases.

Variable cost per unit is constant as activity increases.

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Fixed Costs

Total fixed costs remain constant as activity increases.

Cost per cup declines as activity increases.

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Cost Behavior Summary

Cost Variable Fixed In Total Changes proportionately with changes in activity within the relevant range.

Remains the same even when activity changes within the relevant range.

Per Unit Remains constant for each additional unit as long as activity is in the relevant range.

The per unit amount changes each time the level of activity changes due to the fixed nature of the related costs.

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Step Costs

Step-variable costs rise in multiple steps across the relevant range.

Step-fixed costs are fixed over a fairly wide range of activities.

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Mixed Costs

Mixed costs contain a fixed portion that is incurred even when the facility is unused, and a variable portion that increases with usage. Utilities typically behave in this manner.

Activity (Kilowatt Hours) Variable Cost per KW Fixed Monthly Utility Charge

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Mixed Costs

Total mixed costs increase as activity increases.

Per unit mixed costs decrease as activity increases.

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Linear Approaches to Analyzing Mixed Costs

y

= total cost, which is plotted on the vertical axis, and is called the dependent variable. a = total fixed cost, an amount that will be incurred regardless of the activity level, and is called the intercept or the constant. b = the slope of the line, the unit variable cost, which tells us how much the total cost (y) will increase for each unit increase in activity (x).

x = the activity that causes total cost (y) to change. Activity (x) is also called the cost driver, or the independent variable.

x a = Intercept = Activity 5- 11

Linear Approaches to Analyzing Mixed Costs There are three different methods to analyze mixed costs, all using the linear assumption as a base.

1.

Scattergraph:

A graph that provides a visual representation of the relationship between total cost (y) and activity level (x). A scattergraph is a useful first step in analyzing cost behavior because it helps determine the nature of the relationship and whether the linearity assumption is valid.

2.

High-low method:

A simple approach that uses the two most extreme data points to determine the slope of the line (variable cost per unit) and the intercept (total fixed cost).

3.

Least-squares regression:

A statistical technique for finding the best fitting line based on historical data. The slope of the line provides an estimate of the variable cost per unit, while the intercept provides an estimate of the total fixed cost.

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Learning Objective 5-2

Prepare a scattergraph to illustrate the relationship between total cost and activity.

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Scattergraph

A scattergraph is a graph with total cost plotted on the vertical (Y) axis and some measure of activity on the horizontal (X) axis. 5- 14

Preparing a Scattergraph

A scattergraph can be created by manually plotting data points on graph-paper, or by using a the following steps in Excel: 1. Enter the data in Excel, and highlight the data that you want to plot.

2. Select the Chart Wizard from the toolbar.

3. Select XY (Scatter) as the chart type. Be sure total cost is on the Y axis, with the activity driver on the X axis.

4. Add a chart title and labels for the X and Y axes.

To apply these steps, consider the following data showing the total overhead cost (Y) of running our hypothetical Starbucks location, along with the number of customers served (X).

January February March April May June Customers Served (X) 9,000 15,000 12,500 6,000 5,000 10,000 Total OH Cost (Y) $ 15,000 15,750 16,000 12,500 13,250 13,000

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Preparing a Scattergraph

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Learning Objective 5-3

Use the high-low method to analyze mixed costs.

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High-Low Method

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High-Low Method

Total Fixed Cost = Total Cost _ Variable Cost per Unit × Activity Total Fixed Cost February Estimate = $15,750 _ Total Fixed Cost = $12,000 $0.25 × 15,000 Total Fixed Cost = May Estimate $13,250 Total Fixed Cost = _ $12,000 $0.25 × 5,000 5- 19

High-Low Method

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Learning Objective 5-4

Use least-squares regression to analyze mixed costs.

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Least-Squares Regression Method

16 000 14 000 12 000 10 000 8 000 6 000 4 000 2 000

} Error

2 000 4 000 6 000 8 000 10 000

Customers Served

12 000 14 000 16 000 The goal of this method is to

minimize the sum of the squared errors

.

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Least-Squares Regression Method

 Software such as Excel can be used to fit a regression line through the data points.

 The cost analysis objective is the same: y = a + bx

The output from the regression analysis can be used to create an equation that enables you to estimate total costs at any activity level.

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Least-Squares Regression Method

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Least-Squares Regression Method

SUMMARY OUTPUT Multiple R

Regression Statistics

0.802489134

R Square Adjusted R Square Standard Error Observations 0.643988811

0.554986013

1011.697667

6 ANOVA R 2 tell us how closely we can explain the relationship between our two variables. In our example, the number of customers explains about 64% of the overhead costs.

Regression Residual Total Intercept Customers Served (X)

df

1 3 4

SS

7405871.321

4094128.679

11500000

Coefficients Standard Error

11180.90017 1213.424073

0.320253895

0.11905759

The intercept and x coefficient, respectively, are estimated total fixed cost and variable cost per unit.

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Least-Squares Regression Method

Total Cost = Total Fixed Cost + Total Variable Cost (Variable Cost per Unit × X) Using our regression output, if Starbucks expected to serve 8,000 customers in July, we would estimate total overhead costs as follows: $0.32 × 8,000 = $2,560 + $11,181 = $13,741 5- 26

Summary of Linear Methods

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Learning Objective 5-5

Prepare and interpret a contribution margin income statement.

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Contribution Margin Approach

Contribution margin is the difference between sales revenue and variable costs.

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Contribution Margin Ratio

Contribution Margin Formula Contribution Margin = Sales Revenue ‒ Variable Costs Contribution Margin Ratio Contribution Margin Ratio = Contribution Margin Sales Revenue 5- 30

Contribution Margin

Unit contribution margin Contribution margin ratio 5- 31

Contribution Margin

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Supplement 5A

Variable Versus Full Absorption Costing PowerPoint Authors: Susan Coomer Galbreath, Ph.D., CPA Charles W. Caldwell, D.B.A., CMA Jon A. Booker, Ph.D., CPA, CIA Cynthia J. Rooney, Ph.D., CPA

McGraw-Hill/Irwin Copyright © 2014 by The McGraw-Hill Companies, Inc. All rights reserved.

Learning Objective 5-S1

Compare variable costing to full absorption costing.

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Variable Versus Full Absorption Costing 5- 35

Reconciling Variable and Full Absorption Costing 5- 36

Full Absorption Costing Income Statement 5- 37

Variable Costing Income Statement

Variable costs only.

All fixed manufacturing overhead is expensed.

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Reconciling Variable and Full Absorption Costing Difference between Full Absorption and Variable Costing Income

=

Change in Units in Ending Inventory (Production ‒ Sales)

×

Fixed Manufacturing Overhead Cost per Unit $40,000

=

2,000 units

×

$20 per unit 5- 39

Effect of Changes in Inventory Under Full Absorption and Variable Costing 5- 40

End of Chapter 5

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