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### COST BEHAVIOR

Chapter 3

CHAPTER 3 Objectives

- Define and describe fixed, variable, and mixed costs
- Explain the use of resources and activities and their relationship to cost behavior
- Explain how several methods of cost estimation can be used
- Separate mixed costs into their fixed and variable components using the high-low method, the scatterplot method, and the method of least squares

CHAPTER 3 Objectives

- Evaluate the reliability of the cost formula
- Explain how multiple regression can be used to assess cost behavior
- Define the learning curve, and discuss its impact on cost behavior
- Discuss the use of managerial judgment in determining cost behavior

BASICS OF Cost Behavior

Cost Behavior

- The term used to describe whether a cost changes when the level of output changes
- Fixed costs do not change as output changes
- Variable costs increase in total with an increase in output and decrease in total with a decrease in output

LO-1

BASICS OF Cost Behavior

Cost Objects

- An item for which managers want cost information
- For manufacturing or merchandising firms, it is usually the tangible product
- For service firms, it is usually the service provided

LO-1

BASICS OF Cost Behavior

Measures of Output

- Activity drivers explain changes in activity costs by measuring changes in activity output (usage)
- The two general categories of activity drivers
- Unit-level drivers
- Non-unit-level drivers

LO-1

Basics of Cost Behavior

LO-1

Fixed costs are costs that in total are constant within the relevant range as the level of the activity driver varies

Fixed Costs

Basics of Cost Behavior

LO-1

JCM Audio Systems, Inc. produces speakers for home audio systems. One department produces voice coils. There are two production lines that can each make up to 100,000 voice coils per year. The production-line manager is paid $60,000 per year. For production up to 100,000 units only one manager is needed; above that (to 200,000 units) two managers are needed.

Fixed Costs

Basics of Cost Behavior

JCM Audio Systems, Inc.

The total cost of supervision remains the same within the relevant range, but the unit cost decreases as production increases.

LO-1

Fixed Costs

Basics of Cost Behavior

JCM Audio Systems, Inc.

The total cost of supervision remains the same within the relevant range, but the unit cost decreases as production increases

LO-1

Fixed Costs

Basics of Cost Behavior

LO-1

Variable costs are costs that in total vary in direct proportion to changes in an activity driver

The total cost of direct materials for each level of production varies, but the unit cost stays the same

Variable Costs

Basics of Cost Behavior

JCM Audio Systems, Inc.

The total cost of supervision remains the same within the relevant range, but the unit cost decreases as production increases.

LO-1

Variable Costs

BASICS OF COST BEHAVIOR

Y = Fixed cost + Total variable cost

Y = F + VX

where

Y = Total cost (Usually a mixed cost)

LO-1

Mixed costs are costs that has both a fixed and a variable component

Mixed Costs

BASICS OF COST BEHAVIOR

Y = $300,000 + $5X

Fixed - salaries

Variable - commission

LO-1

JCM’s sales costs are mixed. There are 10 sales representatives who each earn $30,000 plus receive a commission of $5 per speaker sold. This function can be represented by the following equation

Mixed Costs

BASICS OF COST BEHAVIOR

JCM Audio Systems, Inc.

Selling Cost Per Unit

Fixed Cost of Selling

Speakers Sold

Variable Cost of Selling

Total Cost

$300,000 $200,000 $ 500,000 40,000 $12.50

300,000 400,000 700,000 80,000 8.75

300,000 600,000 900,000 120,000 7.50

300,000 800,000 1,100,000 160,000 6.88

300,000 1,000,000 1,300,000 200,000 6.50

LO-1

Mixed Cost

Resources, Activities, and Cost Behavior

Resources

Economic elements that enable one to perform activities

When a firm acquires the resources needed to perform an activity, it obtains activity capacity

Practical capacity is the activity level where the activity is performed efficiently

LO-2

Resources, Activities, and Cost Behavior

Flexible Resources

Supplied as needed and used

Quantity of resource supplied equals quantity demanded

No unused capacity

LO-2

Resources, Activities, and Cost Behavior

Committed Resources

Supplied in advance of usage

A given quantity is obtained, whether or not that full amount is used

- Unused capacity is possible

LO-2

Resources, Activities, and Cost Behavior

LO-2

A step cost function displays a constant level of cost for a range of output and then jumps to a higher level of cost at some point

Step-Cost Behavior

Resources, Activities, and Cost Behavior

LO-2

Step-variable Costs

Follow a step-cost behavior with narrow steps

Step-fixed Costs

Follow a step-cost function

Exceed the relevant range, and the costs increase “one step”

Step-Cost Behavior

Resources, Activities, and Cost Behavior

Activities and Mixed Cost Behavior

Many activities have characteristics of both flexible and committed resources

- For example, a power department acquires long-term capacity for supplying power by investing in a building and equipment
- It also acquires fuel to produce power on an as-needed basis

LO-2

Resources, Activities, and Cost Behavior

Need for Cost Separation

Sometimes it is easy to spot the variable and fixed portion of a cost

- Other times it is not; thus there is a need for a method to separate costs into their fixed and variable components

LO-2

Methods of Determining Cost Behavior

The Industrial Engineering Method

A forward-looking method of determining, through physical observation and analysis, just what activities, in what amounts, are needed to complete a process

The Account Analysis Method

Used to estimate costs by classifying accounts in the general ledger as fixed, variable, or mixed

LO-3

Quantitative Methods for Separating MIXED COSTS INTO FIXED AND VARIABLE COMPONENTS

LO-4

Y = F + VX

where

Y = Total cost (the dependent variable)

F = Fixed cost (the intercept parameter)

V = Variable cost per unit (the slope parameter)

X = Measure of output (the independent variable)

Quantitative Methods for Separating MIXED COSTS INTO FIXED AND VARIABLE COMPONENTS

LO-4

Take two points (the high and the low by volume of activity) and determine the slope and intercept

- Slope is variable rate
- Intercept is fixed cost

The High-Low Method

Quantitative Methods for Separating MIXED COSTS INTO FIXED AND VARIABLE COMPONENTS

LO-4

Advantages

- It is objective
- It is simple to calculate

Disadvantages

- The high and low points may be “outliers”
- Other pairs of points may clearly be more representative

The High-Low Method

Quantitative Methods for Separating MIXED COSTS INTO FIXED AND VARIABLE COMPONENTS

LO-4

Uses a scattergraph to visually assess the relationship between cost and output

- Intercept is fixed cost
- Slope is variable rate

Scatterplot Method

Quantitative Methods for Separating MIXED COSTS INTO FIXED AND VARIABLE COMPONENTS

LO-4

Advantages

Allows for visual inspection of the data

Identifies nonlinearity, outliers, and shifts in the cost relationship

Disadvantages

It is subjective

Scatterplot Method

EXHIBIT 3.8—Scattergraph for Anderson Company’s Materials Handling Costs

LO-4

EXHIBIT 3.8—Scattergraph for Anderson Company’s Materials Handling Costs (CONTINUED)

LO-4

EXHIBIT 3.8—Scattergraph for Anderson Company’s Materials Handling Costs (CONTINUED)

LO-4

EXHIBIT 3.9—Scattergraph for VARIOUS COST BEHAVIOR PATTERNS

LO-4

EXHIBIT 3.9—Scattergraph for VARIOUS COST BEHAVIOR PATTERNS (CONTINUED)

LO-4

EXHIBIT 3.9—Scattergraph for VARIOUS COST BEHAVIOR PATTERNS (CONTINUED)

LO-4

EXHIBIT 3.11—Spreadsheet Data for Anderson Company’s Materials Handling Cost

LO-4

Quantitative Methods for Separating MIXED COSTS INTO FIXED AND VARIABLE COMPONENTS

Using Regression Programs

- Enter the data
- Choose the “Tools” menu
- Choose the “Data Analysis” option
- If this is not available, you may have to manage add-ins
- Scroll down to “Regression”
- Click on “Input Y Range” and highlight the cost cells
- Click on “Input X Range” and highlight the driver cells
- Choose your preferred location for output
- Click ok

LO-4

EXHIBIT-3.12— Regression Results for Anderson Company’s Materials Handling Cost

LO-4

Quantitative Methods for Separating MIXED COSTS INTO FIXED AND VARIABLE COMPONENTS

Using Regression Programs

Interpreting the results

- Under “coefficients” in the bottom left of the output find the intercept and the slope
- Write the equation
- Y = $12.39X + $854.50
- Use the equation to make a point estimate
- At a point of 350 moves, total cost is predicted
- Y = $12.39(350) + $854.50
- Y = $4,336.50

LO-4

Reliability of Cost Formulas

Three statistical assessments concerning the cost formula’s reliability

- Hypothesis test of cost parameters
- Goodness of fit
- Confidence intervals

LO-5

Reliability of Cost Formulas

Hypothesis Test of Cost Parameters

- The “t Stat” tests the hypothesis that the parameters are different from zero
- The “P-value” is the level of significance achieved
- Generally, a P-value of 0.05 or less is needed for significance

LO-5

Reliability of Cost Formulas

Goodness of Fit Measures

The coefficient of determination, or R2, shows the percentage of variability in the dependent variable explained by the independent variable

Since R2 is the percentage of variability explained, it always has a value between 0 and 1.00

Typically, the Adjusted R Square is used because this value has been adjusted for the number of variables included in the equation

LO-5

Reliability of Cost Formulas

Coefficient of Correlation

It is the square root of the coefficient of determination when there is one independent variable

Range between −1 and +1

The higher the magnitude, the greater the correlation

A coefficient of correlation value close to zero indicates no correlation

LO-5

Reliability of Cost Formulas

LO-5

Confidence Intervals

Yf ± tSe

- This is the formula for calculating the desired level of confidence
- Yf is the predicted cost for a given level of activity
- t is the t distribution (get this from the table in your book
- Se is the standard error shown in the regression output

Multiple Regression

Whenever least squares is used to fit an equation involving two or more independent variables, the method is called multiple regression

In the case of two explanatory variables, the linear equation is expanded to include the additional variable

Y = F + V1X1 + V2X2

where

X1 = Number of moves

X2 = Number of pounds moved

LO-6

Multiple Regression

Adding another independent variable might increase the explanatory power of our model

Performing the regression is very similar to simple regression

- Input the data – make sure the two independent variables are side by side.
- Follow the same directions, but select both independent variable columns for the “input X range”

LO-6

EXHIBIT 3.15—Multiple Regression Results for Anderson Company’s Materials Handling Cost

LO-6

Multiple Regression

Interpreting the results

- Under “coefficients” in the bottom left of the output find the intercept and the slope
- Write the equation
- Y = $507.31 + $7.84X1 + $0.11X2

Examine reliability of the new model

- Adjusted R2 is 99% - a significant improvement
- The p-values are all very good as well
- the t statistic drops to 7 degrees of freedom because another independent variable is used

LO-6

The Learning Curve and Nonlinear Cost Behavior

The learning curve shows how labor hours per unit decreases as units produced increases

The experience curve relates cost to increased efficiency – the more you perform a task the lower the cost is of doing it

LO-7

The Learning Curve and Nonlinear Cost Behavior

Cumulative Average-Time Learning Curve

States that the cumulative average time per unit decreases by a constant percentage

The learning rate is expressed as a percent

LO-7

The Learning Curve and Nonlinear Cost Behavior

Incremental Unit-Time Learning Curve

The incremental unit-time learning curve model decreases by a constant percentage each time the cumulative quantity of units produced doubles

LO-7

EXHIBIT 3.16—Spreadsheet for Cumulative Average-Time Learning Model

LO-7

EXHIBIT 3.17—Graph of Cumulative Total Hours Required and the Cumulative Average Time per Unit

LO-7

MANAGERIAL JUDGMENT

The most widely used method in practice

Managers may just use their experiences and observations to determine fixed and variable costs

Managers may identify mixed costs and use experience to determine what part is fixed – thus denoting the rest as variable

LO-8

MANAGERIAL JUDGMENT

This is a simple method and can yield good results when the manager has a good understanding of the processes

- However poor judgment yields poor results

LO-8

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