Cost Behavior: Analysis and Use

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```					ACC 202 Intro to
Management Accounting
Chapter 5: Cost Behavior: Analysis and Use

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Homework Info
 Exercise

#5-11 (2)

–“quick and dirty” method means make a scattergraph

Learning Objectives
Behavior: variable, step, curvilinear, fixed, and mixed  Committed & Discretionary Fixed Costs  Analysis of Mixed Costs using a scattergraph & high-low method  Contribution Format Income Statement
 Cost

Cost Behavior
Structure – relative proportion of types of costs in an organization  Variable Costs – vary relative to something, which is called the “Activity Base”  Relevant Range – range of activity within which assumptions made about cost behavior are valid
 Cost

Types of Cost Behavior Patterns
Summary of cost behavior from chapter 2.
Summary of Variable and Fixed Cost Behavior
Cost Variable In Total Total variable cost changes as the activity level changes. Total fixed cost remains the same even when the activity level changes within the relevant range. Per Unit Variable cost per unit remains the same over wide ranges of activity. Fixed cost per unit goes down as activity level goes up.

Fixed

The Activity Base
Units produce d A measure of what causes a variable cost to be incurred Miles driven Labor hours Machine hours

A Variable Cost:
Is a cost whose total dollar amount varies with changes in the activity level. Ex: your total long distance landline phone bill is based on how many minutes you talk.
Total Long Distance Landline Phone Bill
Minutes Talked

Types of Cost Behavior Patterns
Summary of cost behavior from chapter 2.
Summary of Variable and Fixed Cost Behavior
Cost Variable In Total Total variable cost changes as activity level changes. Total fixed cost remains the same even when the activity level changes within the relevant range. Per Unit Variable cost per unit remains the same over wide ranges of activity. Fixed cost per unit goes down as activity level goes up.

Fixed

Variable Cost Per Unit
A variable cost remains constant if expressed on a per unit basis. The cost per minute talked is constant. For example, 10 cents per minute.
Per Minute Telephone Charge Minutes Talked

Extent of Variable Costs
The proportion of variable costs differs across organizations. For example . . .
A public utility with large investments in equipment will tend to have fewer variable costs. A manufacturing company will often have many variable costs.

A service company will normally have a high proportion of variable costs.

A merchandising company usually will have a high proportion of variable costs like cost of sales.

Examples of Variable Costs
1. Merchandising companies – cost of goods sold.

2. Manufacturing companies – direct materials, direct labor, and variable overhead. 3. Merchandising and manufacturing companies – commissions, shipping costs, and clerical costs such as invoicing. 4. Service companies – supplies, travel, and clerical.

True Variable Cost
Direct materials is a true or proportionately variable cost because the amount used during a period will vary in direct proportion to the level of production activity.

Cost

Volume

True Variable Cost Example
Direct materials cost varies in direct proportion to the volume of units produced. So, each additional table produced, incurs an additional \$100 of direct materials cost.
Cost

Volume

Step-Variable Costs
A resource obtainable only in large chunks (such as maintenance workers) whose costs increase or decrease only in response to fairly wide changes in activity is known as a step-variable cost.

Cost

Volume

Step-Variable Costs
Small changes in the level of production are not likely to have any effect on the number of maintenance workers employed.

Cost

Volume

Step-Variable Costs
Only fairly wide changes in the activity level will cause a change in the number of maintenance workers employed

Cost

Volume

The Linearity Assumption & the Relevant Range
A straight line Economist’s closely Curvilinear Cost approximates a Function curvilinear

Total Cost

Relevant Range

variable cost line within the relevant range.

Accountant’s Straight-Line Approximation (constant unit variable cost) Activity

Types of Cost Behavior Patterns
Summary of cost behavior from chapter 2.
Summary of Variable and Fixed Cost Behavior
Cost Variable In Total Total variable cost changes as activity level changes. Total fixed cost remains the same even when the activity level changes. Per Unit Variable cost per unit remains the same over wide ranges of activity.

Fixed

A Fixed Cost:
Is a cost whose total dollar amount remains constant as the activity level changes. Ex: Your monthly basic landline phone bill is probably fixed & doesn’t change when you make more local calls.
Monthly Basic Landline Phone Bill Number of Local Calls

Types of Cost Behavior Patterns
Summary of cost behavior from chapter 2.
Summary of Variable and Fixed Cost Behavior
Cost Variable In Total Total variable cost changes as activity level changes. Total fixed cost remains the same even when the activity level changes. Per Unit Variable cost per unit remains the same over wide ranges of activity. Average fixed cost per unit goes down as activity level goes up.

Fixed

Fixed Cost Per Unit
Average fixed costs per unit decrease as the activity level increases. The fixed cost per local call decreases as more local calls are made.
Monthly Basic phone Bill per Local Call Number of Local Calls

Types of Fixed Costs
Committed
Long-term & cannot be significantly reduced in the short term.

Discretionary
Can be altered in the short-term by current managerial decisions

Examples
Depreciation on Equipment & Real Estate Taxes

Examples

The Trend Toward Fixed Costs
The trend in many industries is toward greater fixed costs relative to variable costs.
Machines now perform many mundane tasks previously done by human beings. “Knowledge workers” are in demand for their minds rather than their muscles Knowledge workers tend to be salaried, highly-trained & difficult to replace. The cost to compensate these valued employees is relatively fixed rather than variable.

Is Labor a Variable or a Fixed Cost?
The behavior of wage and salary costs can differ across countries, depending on labor regulations, labor contracts, and custom.
In France, Germany, China, and Japan management has little flexibility in adjusting the size of the labor force. Labor costs are more fixed in nature. In the United States and the United Kingdom management has greater latitude. Labor costs are more variable in nature.

Fixed Costs & Relevant Range
The relevant range of activity for a fixed cost is the range of activity over which the graph of the cost is flat.
Example: Insurance on office space is available at a rate of \$10,000 per year in increments of 1,000 square feet. As the business grows and more space is needed, the total cost of insurance increases.

Fixed Costs & Relevant Range
Insurance Cost in Thousands of Dollars

30
Relevant Range
Total cost doesn’t change for a wide range of activity, and then jumps to a new higher cost for the next higher range of activity.

20

10 0

0

1,000 2,000 3,000 Office Area in Square Feet

Fixed Costs and Relevant Range

How does this type of fixed cost differ from a stepvariable cost?

Step-variable costs can be adjusted more quickly and . . . The width of the activity steps is much wider for the fixed cost.

Mixed Costs
A mixed cost has both fixed and variable components. Consider the example of utility cost.
Y Total Utility Cost

Variable Cost per KW

X
Activity (Kilowatt Hours)

Fixed Monthly
Utility Charge

Mixed Costs
fixed portion of a mixed cost is the minimum cost of having a service ready and available for use.  The variable portion is the cost incurred for actual consumption of the service, and varies in proportion to the amount of service consumed.
 The

Mixed Cost Equation
Y = a + bX
= total mixed cost  a = total fixed cost  b = variable cost per unit of activity  X = level of activity
Y

TC = FC + VC p/u (volume)

Mixed Costs
The total mixed cost line can be expressed as an equation: Y = a + bX Where: Y = the total mixed cost a = the total fixed cost (the vertical intercept of the line) b = the variable cost per unit of activity (the slope of the line) X = the level of activity

Y Total Utility Cost

Variable Cost per KW

X
Activity (Kilowatt Hours)

Fixed Monthly
Utility Charge

Mixed Costs Question
If your fixed monthly utility charge is \$40, your variable cost is \$0.03 per kilowatt hour, and your monthly activity level is 2,000 kilowatt hours, what is the amount of your utility bill?

Analysis of Mixed Costs
Gather and analyze past cost and activity data to estimate variable and fixed cost elements.
Account Analysis Method Each account is classified as either variable or fixed based on the analyst’s knowledge of how the account behaves.

Engineering Method Cost estimates are based on an evaluation of production methods, and material, labor and overhead requirements.

Analysis of Mixed Costs
past cost and activity data.  Plot the data on a scattergraph to test for linearity.  Cost behavior is linear when a straight line can approximately pass through the cost and activity data points.  Estimate the variable and fixed cost elements using the scattergragh, highlow, or least squares regression methods.
 Gather

The Scattergraph Method
Y
Maintenance Cost 1,000’s of Dollars

Step 1: Plot the data points on a graph (total cost vs. activity).

20

10

* * * *
0 1 2

* ** * **
X

0

3

4

Patient-days in 1,000’s

The Scattergraph Method
Step 2: Draw a line through the data points with about an equal numbers of points above and below the line. Y
Maintenance Cost 1,000’s of Dollars

20

10

* * * *
0 1 2

* ** * **
X

0

3

4

Patient-days in 1,000’s

The Scattergraph Method
Step 3: Use one data point to estimate the total level of activity and the total cost.

Maintenance Cost 1,000’s of Dollars

Y Total maintenance cost = \$11,000 20

10

* * * *
0 1 2

* ** * **
X

Intercept = Fixed cost: \$10,000

0

3

4

Patient-days in 1,000’s Patient days = 800

The Scattergraph Method
Step 4: Make a “quick & dirty” estimate of variable cost per unit and determine the cost equation.
Total maintenance at 800 patients Less: Fixed cost Estimated total variable cost for 800 patients \$ 11,000 10,000 \$ 1,000

Variable cost per unit =

\$1,000 800

= \$1.25/patient-day

Y = \$10,000 + \$1.25(X)
Total maintenance cost Number of patient days

The High-Low Method
Assume the following hours of maintenance work and the total maintenance costs for six months.

High – Low Method
scattergraph shows linearity:  Select highest and lowest activity points (not the highest and lowest cost points)  Calculate the variable cost per unit:
high cost – low cost high activity – low activity
 Calculate  Use  Assuming

total fixed cost using either pt:

total cost – total variable cost

this cost equation to predict the mixed cost.

The High-Low Method
The variable cost per hour of maintenance is equal to the change in cost divided by the change in hours. \$2,400 = \$8.00/hour 300

The High-Low Method

Total Fixed Cost = Total Cost – Total Variable Cost
Total Fixed Cost = \$9,800 – (\$8/hour × 800 hours)

Total Fixed Cost = \$9,800 – \$6,400
Total Fixed Cost = \$3,400

The High-Low Method

The Cost Equation for Maintenance

TC = \$3,400 + \$8.00(X)

Least-Squares Regression Method
A method used to analyze mixed costs if a scattergraph plot reveals an approximately linear relationship between the X and Y variables.
This method uses all of the data points to estimate the fixed and variable cost components of a mixed cost.

The goal of this method is to fit a straight line to the data that minimizes the sum of the squared errors.

Comparing Results From the Three Methods
The three methods just discussed provide slightly different estimates of the fixed and variable cost components of the mixed cost. This is to be expected because each method uses differing amounts of the data points to provide estimates. Least-squares regression provides the most accurate estimate because it uses all the data points.

The Contribution Format
Sales Revenue Less: Variable costs Contribution margin Less: Fixed costs Net operating income Total \$ 100,000 60,000 \$ 40,000 30,000 \$ 10,000 Per Unit \$ 50 30 \$ 20

The contribution margin format emphasizes cost behavior. Contribution margin (CM) covers fixed costs and provides for income.

Uses of the Contribution Format
The contribution income statement format is used as an internal planning and decision making tool. We will use this approach for: 1. Cost-volume-profit analysis (Chapter 6).

2. Budgeting (Chapter 9).
3. Segmented reporting of profit data (Chapter 12). 4. Special decisions such as pricing and make-orbuy analysis (Chapter 13).

The Contribution Format

Used primarily for external reporting.

Used primarily by management.

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