Cost Behavior: Analysis and Use

UAA – ACCT 202 Principles of Managerial Accounting Dr. Fred Barbee

$

Volume (Activity Base)

As the volume of activity goes up

How does the cost react?

Why do I need to know this

information?

Good question. Here are some examples of

when you would want to

know this.

$

Volume (Activity Base)

For decision making purposes, it’s important for a manager to know the cost behavior pattern and the relative proportion of each cost.

Knowledge of Cost Behavior

Setting Sales Prices

Entering new markets

Introducing new products

Buying/Replacing Equipment

Make-or-Buy decisions

Total Variable Costs

$

Volume (Activity Base)

Per Unit Variable Costs

$

Volume (Activity Base)

Variable Costs - Example

A company manufacturers microwave ovens. Each oven requires a timing device that costs $30. The per unit and total cost of the timing device at various levels of activity would be:# of Units Cost/Unit Total Cost

1 $30 $3010 30 300

100 30 3,000200 30 6,000

Linearity is assumed

Variable Costs

The equation for total VC:

TVC = VC x Activity Base

Thus, a 50% increase in volume results in a 50% increase in total VC.

Step-Variable Costs

But differentbetween rangesof activity

$

Volume (Activity Base)

Step Costs are constant withina range of activity.

Total Fixed Costs

$

Volume (Activity Base)

$

Volume (Activity Base)

Per-Unit Fixed Costs

Fixed Costs - Example

A company manufacturers microwave ovens. The company pays $9,000 per month for rental of its factory building. The total and per unit cost of the rent at various levels of activity would be:

# of Units Monthly Cost Average Cost1 $9,000 $9,000

10 9,000 900100 9,000 90200 9,000 45

RelevantRange

Curvilinear Costs & the Relevant Range

$

Volume (Activity Base)

Accountant’s Straight-Line Approximation

Economist’s CurvilinearCost Function

Mixed Costs

$

Volume (Activity Base)

Variable costs

Fixed costs

Intercept Slope

This is probably how you learned this equation in

algebra.

Total Costs

VC Per Unit

(Slope)

Fixed Cost

(Intercept)

Level of Activity

Total Costs

VC Per Unit

(Slope)

Fixed Cost

(Intercept)

Level of Activity

Dependent Variable

Independent Variable

20

• Account Analysis

• Engineering Approach

• High-Low Method

• Scattergraph Plot

• Regression Analysis

Methods of Analysis

Account Analysis

Each account is classified as either – variable or – fixed

based on the analyst’s prior knowledge of how the cost in the account behaves.

Engineering Approach

Detailed analysis of cost behavior based on an industrial engineer’s evaluation of required inputs for various activities and the cost of those inputs.

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

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Activity, 1,000’s of Units Produced

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The Scattergraph Method

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Quick-and-Dirty Method

Intercept is the estimated fixed cost = $10,000

Draw a line through the data points with about anequal numbers of points above and below the line.

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Activity, 1,000’s of Units Produced

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Quick-and-Dirty MethodThe slope is the estimated variable cost per unit.

Slope = Change in cost ÷ Change in units

Vertical distance is the change in cost.

Horizontal distance is

the change in activity.

Advantages

• One of the principal advantages of this method is that it lets us “see” the data.

• What are the advantages of “seeing” the data?

Nonlinear Relationship

ActivityCost

0 Activity Output

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* **

Upward Shift in Cost Relationship

ActivityCost

0 Activity Output

* * *

***

Presence of Outliers

ActivityCost

0 Activity Output

* * *

*

* *

Month Activity Level: Patient Days

Maintenance Cost Incurred

January 5,600 $7,900February 7,100 8,500March 5,000 7,400April 6,500 8,200May 7,300 9,100June 8,000 9,800July 6,200 7,800

Brentline Hospital Patient Data

Textbook Example

Brentline Hospital Patient Data

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Patient-Days

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Brentline Hospital Patient Data

y = 0.7589x + 3430.90

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Brentline Hospital Patient Data

y = 0.7589x + 3430.90

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Brentline Hospital Patient Data

y = 0.7589x + 3430.9R2 = 0.8964

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From Algebra . . .

• If we know any two points on a line, we can determine the slope of that line.

High-Low Method

• A non-statistical method whereby we examine two points out of a set of data . . .

–The high point; and

–The low point

High-Low Method

• Using these two points, we determine the equation for that line . . .

–The intercept; and

–The Slope parameters

High-Low Method

• To get the variable costs . . .

–We compare the difference in costs between the two periods to

–The difference in activity between the two periods.

Month Activity Level: Patient Days

Maintenance Cost Incurred

January 5,600 $7,900February 7,100 8,500March 5,000 7,400April 6,500 8,200May 7,300 9,100June 8,000 9,800July 6,200 7,800

Brentline Hospital Patient Data

Textbook Example

High/ Low Month Patient

DaysMaint. Cost

High June 8,000 $9,800

Low March 5,000 7,400

Difference 3,000 $2,400

Change in Cost V = ------------------ Change in Activity

(Y2 - Y1) V = ------------ (X2 - X1)

High/ Low Month Patient

DaysMaint. Cost

High June 8,000 $9,800

Low March 5,000 7,400

Difference 3,000 $2,400

The Change in Cost

Divided by the change in activity

Change in Cost V = ------------------ Change in Activity

$2,400 V = ------------ 3,000

= $0.80 Per Unit

Total Cost (TC) = FC + VC- FC = - TC + VC

FC = TC - VC

FC = $9,800 - (8,000 x $0.80) = $3,400

FC = $7,400 - (5,000 x $0.80) = $3,400

TC = $3,400 + $0.80X

Month Activity Level: Patient Days

Maintenance Cost Incurred

January 5,600 $7,900February 7,100 8,500March 5,000 7,400April 6,500 8,200May 7,300 9,100June 8,000 9,800July 6,200 7,800

We have taken “Total Costs” which is a mixed cost and

we have separated it into its VC and FC

components.

So what? You say! Thank you for asking! Now I can use this formula for planning purposes. For example, what if I believe my activity level will be 6,325 patient days in February. What would I expect my total maintenance cost to be?

What is the estimated total cost if the activity level for February is expected to be 6,325 patient days?

Y = a + bxTC = $3,400 + 6,325 x $0.80

TC = $8,460

Some Important Considerations

• We have used historical cost to arrive at the cost equation.

• Therefore, we have to be careful in how we use the formula.

• Never forget the relevant range.

Relevant Range

$

Volume (Activity Base)

Strengths of High-Low Method

• Simple to use

• Easy to understand

Weaknesses of High-Low

• Only two data points are used in the analysis.

• Can be problematic if either (or both) high or low are extreme (i.e., Outliers).

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. ... .. .. ..

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Extreme values - not necessarily representative

Representative High/Low Values

.

Weaknesses of High-Low

• Other months may not yield the same formula.

FC = $8,500 - (7,100 x $0.80) = $2,820

FC = $7,800 - (6,200 x $0.80) = $2,840

Regression Analysis

• A statistical technique used to separate mixed costs into fixed and variable components.

• All observations are used to fit a regression line which represents the average of all data points.

Regression Analysis

• Requires the simultaneous solution of two linear equations

• So that the squared deviations from the regression line of each of the plotted points cancel out (are equal to zero).

Production

Cost

Actual Y

Estimated yError

2)( yY

The objective is to find values of a and b in the equation y = a + bX that minimize

y = a + bX

The equation for a linear function (straight line) with one independent variable is . . .

Where:

y = The Dependent Variable a = The Constant term (Intercept)

b = The Slope of the line X = The Independent variable

y = a + bX

The equation for a linear function (straight line) with one independent variable is . . .

Where:

y = The Dependent Variable a = The Constant term (Intercept)

b = The Slope of the line X = The Independent variable

The Dependent Variable

The Independent

Variable

Regression Analysis

• With this equation and given a set of data.

• Two simultaneous linear equations can be developed that will fit a regression line to the data.

Where: a = Fixed cost b = Variable cost n = Number of observations X = Activity measure (Hours, etc.) Y = Total cost

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xbnay

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YXXnXYXXYa

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2 XXXnYXXYnb

Fixed Costs

Variable Costs

R2, the Coefficient of Determination is the percentage of variability in the

dependent variable being explained by the independent variable.

This is referred to as a “goodness of fit” measure.

R, the Coefficient of Correlation is square root of R2. Can range from -1 to +1. Positive correlation means the

variables move together. Negative correlation means they move in

opposite directions.

Method Fixed Cost

Variable Cost

High-Low

Scattergraph

Regression

$3,400

$3,300

$3,431

$0.80

$0.79

$0.76

Coefficient of Determination

• R2 is the percentage of variability in the dependent variable that is explained by the independent variable.

Coefficient of Determination

• This is a measure of goodness-of-fit.

• The higher the R2, the better the fit.

Coefficient of Determination

• The higher the R2, the more variation (in the dependent variable) being explained by the independent variable.

Coefficient of Determination

• R2 ranges from 0 to 1.0• Good Vs. Bad R2s is relative.• There is no magic cutoff

Coefficient of Correlation

• The relationship between two variables can be described by a correlation coefficient.

• The coefficient of correlation is the square root of the coefficient of determination.

Coefficient of Correlation

• Provides a measure of strength of association between two variables.

• The correlation provides an index of how closely two variables “go together.”

Machine Hours

Utility Costs

Machine Hours

Utility Costs

Hours of Safety

Training

Industrial Accidents

Industrial Accidents

Hours of Safety

Training

Hair Length

202 Grade

Hair Length

202 Grade