2009 Foster School of Business Cost Accounting L.DuCharme 1 Determining How Costs Behave Chapter 10.

2009 Foster School of Business Cost Accounting L.DuCharme 1

Determining HowCosts Behave

Chapter 10


Overview

1) Assumptions2) Model: Y = a + bX3) Determinates of Fixed vs. Variable costs4) Cost Estimation

Industrial EngineeringConference MethodAccount AnalysisQuantitative Analysis: H-L & OLS

5) Non-linear cost functions


Two assumptions frequently used in cost-behavior estimation

1. Changes in total costs can be explained bychanges in the level of a single activity.

2. Cost behavior can adequately be approximated by a linear function of the activity level within the relevant range.


Cost Function

What is a cost function?

It is a mathematical expressiondescribing how costs change

with changes in the levelof an activity.


Cost Function—variable cost

La Playa Hotel offers an airlinethree alternative cost structures toaccommodate its crew overnight:

1. $60 per night per room usage

y = $60x

The slope of the cost function is $60.


Cost Function

$0

$5,000

$10,000

$15,000

$20,000

0 100 200 300

x = Number of rooms

y =

Cos

t


Cost Function—fixed cost

2. $8,000 per month

y = $8,000

$8,000 is called a constant or intercept.

The slope of the cost function is zero.


Cost Function

$0

$5,000

$10,000

$15,000

$20,000

0 100 200 300

x = Number of rooms

y =

Cos

t


Cost Function—mixed cost

3. $3,000 per month plus $24 per room

This is an example of a mixed cost.

y = $3,000 + $24x

y = a + bx


Cost Function

$0

$5,000

$10,000

$15,000

$20,000

0 100 200 300

x = Number of rooms

y =

Cos

t


Cost Classificationand Estimation Function

Choice of cost object

Time span

Relevant range


Choice of Cost Object Example

If the total cost to operate all taxis owned by a taxi company is the cost object, annual taxi registration andlicense fees would be variable costs (number of taxis).

If the cost to operate a particular taxiis the cost object, registration and license fees

for that taxi are fixed costs.


Time Span

Whether a cost is variable or fixed with respectto a particular activity depends on the time span.

More costs are variable with longer time spans.


Relevant Range

Variable and fixed cost behavior patterns arevalid for linear cost functions only within

the given relevant range.

Costs may behave nonlinear outside the range.


Cost Estimation

What is cost estimation?

It is the attempt to measure a pastcost relationship between costs

and the level of an activity.

Past cost-behavior functions can helpmanagers make more accurate

cost predictions.


The Cause-and-Effect CriterionIn Choosing Cost Drivers

Physical relationship

Contractual agreements

Implicitly established by logic


Cost Estimation Approaches

Industrial engineering method

Conference method

Account analysis method

Quantitative analysis methods


Steps In EstimatingA Cost Function

Step 1:Choose the dependent variable.

Step 2:Identify the independent variable cost driver(s).

Step 3:Collect data on the dependent variable

and the cost driver(s).


Steps In Estimating A Cost Function

Step 5:Estimate the cost function.

Step 6:Evaluate the estimated cost function.

Step 4:Plot the data.


High-Low Method Example (A quantitative analysis method)

High capacity December: 55,000 machine-hours

Cost of electricity: $80,450

Low capacity September: 30,000 machine-hours

Cost of electricity: $64,200

What is the variable rate?


High-Low Method Example

($80,450 – $64,200) ÷ (55,000 – 30,000)

$16,250 ÷ 25,000 = $0.65

What is the fixed cost?


High-Low Method Example

$80,450 = Fixed cost + (55,000 × $0.65)

Fixed cost = $80,450 – $35,750 = $44,700

$64,200 = Fixed cost + (30,000 × $0.65)

Fixed cost = $64,200 – $19,500 = $44,700

y = a + bx

y = $44,700 + ($0.65 × Machine-hours)


Regression Analysis--OLS (A quantitative analysis method)

It is used to measure the average amount ofchange in a dependent variable, such aselectricity, that is associated with unit

increases in the amounts of one ormore independent variables,

such as machine-hours.

Regression analysis uses all availabledata to estimate the cost function.


Regression Analysis

Simple regression analysis estimates therelationship between the dependent

variable and one independent variable.

Multiple regression analysis estimates therelationship between the dependent variable

and multiple independent variables.


Regression Analysis

The regression equation and regression lineare derived using the least-squares technique.

The objective of least-squares is to developestimates of the parameters a and b.


Regression Analysis

The vertical difference (residual term) measuresthe distance between the actual cost and the

estimated cost for each observation.

The regression method is more accurate thanthe high-low method.


Criteria to Evaluate andChoose Cost Drivers

Economic plausibility

Goodness of fit

Slope of the regression line


Goodness of Fit

The coefficient of determination (r2)expresses the extent to which the changes

in (x) explain the variation in (y).

An (r2) of 0.80 indicates that80% of the change in the dependent

variable can be explained by thechange in the independent variable.


Slope of Regression Line

A relatively steep slope indicates a strongrelationship between the cost driver and costs.

A relatively flat regression line indicates a weakrelationship between the cost driver and costs.

Everything else equal:


Slope of Regression Line

The closer the value of the correlationcoefficient (r) is to ±1, the stronger the

statistical relation between the variables.


Excel Regression--Data

Y X1 X2

Week MOH MH DLH

1 $ 1,190.00 68 30

2 $ 1,211.00 88 35

3 $ 1,004.00 62 36

4 $ 917.00 72 20

5 $ 770.00 60 47

6 $ 1,456.00 96 45

7 $ 1,180.00 78 44

8 $ 710.00 46 38

9 $ 1,316.00 82 70

10 $ 1,032.00 94 30

11 $ 752.00 68 29

12 $ 963.00 48 38


Excel Regression--results

• Interpret Excel regression output (in class)


Non-linear Cost Functions

A nonlinear cost function is a cost function inwhich the graph of total costs versus the levelof a single activity is not a straight line within

the relevant range.

Economies of scale

Quantity discounts

Step cost functions


Concave Cost Functions

Learning versus experiencecurves


Data Issues

Data problemsencountered in estimating

cost functions.

2009 Foster School of Business Cost Accounting L.DuCharme 1 Determining How Costs Behave Chapter 10.

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