10 - 1 ©2003 Prentice Hall Business Publishing, Cost Accounting 11/e, Horngren/Datar/Foster...

Determining HowCosts Behave

Chapter 10

Learning Objective 1Learning Objective 1

Explain the two assumptions

frequently used in

cost-behavior estimation.

Assumptions in Cost-BehaviorEstimation

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

Cost behavior can adequately beapproximated by a linear function of theactivity level within the relevant range.

Describe linear cost functions

and three common ways in

which they behave.

Cost FunctionCost Function

What is a cost function?

It is a mathematical expressiondescribing how costs change

with changes in the levelof an activity.

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.

$5,000

$10,000

$15,000

$20,000

0 100 200 300

x = Number of rooms

2. $8,000 per month

y = $8,000

$8,000 is called a constant or intercept.

The slope of the cost function is zero.

$5,000

$10,000

$15,000

$20,000

0 100 200 300

x = Number of rooms

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

This is an example of a mixed cost.

y = $3,000 + $24x

y = a + bx

$5,000

$10,000

$15,000

$20,000

0 100 200 300

x = Number of rooms

Cost Classificationand Estimation Function

Choice of cost object

Time span

Relevant range

Choice of Cost Object ExampleChoice of Cost Object Example

If the number of taxis owned by a taxi companyis the cost object, annual taxi registration and

license fees would be variable costs.

If miles driven during a year on a particular taxiis the cost object, registration and license fees

for that taxi are fixed costs.

Time SpanTime 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 RangeRelevant 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 EstimationCost 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

Understand various approaches

to cost estimation.

Cost Estimation ApproachesCost Estimation Approaches

Industrial engineering method

Conference method

Account analysis method

Quantitative analysis methods

Account Analysis ExampleAccount Analysis Example

The cost analyst uses experience andjudgment to separate total costs into

fixed and variable.

Avisha & Co. sells software programs.

Total sales = $390,000

The company sold 1,000 programs.

Cost of goods sold = $130,000

Manager’s salary = $60,000

Secretary’s salary = $29,000

Commissions = 12% of sales

What is the total fixed cost?

$60,000 + $29,000 = $89,000

What is the fixed cost per unit sold?

$89,000 ÷ 1,000 = $89.00

What is the variable cost per unit sold?

Cost of goods sold: $130,000

Commissions: $390,000 × .12 = $46,800

($130,000 + $46,800) ÷ 1,000 = $176.80

Outline six steps in estimatinga cost function on the basisof past cost relationships.

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 ExampleHigh-Low Method Example

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?

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

$16,250 ÷ 25,000 = $0.65

What is the fixed cost?

$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 AnalysisRegression Analysis

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.

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.

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.

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.

Describe three criteria used toevaluate and choose cost drivers.

Criteria to Evaluate andChoose Cost Drivers

Economic plausibility

Goodness of fit

Slope of the regression line

Goodness of FitGoodness 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 that more than80% of the change in the dependent

variable can be explained by thechange in the independent variable.

Slope of Regression LineSlope 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.

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

statistical relation between the variables.

As (r) approaches +1, a positive relationshipis implied, meaning the dependent variable (y)

increases as the independent variable (x) increases.

As (r) approaches –1, a negative, or inverse,relationship is implied, meaning the dependent

variable (y) decreases as the independentvariable (x) increases.

Explain and give examples

of nonlinear cost functions.

Nonlinearity and Cost FunctionsNonlinearity and 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

Economies of scale in advertising may enablean advertising agency to double the number

of advertisements for less than double the cost.

Quantity discounts on direct materialspurchases produce a lower cost perunit purchased with larger orders.

A step function is a cost function in which thecost is constant over various ranges of the level

of activity, but the cost increases by discreteamounts as the level of activity changes

from one range to the next.

Distinguish the cumulativeaverage-time learning model

from the incrementalunit-time learning model.

Learning CurvesLearning Curves

A learning curve is a function that showshow labor-hours per unit decline as units

of output increase.

Experience CurveExperience Curve

This is a function that shows how the costsper unit in various value chain areas decline

as units produced and sold increase.

Cumulative Average-TimeLearning Model

Cumulative average time per unit is reduced bya constant percentage each time the cumulative

quantity of units produced is doubled.

Incremental Unit-TimeLearning Model

The time needed to produce the last unit isreduced by a constant percentage each timethe cumulative quantity of units produced

is doubled.

Be aware of data problemsencountered in estimating

cost functions.

Data Collection andAdjustment Issues

The ideal database for cost estimationhas two characteristics:

1. It contains numerous reliably measuredobservations of the cost driver(s) and the

cost that is the dependent variable.

2. It considers many values for the costdriver that span a wide range.

Time periods do not match.

Fixed costs are allocated as if they were variable.

Data are either not available or not reliable.

Inflation may play a role.

Extreme values of observations occur fromerrors in recording costs.

Analysts should adjust or eliminate unusualobservations before estimating a cost relationship.

There is no homogeneous relationship.

The relationship between the cost driverand the cost is not stationary.

The most difficult task in cost estimationis collecting high-quality, reliablymeasured data on the dependentvariable and the cost driver(s).

End of Chapter 10End of Chapter 10

10 - 1 ©2003 Prentice Hall Business Publishing, Cost Accounting 11/e, Horngren/Datar/Foster...

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