10 - 1 ©2003 prentice hall business publishing, cost accounting 11/e, horngren/datar/foster...

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

Determining HowCosts Behave

Determining HowCosts Behave

Chapter 102/07/05


Learning Objective 1Learning Objective 1

Explain the two assumptions

frequently used in

cost-behavior estimation.

Costs are driven by activities called cost drivers and are linear within the relevant range


Assumptions in Cost-BehaviorEstimation

Assumptions in Cost-BehaviorEstimation

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

i.e., a cost driver.Cost behavior can adequately be

approximated by a linear function of theactivity level within the relevant range.For example, fixed costs are fixed and

variable costs are constant per unit of activity.



Describe linear cost functions

and three common ways in

which they behave.(Variable, Fixed and Mixed)


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,because all costs are variable in this case.



$0

$5,000

$10,000

$15,000

$20,000

0 100 200 300

x = Number of rooms

y =

Cos

t



2. $8,000 per month

y = $8,000

$8,000 is called a constant or intercept.

The slope of the cost function is zero,because fixed costs don’t change

with the level of activity.



$0

$5,000

$10,000

$15,000

$20,000

0 100 200 300

x = Number of rooms

y =

Cos

t



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

This is an example of a mixed cost. Partof the total cost is fixed, and part of the cost varies with the level of activity (x).

y = $3,000 + $24xy = a + bx



$0

$5,000

$10,000

$15,000

$20,000

0 100 200 300

x = Number of rooms

y =

Cos

t


Cost Classification (fixed or variable) determined by:

Cost Classification (fixed or variable) determined by:

Choice of cost object(Fleet of Vans vs. one Van)

Time span (the longer the timethe more likely the cost will vary)

Relevant range of activity(Within which cost behavior

patterns hold true)


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

The Cause-and-Effect CriterionIn Choosing Cost Drivers

Physical relationship(between the cost and the driver)

Contractual agreements(x amount of cost per unit of activity)

Implicitly established by logic(the more the units, the more the cost)



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


Steps In EstimatingA Cost Function

Steps In EstimatingA Cost Function

Step 1:Choose the dependent variable

(the cost to be estimated).Step 2:

Identify the independent variable (cost driver).

Step 3:Collect data on the dependent variable

and the cost driver(s).


Steps In Estimating A Cost Function

Steps In Estimating A Cost Function

Step 5:Estimate the cost function,

(using High-Low or Regression analysis).

Step 6:Evaluate the estimated cost function.

Step 4:Plot the data on a graph.


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? Solving for b in general formula Y = a + b (X), Where Y is total cost,

a is fixed cost, and b is variable cost per activity (X)


High-Low Method ExampleHigh-Low Method Example

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

$16,250 ÷ 25,000 = $0.65Variable cost per unit of activity (b)

What is the fixed cost (a)?


High-Low Method ExampleHigh-Low Method ExampleUsing the high level of activity,

$80,450 = Fixed cost + (55,000 × $0.65)Fixed cost = $80,450 – $35,750 = $44,700

Or, using the low level of activity,$64,200 = Fixed cost + (30,000 × $0.65)

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

General Formula: y = a + bx

y = $44,700 + $0.65 × (X) Machine-hours


Regression AnalysisRegression Analysis

It is used to measure the average amount ofchange in a dependent variable, such as

Electricity cost, that is associated with unitincreases in the amounts of one or

more 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.

Regression analysis also provides R2,which is an indication of the ‘goodness

of fit’ of the general formula for estimatingpurposes.



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

See appendix : Regression Analysis

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



The regression method is more accurate thanthe high-low method, because it uses

information from all observations.A possible downside would be “outliers”

which are non-representative observations.



Describe criteria used toevaluate and choose cost drivers.


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.

(Good for accurately estimating costs)

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


Slope of Regression LineSlope of Regression Line

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.



Explain and give examples

of nonlinear cost functions.(These would negate the linear

assumption we make for Cost Behavior

within the Relevant range)


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.


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.



Be aware of data problemsencountered in estimating

cost functions.


Data Collection andAdjustment Issues


Time periods do not match between recording dependent variable cost and cost driver activity.

Fixed costs are allocated as if they were variable.i.e., rent cost allocated to products

Data are either not available or not reliable.

Inflation may change relationship between cost and driver.




Extreme values of observations occur frommechanical errors 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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