C ost+behaviour+estimation

Determining How Determining How Costs BehaveCosts Behave

CRASH CLASSES OF CA MODULE DCRASH CLASSES OF CA MODULE D COST ACCOUNTINGCOST ACCOUNTING CONTACT:CONTACT: KHALID AZIZKHALID AZIZ 0322-33857520322-3385752

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ECONOMICS OF ICMAP, ICAP, MA-ECONOMICS, ECONOMICS OF ICMAP, ICAP, MA-ECONOMICS, B.COM.B.COM.

FINANCIAL ACCOUNTING OF ICMAP STAGE 1,3,4 FINANCIAL ACCOUNTING OF ICMAP STAGE 1,3,4 ICAP MODULE B, B.COM, BBA, MBA & PIPFA.ICAP MODULE B, B.COM, BBA, MBA & PIPFA.

COST ACCOUNTING OF ICMAP STAGE 2,3 ICAP COST ACCOUNTING OF ICMAP STAGE 2,3 ICAP MODULE D, BBA, MBA & PIPFA.MODULE D, BBA, MBA & PIPFA.

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KARACHI, PAKISTAN.KARACHI, PAKISTAN.

IntroductionIntroduction

How do managers know what price to charge, How do managers know what price to charge, whether to make or buy, or other questions whether to make or buy, or other questions related to costs.related to costs.

They need to have an understanding of how They need to have an understanding of how costs change in relation to various factors.costs change in relation to various factors.

This chapter will focus on how to determine This chapter will focus on how to determine cost behavior.cost behavior.

Learning ObjectivesLearning Objectives

1 Explain the two assumptions frequently used Explain the two assumptions frequently used in cost-behavior estimationin cost-behavior estimation

2 Describe linear cost functions and three Describe linear cost functions and three common ways in which they behavecommon ways in which they behave

3 Recognize various approaches to cost Recognize various approaches to cost estimationestimation


4 Outline six steps in estimating a cost function Outline six steps in estimating a cost function on the basis of current or past cost on the basis of current or past cost relationshipsrelationships

5 Describe three criteria to evaluate and choose Describe three criteria to evaluate and choose cost driverscost drivers

6 Explain and give examples of nonlinear cost Explain and give examples of nonlinear cost functionsfunctions


7 Distinguish between the cumulative average-Distinguish between the cumulative average-time learning model and incremental unit-time time learning model and incremental unit-time modelmodel

8 Understand data problems encountered in Understand data problems encountered in estimating cost functionsestimating cost functions

Learning Objective 1Learning Objective 1

Explain the two assumptions Explain the two assumptions frequently used in cost-behavior frequently used in cost-behavior

estimationestimation

Assumptions in Cost-Behavior Assumptions in Cost-Behavior EstimationEstimation

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

– Variation in machine hours can explain Variation in machine hours can explain variations in total cost .variations in total cost .

– Variation in labor hours can explain variations Variation in labor hours can explain variations in total cost.in total cost.

Assumptions in Cost-Behavior Assumptions in Cost-Behavior EstimationEstimation

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

– A linear cost function is a cost function in A linear cost function is a cost function in which the graph of total cost versus the level which the graph of total cost versus the level of a single activity is a straight line.of a single activity is a straight line.


Describe linear cost functions Describe linear cost functions and three common ways in and three common ways in

which they behavewhich they behave

Cost Function...Cost Function...

– is a mathematical expression describing how is a mathematical expression describing how costs change with changes in the level of an costs change with changes in the level of an activity.activity.

Output producedOutput produced Direct manufacturing labor hoursDirect manufacturing labor hours Machine hoursMachine hours Batches of productionBatches of production

Cost FunctionCost Function

La Bella Hotel offers Happy Airline three La Bella Hotel offers Happy Airline three alternative cost structures to accommodate alternative cost structures to accommodate its crew overnight:its crew overnight:

1 $60 per night per room usage$60 per night per room usage Total room usage is the only factor whose Total room usage is the only factor whose

change causes a change in total costs. change causes a change in total costs. The cost is variable.The cost is variable.


What is the cost function?What is the cost function? yy = $60 = $60xx yy measures the total costs of the rooms used. measures the total costs of the rooms used. xx refers to the actual number of rooms used. refers to the actual number of rooms used. The slope of the cost function is $60.The slope of the cost function is $60.


y =y = cost cost yy xx xx = number of rooms = number of rooms


2 $8,000 per month$8,000 per month The total cost will be $8,000 per month The total cost will be $8,000 per month

regardless of room usage.regardless of room usage. The cost is fixed, not variable.The cost is fixed, not variable. What is the cost function?What is the cost function?


yy = $8,000 = $8,000 $8,000 is called a constant or intercept.$8,000 is called a constant or intercept. The slope of the cost function is zero.The slope of the cost function is zero.


y =y = cost cost yy

$8,000 $8,000 xx

xx = number of rooms = number of rooms


3 $3,000 per month plus $24 per room$3,000 per month plus $24 per room This is an example of a mixed cost.This is an example of a mixed cost. yy = $3,000 + $24 = $3,000 + $24xx yy = = aa + + bxbx


y =y = cost cost yy $3,000 $3,000

xx xx = number of rooms = number of rooms

Cost Classification Cost Classification and Estimationand Estimation

– Choice of cost objectChoice of cost object– Time spanTime span– Relevant rangeRelevant range

Choice of Cost ObjectChoice of Cost Object

A cost item may be variable with respect A cost item may be variable with respect to one cost item and fixed with respect to to one cost item and fixed with respect to another.another.

If the number of taxis owned by a taxi If the number of taxis owned by a taxi company is the cost object, annual taxi company is the cost object, annual taxi registration, and license costs would be a registration, and license costs would be a variable cost.variable cost.

Choice of Cost ObjectChoice of Cost Object

If miles driven during a year on a particular If miles driven during a year on a particular taxi is the cost object, registration, and license taxi is the cost object, registration, and license costs for that taxi is a fixed cost.costs for that taxi is a fixed cost.

Time SpanTime Span

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

More costs are variable with longer time spans.More costs are variable with longer time spans.

Relevant RangeRelevant Range

Variable and fixed cost behavior patterns are Variable and fixed cost behavior patterns are valid for linear cost functions only within the valid for linear cost functions only within the given relevant range.given relevant range.

Costs may behave nonlinear outside the range.Costs may behave nonlinear outside the range.

Cost Estimation...Cost Estimation...

– is the attempt to measure a past cost is the attempt to measure a past cost relationship between costs and the level of an relationship between costs and the level of an activity.activity.

Managers are interested in estimating past Managers are interested in estimating past cost-behavior functions primarily because cost-behavior functions primarily because these estimates can help them make more these estimates can help them make more accurate accurate cost predictionscost predictions..

The Cause-and-Effect Criterion The Cause-and-Effect Criterion In Choosing Cost DriversIn Choosing Cost Drivers

– Physical relationship (materials costs)Physical relationship (materials costs)– Contractual agreements (phone charges based Contractual agreements (phone charges based

on minutes)on minutes)– Implicitly established by logic (ordering costs Implicitly established by logic (ordering costs

driven by number of parts)driven by number of parts)


Recognize various approaches Recognize various approaches to cost estimationto cost estimation

Cost Estimation ApproachesCost Estimation Approaches

– Industrial engineering methodIndustrial engineering method– Conference methodConference method– Account analysis methodAccount analysis method– Quantitative analysis methodsQuantitative analysis methods

Industrial Engineering Method...Industrial Engineering Method...

– is also called the is also called the work-measurementwork-measurement methodmethod.. It estimates cost functions by analyzing the It estimates cost functions by analyzing the

relationship between inputs and outputs in relationship between inputs and outputs in physical terms.physical terms.

Conference Method...Conference Method...

– estimates cost functions on the basis of estimates cost functions on the basis of analysis and opinions about costs and their analysis and opinions about costs and their drivers gathered from various sources.drivers gathered from various sources.

This method involves This method involves the pooling of expert the pooling of expert knowledge.knowledge.

Account Analysis...Account Analysis...

– estimates cost functions by classifying cost estimates cost functions by classifying cost accounts in the ledger as variable, fixed, or accounts in the ledger as variable, fixed, or mixed with respect to the identified activity.mixed with respect to the identified activity.

Typically, managers use qualitative rather than Typically, managers use qualitative rather than quantitative analysis when making these cost-quantitative analysis when making these cost-classification decisions.classification decisions.

Account AnalysisAccount Analysis

The cost analyst uses experience and The cost analyst uses experience and judgment to separate total costs into fixed judgment to separate total costs into fixed and variable.and variable.

Quatisha & Co. sells software programs.Quatisha & Co. sells software programs. Total sales = $390,000Total sales = $390,000 The company sold 1,000 programs.The company sold 1,000 programs.


Cost of goods sold = $130,000Cost of goods sold = $130,000 Manager’s salary = $60,000Manager’s salary = $60,000 Secretary’s salary = $29,000Secretary’s salary = $29,000 Commissions = 12% of salesCommissions = 12% of sales What is the total fixed cost?What is the total fixed cost? $60,000 + $29,000 = $89,000$60,000 + $29,000 = $89,000 What is the fixed cost per unit sold?What is the fixed cost per unit sold?


$89,000 ÷ 1,000 = $89.00$89,000 ÷ 1,000 = $89.00 What is the variable cost per unit sold?What is the variable cost per unit sold? Cost of goods sold: $130,000Cost of goods sold: $130,000 Commissions: $390,000 × .12 = $46,800Commissions: $390,000 × .12 = $46,800 ($130,000 + $46,800) ÷ 1,000 = $176.80($130,000 + $46,800) ÷ 1,000 = $176.80

Quantitative Analysis MethodsQuantitative Analysis Methods

Quantitative analysis uses a formal Quantitative analysis uses a formal mathematical method to fit linear cost mathematical method to fit linear cost functions to past data observations.functions to past data observations.


Outline six steps in estimating Outline six steps in estimating a cost function on the basis a cost function on the basis

of current or past cost of current or past cost relationshipsrelationships

Steps In Estimating Steps In Estimating A Cost FunctionA Cost Function

1 Choose the dependent variable.Choose the dependent variable.2 Identify the independent variable cost Identify the independent variable cost

driver(s).driver(s).3 Collect data on the dependent variable and the Collect data on the dependent variable and the

cost driver(s).cost driver(s).4 Plot the data.Plot the data.5 Estimate the cost function.Estimate the cost function.6 Evaluate the estimated cost function.Evaluate the estimated cost function.


1 Choose the dependent variable.Choose the dependent variable. Choice of the dependent variable (the cost to Choice of the dependent variable (the cost to

be predicted) will depend on the purpose for be predicted) will depend on the purpose for estimating a cost function.estimating a cost function.


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

The independent variable (level of activity The independent variable (level of activity or cost driver) is the factor used to predict the or cost driver) is the factor used to predict the dependent variable (costs).dependent variable (costs).


Two important aspects when identifying a Two important aspects when identifying a cost driver:cost driver:

A It should have an economically plausible It should have an economically plausible relationship with the dependent variable.relationship with the dependent variable.

B It should be accurately measurable.It should be accurately measurable.


3 Collect data on the dependent variable and Collect data on the dependent variable and the cost driver(s).the cost driver(s).

Cost analysts obtain data from company Cost analysts obtain data from company documents, from interviews with managers, documents, from interviews with managers, and through special studies.and through special studies.

– Time-series dataTime-series data– Cross-sectional dataCross-sectional data


4 Plot the data.Plot the data. The general relationship between the cost The general relationship between the cost

driver and the dependent variable can readily driver and the dependent variable can readily be observed in a plot of the data.be observed in a plot of the data.

The plot highlights extreme observations that The plot highlights extreme observations that analysts should check.analysts should check.


5 Estimate the cost function.Estimate the cost function.– High-low methodHigh-low method– Regression analysisRegression analysis


6 Evaluate the estimated cost function.Evaluate the estimated cost function. A key aspect of estimating a cost function is A key aspect of estimating a cost function is

choosing the appropriate cost driver.choosing the appropriate cost driver.

High-Low MethodHigh-Low Method

Choose the highest and lowest value of the Choose the highest and lowest value of the cost driver and their respective costs.cost driver and their respective costs.

DetermineDetermine aa andand bb using algebra.using algebra.


High capacity December:High capacity December: 55,000 55,000 machine hoursmachine hours

Cost of electricity: $80,450Cost of electricity: $80,450 Low capacity September:Low capacity September: 30,000 30,000

machine hoursmachine hours Cost of electricity: $64,200Cost of electricity: $64,200 What is the variable rate?What is the variable rate?


($80,450 – $64,200) ÷ (55,000 – 30,000)($80,450 – $64,200) ÷ (55,000 – 30,000) $16,250 ÷ 25,000 = $0.65$16,250 ÷ 25,000 = $0.65 What is the fixed cost?What is the fixed cost?


$80,450 = Fixed cost + 55,000 – $0.65$80,450 = Fixed cost + 55,000 – $0.65 Fixed cost = $80,450 – $35,750 = $44,700Fixed cost = $80,450 – $35,750 = $44,700 $64,200 = Fixed cost + 30,000 x $0.65$64,200 = Fixed cost + 30,000 x $0.65 Fixed cost = $64,200 – $19,500 = $44,700Fixed cost = $64,200 – $19,500 = $44,700 yy = = a a + + bxbx yy = $44,700 + ($0.65 × Machine-hours) = $44,700 + ($0.65 × Machine-hours)

Regression Analysis...Regression Analysis...

– is used to measure the average amount of is used to measure the average amount of change in a dependent variable, such as change in a dependent variable, such as electricity, that is associated with unit electricity, that is associated with unit increases in the amounts of one or more increases in the amounts of one or more independent variables, such as machine hours.independent variables, such as machine hours.

Regression analysis uses all available data to Regression analysis uses all available data to estimate the cost function.estimate the cost function.

Regression AnalysisRegression Analysis

Simple regression analysis estimates the Simple regression analysis estimates the relationship between the dependent variable relationship between the dependent variable and one independent variable.and one independent variable.

Multiple regression analysis estimates the Multiple regression analysis estimates the relationship between the dependent variable relationship between the dependent variable and multiple independent variables.and multiple independent variables.


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

The objective of least-squares is to develop The objective of least-squares is to develop estimates of the parameters estimates of the parameters aa and and bb..


The vertical differenceThe vertical difference (residual term)(residual term) measures the distance between the actual cost measures the distance between the actual cost and the estimated cost for each observation.and the estimated cost for each observation.

The regression method is more accurate than The regression method is more accurate than the high-low method.the high-low method.


Describe three criteria Describe three criteria to evaluate and choose to evaluate and choose

cost driverscost drivers

Criteria to Evaluate and Criteria to Evaluate and Choose Cost DriversChoose Cost Drivers

1 Economic plausibilityEconomic plausibility2 Goodness of fitGoodness of fit3 Slope of the regression lineSlope of the regression line

Goodness of FitGoodness of Fit

The The coefficient of determination (rcoefficient of determination (r22)) expresses the extent to which the changes in expresses the extent to which the changes in (x) (x) explain the variation in explain the variation in (y)(y)..

An An (r(r22) ) of 0.80 indicates that more than 80 of 0.80 indicates that more than 80 percent of the change in the dependent percent of the change in the dependent variable can be explained by the change in variable can be explained by the change in the independent variable.the independent variable.

Slope of Regression LineSlope of Regression Line

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

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


The closer the value of the The closer the value of the correlation correlation coefficientcoefficient (r)(r) to ±1, the stronger the statistical to ±1, the stronger the statistical relation between the variables.relation between the variables.

As As (r) (r) approaches +1, a positive relationship approaches +1, a positive relationship is implied, meaning the dependent variable is implied, meaning the dependent variable (y) (y) increases as the independent variable increases as the independent variable (x) (x) increases.increases.


As As (r) (r) approaches –1, a negative, or inverse, approaches –1, a negative, or inverse, relationship is implied, meaning the dependent relationship is implied, meaning the dependent variable variable (y) (y) decreases as the independent decreases as the independent variable variable (x) (x) increases.increases.


Explain and give examples of Explain and give examples of nonlinear cost functionsnonlinear cost functions

Nonlinearity and Cost FunctionsNonlinearity and Cost Functions

A nonlinear cost function is a cost function in A nonlinear cost function is a cost function in which the graph of total costs versus the level which the graph of total costs versus the level of a single activity is not a straight line within of a single activity is not a straight line within the relevant range.the relevant range.

– Economies of scaleEconomies of scale– Quantity discountsQuantity discounts– Step cost functionsStep cost functions


Economies of scale in advertising may enable Economies of scale in advertising may enable an advertising agency to double the number of an advertising agency to double the number of advertisements for less than double the cost.advertisements for less than double the cost.


Quantity discounts on direct materials Quantity discounts on direct materials purchases produce a lower cost per unit purchases produce a lower cost per unit purchased with larger orders.purchased with larger orders.


A step function is a cost function in which the A step function is a cost function in which the cost is constant over various ranges of the cost is constant over various ranges of the level of activity, but the cost increases by level of activity, but the cost increases by discrete amounts as the level of activity discrete amounts as the level of activity changes from one range to the next.changes from one range to the next.


Distinguish between the Distinguish between the cumulative average-time cumulative average-time

learning model and incremental learning model and incremental unit-time modelunit-time model

Learning Curves Learning Curves

A learning curve is a function that shows how A learning curve is a function that shows how labor-hours per unit decline as units of output labor-hours per unit decline as units of output increase.increase.

Experience Curve...Experience Curve...

– is a function that shows how the costs per unit is a function that shows how the costs per unit in various value chain areas decline as units in various value chain areas decline as units produced and sold increase.produced and sold increase.

Cumulative Average-Time Cumulative Average-Time Learning ModelLearning Model

Cumulative average time per unit is reduced Cumulative average time per unit is reduced by a constant percentage each time the by a constant percentage each time the cumulative quantity of units produced is cumulative quantity of units produced is doubled.doubled.

Incremental Unit-Time Incremental Unit-Time Learning ModelLearning Model

The time needed to produce the last unit is The time needed to produce the last unit is reduced by a constant percentage each time reduced by a constant percentage each time the cumulative quantity of units produced is the cumulative quantity of units produced is doubled.doubled.


Understand data problems Understand data problems encountered in estimating encountered in estimating

cost functionscost functions

Data Collection and Data Collection and Adjustment IssuesAdjustment Issues

The ideal database for cost estimation has two The ideal database for cost estimation has two characteristics:characteristics:

1 It contains numerous reliably measured It contains numerous reliably measured observations of the cost driver(s) and the cost observations of the cost driver(s) and the cost that is the dependent variable.that is the dependent variable.

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


Time periods do not match.Time periods do not match. Fixed costs are allocated as if they were Fixed costs are allocated as if they were

variable.variable. Data are either not available or not reliable.Data are either not available or not reliable. Inflation may play a role.Inflation may play a role.


Extreme values of observations occur from Extreme values of observations occur from errors in recording costs.errors in recording costs.

Analysts should adjust or eliminate unusual Analysts should adjust or eliminate unusual observations before estimating a cost observations before estimating a cost relationship.relationship.

There is no homogeneous relationship.There is no homogeneous relationship. The relationship between the cost driver and the The relationship between the cost driver and the

cost is not stationary.cost is not stationary.


The most difficult task in cost estimation is The most difficult task in cost estimation is collecting high-quality, reliably measured collecting high-quality, reliably measured data on the dependent variable and the cost data on the dependent variable and the cost driver(s).driver(s).

ATTENTION COMMERCE ATTENTION COMMERCE STUDENTSSTUDENTS

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