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Determining How Costs Behave. Chapter 10. Overview. Assumptions Model: Y = a + bX Determinates of Fixed vs. Variable costs Cost Estimation Industrial Engineering Conference Method Account Analysis Quantitative Analysis: H-L & OLS 5) Non-linear cost functions.

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  • Assumptions
  • Model: Y = a + bX
  • Determinates of Fixed vs. Variable costs
  • Cost Estimation

Industrial Engineering

Conference Method

Account Analysis

Quantitative Analysis: H-L & OLS

5) Non-linear cost functions

two assumptions frequently used in cost behavior estimation
Two assumptions frequently used in cost-behavior estimation

1. Changes in total costs can be explained by

changes 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
Cost Function

What is a cost function?

It is a mathematical expression

describing how costs change

with changes in the level

of an activity.

cost function variable cost
Cost Function—variable cost

La Playa Hotel offers an airline

three alternative cost structures to

accommodate its crew overnight:

1. $60 per night per room usage

y = $60x

The slope of the cost function is $60.

cost function fixed cost
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 mixed cost
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 classification and estimation function
Cost Classificationand Estimation Function

Choice of cost object

Time span

Relevant range

choice of cost object example
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 and

license fees would be variable costs (number of taxis).

If the cost to operate a particular taxi

is the cost object, registration and license fees

for that taxi are fixed costs.

time span
Time Span

Whether a cost is variable or fixed with respect

to a particular activity depends on the time span.

More costs are variable with longer time spans.

relevant range
Relevant Range

Variable and fixed cost behavior patterns are

valid for linear cost functions only within

the given relevant range.

Costs may behave nonlinear outside the range.

cost estimation
Cost Estimation

What is cost estimation?

It is the attempt to measure a past

cost relationship between costs

and the level of an activity.

Past cost-behavior functions can help

managers make more accurate

cost predictions.

the cause and effect criterion in choosing cost drivers
The Cause-and-Effect CriterionIn Choosing Cost Drivers

Physical relationship

Contractual agreements

Implicitly established by logic

cost estimation approaches
Cost Estimation Approaches

Industrial engineering method

Conference method

Account analysis method

Quantitative analysis methods

steps in estimating a cost function
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 function19
Steps In Estimating A Cost Function

Step 4:

Plot the data.

Step 5:

Estimate the cost function.

Step 6:

Evaluate the estimated cost function.

high low method example a q uantitative analysis method
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
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 example22
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 q uantitative analysis method
Regression Analysis--OLS(A quantitative analysis method)

It is used to measure the average amount of

change in a dependent variable, such as

electricity, that is associated with unit

increases in the amounts of one or

more independent variables,

such as machine-hours.

Regression analysis uses all available

data to estimate the cost function.

regression analysis
Regression Analysis

Simple regression analysis estimates the

relationship between the dependent

variable and one independent variable.

Multiple regression analysis estimates the

relationship between the dependent variable

and multiple independent variables.

regression analysis25
Regression Analysis

The regression equation and regression line

are derived using the least-squares technique.

The objective of least-squares is to develop

estimates of the parameters aand b.

regression analysis26
Regression Analysis

The vertical difference (residual term) measures

the distance between the actual cost and the

estimated cost for each observation.

The regression method is more accurate than

the high-low method.

criteria to evaluate and choose cost drivers
Criteria to Evaluate andChoose Cost Drivers

Economic plausibility

Goodness of fit

Slope of the regression line

goodness of fit
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 that

80% of the change in the dependent

variable can be explained by the

change in the independent variable.

slope of regression line
Slope of Regression Line

Everything else equal:

A relatively steep slope indicates a strong

relationship between the cost driver and costs.

A relatively flat regression line indicates a weak

relationship between the cost driver and costs.

slope of regression line30
Slope of Regression Line

The closer the value of the correlation

coefficient (r) is to ±1, the stronger the

statistical relation between the variables.

excel regression results
Excel Regression--results
  • Interpret Excel regression output (in class)
non linear cost functions
Non-linear Cost Functions

A nonlinear cost function is a cost function in

which the graph of total costs versus the level

of a single activity is not a straight line within

the relevant range.

Economies of scale

Quantity discounts

Step cost functions

concave cost functions
Concave Cost Functions

Learning versus experience


data issues
Data Issues

Data problems

encountered in estimating

cost functions.