Determining How
Costs Behave
Determining How
Costs Behave
Learning Objective 1
Learning Objective 1
Explain the two assumptions
frequently used in
Assumptions in Cost-Behavior
Estimation
Assumptions in Cost-Behavior
Estimation
Changes in total costs can be explained by changes in the level of a single activity.
Cost behavior can adequately be
Learning Objective 2
Learning Objective 2
Describe linear cost functions
and three common ways in
Cost Function
Cost Function
What is a cost function?
It is a mathematical expression describing how costs change
Cost Function
Cost Function
La Playa Hotel offers an airline three alternative cost structures to
accommodate its crew overnight: 1. $60 per night per room usage
y = $60x
Cost Function
Cost Function
$0 $5,000 $10,000 $15,000 $20,0000 100 200 300
y
=
C
os
Cost Function
Cost Function
2. $8,000 per month
y = $8,000
Cost Function
Cost Function
$0 $5,000 $10,000 $15,000 $20,0000 100 200 300
y
=
C
os
Cost Function
Cost Function
3. $3,000 per month plus $24 per room This is an example of a mixed cost.
Cost Function
Cost Function
$0 $5,000 $10,000 $15,000 $20,0000 100 200 300
y
=
C
os
Cost Classification
and Estimation Function
Cost Classification
and Estimation Function
Choice of cost object
Time span
Choice of Cost Object Example
Choice of Cost Object Example
If the number of taxis owned by a taxi company is the cost object, annual taxi registration and
license fees would be variable costs.
If miles driven during a year on a particular taxi is the cost object, registration and license fees
Time Span
Time Span
Whether a cost is variable or fixed with respect to a particular activity depends on the time span.
Relevant Range
Relevant Range
Variable and fixed cost behavior patterns are valid for linear cost functions only within
the given relevant 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
The Cause-and-Effect Criterion
In Choosing Cost Drivers
The Cause-and-Effect Criterion
In Choosing Cost Drivers
Physical relationship
Contractual agreements
Learning Objective 3
Learning Objective 3
Cost Estimation Approaches
Cost Estimation Approaches
Industrial engineering method
Conference method
Account Analysis Example
Account Analysis Example
The cost analyst uses experience and judgment to separate total costs into
fixed and variable.
Avisha & Co. sells software programs. Total sales = $390,000
Account Analysis Example
Account Analysis Example
Cost of goods sold = $130,000 Manager’s salary = $60,000 Secretary’s salary = $29,000 Commissions = 12% of sales
Account Analysis Example
Account Analysis Example
$89,000 ÷ 1,000 = $89.00
What is the variable cost per unit sold? Cost of goods sold: $130,000
Learning Objective 4
Learning Objective 4
Outline six steps in estimating
a cost function on the basis
Steps In Estimating
A Cost Function
Steps In Estimating
A Cost Function
Step 1:
Choose the dependent variable.
Step 2:
Identify the independent variable cost driver(s).
Step 3:
Steps In Estimating
A Cost Function
Steps In Estimating
A Cost Function
Step 5:
Estimate the cost function.
Step 6:
Evaluate the estimated cost function.
Step 4:
High-Low Method Example
High-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
High-Low Method Example
High-Low Method Example
($80,450 – $64,200) ÷ (55,000 – 30,000) $16,250 ÷ 25,000 = $0.65
High-Low Method Example
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
Regression Analysis
Regression Analysis
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
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
Regression Analysis
Regression Analysis
The regression equation and regression line are derived using the least-squares technique.
Regression Analysis
Regression Analysis
The vertical difference (residual term) measures the distance between the actual cost and the
estimated cost for each observation.
Learning Objective 5
Learning Objective 5
Criteria to Evaluate and
Choose Cost Drivers
Criteria to Evaluate and
Choose Cost Drivers
Economic plausibility
Goodness of fit
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 more than
Slope of Regression Line
Slope of Regression Line
A relatively steep slope indicates a strong relationship between the cost driver and costs. A relatively flat regression line indicates a weak
Slope of Regression Line
Slope of Regression Line
The closer the value of the correlation
coefficient (r) to ±1, the stronger the
statistical relation between the variables. As (r) approaches +1, a positive relationship is implied, meaning the dependent variable (y)
Slope of Regression Line
Slope of Regression Line
As (r) approaches –1, a negative, or inverse, relationship is implied, meaning the dependent
Learning Objective 6
Learning Objective 6
Nonlinearity and Cost Functions
Nonlinearity and 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
Nonlinearity and Cost Functions
Nonlinearity and Cost Functions
Economies of scale in advertising may enable an advertising agency to double the number of advertisements for less than double the cost.
Quantity discounts on direct materials purchases produce a lower cost per
Nonlinearity and Cost Functions
Nonlinearity and Cost Functions
A step function is a cost function in which the cost is constant over various ranges of the level
of activity, but the cost increases by discrete amounts as the level of activity changes
Learning Objective 7
Learning Objective 7
Distinguish the cumulative
average-time learning model
from the incremental
Learning Curves
Learning Curves
A learning curve is a function that shows how labor-hours per unit decline as units
Experience Curve
Experience Curve
This is a function that shows how the costs per unit in various value chain areas decline
Cumulative Average-Time
Learning Model
Cumulative Average-Time
Learning Model
Cumulative average time per unit is reduced by a constant percentage each time the cumulative
Incremental Unit-Time
Learning Model
Incremental Unit-Time
Learning Model
The time needed to produce the last unit is reduced by a constant percentage each time
Learning Objective 8
Learning Objective 8
Be aware of data problems
encountered in estimating
Data Collection and
Adjustment Issues
Data Collection and
Adjustment Issues
The ideal database for cost estimation has two characteristics:
1. It contains numerous reliably measured observations of the cost driver(s) and the
cost that is the dependent variable. 2. It considers many values for the cost
Data Collection and
Adjustment Issues
Data Collection and
Adjustment Issues
Time periods do not match.
Fixed costs are allocated as if they were variable. Data are either not available or not reliable.
Data Collection and
Adjustment Issues
Data Collection and
Adjustment Issues
Extreme values of observations occur from errors in recording costs.
Analysts should adjust or eliminate unusual
observations before estimating a cost relationship. There is no homogeneous relationship.
Data Collection and
Adjustment Issues
Data Collection and
Adjustment Issues
The most difficult task in cost estimation is collecting high-quality, reliably
