Transcript Strategic Transfer Pricing, Absorption Costing and

Chapter 10
Determining how costs behave
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Introduction
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How do managers know what price to charge,
whether to make or buy, or other questions related to
costs.
They need to have an understanding of how costs
change in relation to various factors.
This chapter will focus on how to determine cost
behavior.
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Two Assumptions in Cost-Behavior Estimation
1. Changes in total costs can be explained by changes
in the level of a single activity.

Variation in machine hours can explain variations in total cost
 Variation in labor hours can explain variations in total cost.
2. Cost behavior can adequately be approximated by a
linear function of the activity level within the relevant
range.
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A linear cost function is a cost function in which the graph of total
cost versus the level of a single activity is a straight line.
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Cost Function...
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is a mathematical expression describing how costs
change with changes in the level of an activity.
Output produced
Direct manufacturing labor hours
Machine hours
Batches of production
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Cost Function
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La Bella Hotel offers Happy Airline three alternative cost
structures to accommodate its crew overnight:
$60 per night per room usage
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Total room usage is the only factor whose change causes a change
in total costs.
 The cost is variable.
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$8,000 per month
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$3,000 per month plus $24 per room
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The total cost will be $8,000 per month regardless of room usage.
The cost is fixed, not variable.
This is an example of a mixed cost.
What are the cost functions?
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Linear Cost Function
y = cost
y
x
x = activity level
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Constant Cost Function
y = cost
y
$8,000
x
x = activity level
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„Mixed“ Cost Function
y = cost
y
$3,000
x
x = activity level
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Cost Classification and Estimation
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Choice of cost object
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Time span
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A cost item may be variable with respect to one cost object
and fixed with respect to another.
 Example: If the number of taxis owned by a taxi company is
the cost object, annual taxi registration, and license costs
would be a variable cost.
 If miles driven during a year on a particular taxi is the cost
object, registration, and license costs for that taxi is a fixed
cost.
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
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Relevant Range
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Variable and fixed cost behavior patterns are valid for
linear cost functions only within the given relevant
range.
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Costs may behave nonlinear outside the range.
pseudo-fixed
cost
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Cost Estimation...
–
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is the attempt to measure a past cost relationship
between costs and the level of an activity.
Managers are interested in estimating past costbehavior functions primarily because these
estimates can help them make more accurate cost
predictions.
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The Cause-and-Effect Criterion In Choosing
Cost Drivers
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Physical relationship (materials costs)
Contractual agreements (phone charges based on
minutes)
Implicitly established by logic (ordering costs driven
by number of parts)
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Cost Estimation Approaches
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Industrial engineering method
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also called the work-measurement method.
 estimates cost functions by analyzing the relationship between
inputs and outputs in physical terms.
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Conference method
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estimates cost functions on the basis of analysis and opinions
about costs and their drivers gathered from various sources.
 This method involves the pooling of expert knowledge.
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Account analysis method
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estimates cost functions by classifying cost accounts in the ledger
as variable, fixed, or mixed with respect to the identified activity.
 Typically, managers use qualitative rather than quantitative
analysis when making these cost-classification decisions.
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Quantitative analysis methods
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High-low-method
– Regression analysis
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Account Analysis
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Managers use judgment and experience to
decompose different cost categories in different
accounts
 Example: Quatisha & Co. sells software programs.
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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
the total fixed cost = $60,000 + $29,000 = $89,000
Classify these items according to fixed,
proportional and mixed, and explain how to
decompose mixed costs into fixed and variable
components
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Quantitative Analysis Methods

Quantitative analysis uses a formal mathematical
method to fit linear cost functions to past data
observations.
 Steps in Estimating a Cost Function
1 Choose the dependent variable.
2 Identify the independent variable cost driver(s).
3 Collect data on the dependent variable and the cost
driver(s).
4 Plot the data.
5 Estimate the cost function.
6 Evaluate the estimated cost function.
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1
Choose the dependent variable.
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2
Choice of the dependent variable (the cost to be predicted) will
depend on the purpose for estimating a cost function.
Identify the independent variable cost driver(s).
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The independent variable (level of activity or cost driver) is the
factor used to predict the dependent variable (costs).
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Requirements
It should have an economically plausible
relationship with the dependent variable.
B It should be accurately measurable.
Collect data on the dependent variable and the cost
driver(s).
A
3.
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Cost analysts obtain data from company documents, from
interviews with managers, and through special studies.
– Time-series data
– Cross-sectional data
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4
Plot the data.
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The general relationship between the cost driver and the
dependent variable can readily be observed in a plot of the
data.
The plot highlights extreme observations that analysts
should check.
Cost of
activity
Estimated cost function
Fixed cost
Level of activity
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5
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Estimate the cost function C(x) = a + bx.
High-low method
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Choose the highest and lowest value of the cost driver and
their respective costs.
Determine a and b
pseudo-fixed
cost
b = C(hh) –– lC(l )
a
l
h
a = C(h ) – bh = C(l ) – bl
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High-Low Method
High capacity December:55,000 machine hours
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Cost of electricity: $80,450
Low capacity September: 30,000 machine hours
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Cost of electricity: $64,200
What is the variable rate?
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($80,450 – $64,200) ÷ (55,000 – 30,000) = $0.65
What is the fixed cost?
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$80,450 = Fixed cost + 55,000 x $0.65
Fixed cost = $80,450 – $35,750 = $44,700
$64,200 = Fixed cost + 30,000 x $0.65
Fixed cost = $64,200 – $19,500 = $44,700
Cost = $44,700 + ($0.65 × Machine-hours)
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Regression Analysis...
–
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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.
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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.
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Regression Analysis
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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 a and b.
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.
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6. Evaluate the estimated cost function.
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1
2
A key aspect of estimating a cost function is
choosing the appropriate cost driver.
Criteria to Evaluate and Choose Cost Drivers
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y
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y
k k
Economic plausibility
r2 
2
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y
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y
k k
Goodness of fit
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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 80 percent of the change in
the dependent variable can be explained by the change in the
independent variable.
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Slope of the regression line
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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.
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Nonlinearity and Cost Functions
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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
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Quantity discounts
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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 unit purchased with larger orders.
Learning Curves / Experience Curve
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a function that shows how labor-hours per unit decline as units of
output increase.
 a function that shows how the costs per unit in various value chain
areas decline as units produced and sold increase.
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Step cost functions
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cost is constant over various ranges of the level of activity, but the
cost increases by discrete amounts as the level of activity changes
from one range to the next.
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Learning Models
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Cumulative Average Time Learning Model:
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Cumulative average time per unit is reduced by a
constant percentage each time the cumulative
quantity of units produced is doubled.
Cumulative average time per unit =
Y/X= aXb
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Total time for cumulative output (Y)
Cumulative output (X)
Incremental unit-time Learning Model:
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The time needed to produce the last unit is
reduced by a constant percentage each time the
cumulative quantity of units produced is doubled.
dY = aX b
dX
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a = 100, learning rate = 80%, X = 1,2,3,4
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Cumulative Average-Time Learning Model
Number of units
1
2
3
4
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Cumulative average Cumulative total labor
labor hours per unit
hours
100
100
80
160
70.21
210.63
64
256
Individual time for
Xth unit
100
60
50.63
45.37
Incremental Unit-Time Learning Model
Number of units
1
2
3
4
Individual time for
Xth unit
100
80
70.21
64
Cumulative total labor
hours
100
180
250.21
314.21
Cumulative average
labor hours per unit
100
90
83.40
78.55
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Data Collection and Adjustment Issues
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1
2
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The ideal database for cost estimation has two characteristics:
It contains numerous reliably measured observations of the
cost driver(s) and the cost that is the dependent variable.
It considers many values for the cost driver that span a wide
range.
Pitfalls:
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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 from errors in recording
costs.
 Analysts should adjust or eliminate unusual observations before
estimating a cost relationship.
There is no homogeneous relationship.
The relationship between the cost driver and the cost is not
stationary
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Multivariate Regression: Tests
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F-Test: Can the null hypothesis be rejected that all
the estimated coefficients are zero?
t-Test: Is a single cost driver „significant“?
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means: is the estimated b-value for the cost driver greater
than its standard error (the expected random effects on the
estimate, according to the assumed normal error
distribution) ?
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Durbin-Watson Test: independence of residuals,
autocorrelation
 Linearity: look at the plot
 Goldfeldt-Quandt Test: Heteroscedasticity would
lead to erroneous estimated standard errors
 Multicollinearity: cost drivers in a multivariate
regression are correlated: standard errors are over
estimated; t-Test disturbed.
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CCs for chapter 10
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10-19
 10-21
as in 11th ed.
 10-17
 10-25(=11.10-24)
 10-27 (similar to 11-10-26)
with explanation of EXCEL solution (10%)
 10-33 (=11.10-31) with explanation of EXCEL solution
(10%)
 10-35 (=11.10-33)
 10-39 (=11.10-37)
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Data for 10-35
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First PT109:
$
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Direct materials
100,000
 Direct manuf. labor
300,000
 Tooling cost
50,000
 variable MOH ($20 per dmlhr)
 other MOH (25% of Direct manuf. labor)
 seven further units to be built, 85% learning curve
(b =  0.2345)
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