Chapter 9
Inventory Costing and Capacity Analysis
1
Introduction
z
The reported income number captures the attention of
managers in a way few other numbers do.
z This chapter examines two types of cost accounting choices
in which the reported income number of manufacturing
companies is affected by inventories.
z Variable costing and absorption costing
¾
¾
¾
methods treat fixed manufacturing overhead differently:
Under variable costing, fixed manufacturing overhead costs are
excluded from inventoriable costs and are a cost of the period in
which they are incurred.
Under absorption costing, these costs are inventoriable and
become expenses only when a sale occurs.
z
Under both methods all nonmanufacturing costs in the
value chain (such as research and development and
marketing), whether variable or fixed, are recorded as
expenses when incurred.
z IAS 2,10-18 mandates absorption costing for inventory
valuation.
2
Variable Costing
z
z
All variable manufacturing costs are assigned to
production and they become part of the unit cost.
Fixed costs are charged to the Income Summary
Direct Material Inventory
Payroll
Work-in-Process Inventory
Variable
factory
labor
Variable Overhead
3
Variable Costing
Payroll
Work-in-Process Inventory
Fixed Absorption costing
factory
labor
Income Summary
Finished Goods
Cost of Goods Sold
4
Comparison of Variable and Absorption Costing
z
z
z
z
Inventory values are lower with variable costing
because it capitalizes only variable cost as an asset.
Inventory values using absorption costing have an
additional fixed factory overhead per unit
Income in periods of increasing (decreasing)
inventory are higher (lower) with absorption costing
than with variable costing
Absorption costing operating income
– Variable costing operating income
= Fixed manufacturing costs in ending inventory
under absorption costing
– Fixed manufacturing costs in beginning
inventory under absorption costing
5
Inventory Buildup
z
z
Absorption costing enables a manager to increase
operating income in a specific period by increasing
the production schedule, even if there is no customer
demand for the additional production.
While the utilized part of fixed costs is inventoried,
production volume variance is not.
¾
z
Reducing volume variance by producing to inventory
evades disclosing a larger loss due to low demand
the loss is shifted to the future unless demand rises
Cost in inventory
fixed cost in inventory
6
Undesirable incentive effects
z
z
z
Production of items that absorb minimal fixed
manufacturing costs may be delayed, even if they
have a higher contribution margin.
A plant manager may accept a particular order to
increase production even though another plant in
the same company is better suited to handle that
order.
A plant manager may defer maintenance and use the
idle time to produce to inventory
¾
this reduces disclosed cost and increases inventory
7
Revising Performance Evaluation
1
2
3
4
5
Budget carefully and use inventory planning.
Discontinue the use of absorption costing for
internal reporting and instead use variable costing.
Incorporate a carrying charge for inventory.
Lengthen the time period used to evaluate
performance
Include nonfinancial as well as financial variables in
the measures used to evaluate performance.
¾
Sales in units this period
÷ Ending inventory in units this period
¾ Ending inventory in units this period
÷ Ending inventory in units last period
8
Throughput Costing...
treats all costs except those related to variable direct
materials as period costs.
Only direct materials costs are inventoriable costs.
Inventoriable costs
absorption costing
t
c os
le
b
i
x
Fle loss
et
g
d
bu
variable costing
Reported loss
absorption costing
variable costing
Throughput costing
Revenue,
both periods
Throughput costing
sales volume
production volume
9
Comparison of Inventory Costing Methods
Actual
or Normal
or Standard
Costing
Variable
Costing
Absorption
Costing
Throughput
Costing
10
Alternative Denominator-Level Concepts
z
The choice of the denominator used to allocate budgeted fixed
manufacturing costs to products can greatly affect the
numbers a normal or standard (absorption) costing system will
report prior to the end of an accounting period.
z
Alternative Denominator-Level Concepts
¾
¾
¾
¾
Theoretical capacity xt (maximum or ideal capacity)
• based on producing at full (peak) efficiency all the time.
Practical capacity xp
• reduces theoretical capacity by unavoidable operating interruptions
• The use of practical capacity is required by the IRS.
Normal capacityxn
• based on the level of capacity utilization that satisfies average
customer demand over several periods
• mandated in IAS 2,13
• includes seasonal, cyclical, and trend factors.
Master-budget capacity xm
• based on the expected level of capacity utilization for the next
11
budget period (typically one year).
Budgeted Fixed Manufacturing Overhead Rate
for xt
negative volume variance
Budgeted Fixed cost
volume variance for
normal capacity
volume variance for xp
Slope = fixed overhead rate
xm
xn xp x t
xa
12
Decision Making
z
z
Cost data from a normal or standard costing
system are often used in pricing or productemphasis decisions.
Downward Demand Spiral
¾
π ( x)
φ ( x)
φ2
The use of normal capacity utilization or master-budget
capacity utilization can result in capacity costs being
spread over a small number of output units.
¾ Downward demand spiral: continuing reduction in
demand that occurs when the prices of competitors are
not met and demand drops.
φ1
D2
D1
x
13
Chapter 10
Determining how costs behave
14
Introduction
z
z
z
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.
15
Two Assumptions in Cost-Behavior
Estimation
1. Changes in total costs can be explained by changes
in the level of a single activity.
¾
¾
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.
¾
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.
16
Cost Function...
is a mathematical expression describing how costs
change with changes in the level of an activity.
z Output produced
z Direct manufacturing labor hours
z Machine hours
z Batches of production
17
Cost Function
z
z
La Bella Hotel offers Happy Airline three alternative
cost structures to accommodate its crew overnight:
$60 per night per room usage
¾
Total room usage is the only factor whose change causes a
change in total costs.
¾ The cost is variable.
z
$8,000 per month
¾
The total cost will be $8,000 per month regardless of room
usage.
¾ The cost is fixed, not variable.
z
$3,000 per month plus $24 per room
¾
z
This is an example of a mixed cost.
What are the cost functions?
18
Linear Cost Function
y = cost
y
x
x = activity level
19
Constant Cost Function
y = cost
y
$8,000
x
x = activity level
20
„Mixed“ Cost Function
y = cost
y
$3,000
x
x = activity level
21
Cost Classification and Estimation
z
Choice of cost object
¾
z
Time span
¾
z
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
22
Relevant Range
z
Variable and fixed cost behavior patterns are valid for
linear cost functions only within the given relevant
range.
¾
Costs may behave nonlinear outside the range.
pseudo-fixed cost
23
Cost Estimation...
z
z
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.
The Cause-and-Effect Criterion In Choosing Cost
Drivers
¾
Physical relationship (materials costs)
¾ Contractual agreements (phone charges based on minutes)
¾ Implicitly established by logic (ordering costs driven by
number of parts)
24
Cost Estimation Approaches
z
Industrial engineering method
¾
¾
z
Conference method
¾
¾
z
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.
Account analysis method
¾
¾
z
also called the work-measurement method.
estimates cost functions by analyzing the relationship between
inputs and outputs in physical terms.
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.
Quantitative analysis methods
¾
¾
High-low-method
Regression analysis
25
Account Analysis
z
z
Managers use judgment and experience to
decompose different cost categories in different
accounts
Example: Quatisha & Co. sells software programs.
¾
¾
¾
¾
¾
¾
¾
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
26
Quantitative Analysis Methods
z
z
1
2
3
4
5
6
Quantitative analysis uses a formal mathematical
method to fit linear cost functions to past data
observations.
Steps in Estimating a Cost Function
Choose the dependent variable.
Identify the independent variable cost driver(s).
Collect data on the dependent variable and the cost
driver(s).
Plot the data.
Estimate the cost function.
Evaluate the estimated cost function.
27
1
Choose the dependent variable.
¾
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).
¾
The independent variable (level of activity or cost driver) is the
factor used to predict the dependent variable (costs).
¾
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.
¾
Cost analysts obtain data from company documents, from
interviews with managers, and through special studies.
– Time-series data
– Cross-sectional data
28
4
Plot the data.
¾
The general relationship between the cost driver and the
dependent variable can readily be observed in a plot of the
data.
¾ The plot highlights extreme observations that analysts
should check.
Cost of
activity
Estimated cost function
Fixed cost
Level of activity
29
5
–
Estimate the cost function C(x) = a + bx.
High-low method
¾
Choose the highest and lowest value of the cost driver and
their respective costs.
¾ Determine a and b
pseudo-fixed
cost
b = C(hh) –– lC(l )
a
l
h
a = C(h) – bh = C(l) – bl
30
High-Low Method
High capacity December:55,000 machine hours
¾
Cost of electricity: $80,450
Low capacity September: 30,000 machine hours
¾
Cost of electricity: $64,200
What is the variable rate?
¾
($80,450 – $64,200) ÷ (55,000 – 30,000) = $0.65
What is the fixed cost?
¾
$80,450 = Fixed cost + 55,000 x $0.65
Fixed cost = $80,450 – $35,750 = $44,700
¾ $64,200 = Fixed cost + 30,000 x $0.65
Fixed cost = $64,200 – $19,500 = $44,700
z
Cost = $44,700 + ($0.65 × Machine-hours)
31
Regression Analysis...
z
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.
¾
Simple regression analysis estimates the relationship
between the dependent variable and one independent
variable.
¾ Multiple regression analysis estimates the relationship
between the dependent variable and multiple independent
variables.
32
Regression Analysis
z
z
z
z
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.
33
6. Evaluate the estimated cost function.
z
z
1
2
A key aspect of estimating a cost function is
choosing the appropriate cost driver.
Criteria to Evaluate and Choose Cost Drivers
2
ˆ
(
)
−
y
y
Economic plausibility
∑k k
r2 =
2
(
)
−
y
y
∑k k
Goodness of fit
¾
¾
3
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.
Slope of the regression line
¾
¾
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.
34
Nonlinearity and Cost Functions
z
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.
z Economies of scale
¾
z
Quantity discounts
¾
z
z
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
¾
a function that shows how labor-hours per unit decline as units of output
increase.
¾
a function that shows how the costs per unit in various value chain
areas decline as units produced and sold increase.
Step cost functions
¾
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.
35
Learning Models
z
Cumulative Average Time Learning Model:
¾
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 = Total time for cumulative output (Y)
Y/X=
z
Cumulative output (X)
aXb
Incremental unit-time Learning Model:
¾
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 = αX β
dX
36
a = 100, learning rate = 80%, X = 1,2,3,4
z
Cumulative Average-Time Learning Model
Number of units
1
2
3
4
z
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
37
Data Collection and Adjustment Issues
z
1
2
z
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:
¾
¾
¾
¾
¾
¾
¾
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
38
Multivariate Regression: Tests
z
z
F-Test: Can the null hypothesis be rejected that all
the estimated coefficients are zero?
t-Test: Is a single cost driver „significant“?
¾
z
z
z
z
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) ?
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.
39
Quiz
1. A mixed cost function has a constant component
of $20,000. If the total cost is $60,000 and the
independent variable has the value 200, what is the
value of the slope coefficient?
a. $200
b. $400
c. $600
d. $40,000
2. Of the following methods, the one that
would not be appropriate for analyzing how a
specific cost behaves is
a.
the scattergraph method.
b.
the industrial engineering approach.
c.
linear programming.
d.
statistical regression analysis.
40
Quiz
3. When the high-low method is used to estimate a cost
function, the variable cost per unit is found by
a.
performing regression analysis on the associated
cost and cost driver database.
b.
subtracting the fixed cost per unit from the total cost
per unit based on either the highest or lowest observation
of the cost driver.
c.
dividing the difference between the highest and
lowest observations of the cost driver by the difference
between costs associated with the highest and lowest
observations of the cost driver.
d.
dividing the difference between costs associated
with the highest and lowest observations of the cost driver
by the difference between the highest and lowest
observations of the cost driver.
41
Quiz
4. Tory Company derived the following cost relationship from a regression
analysis of its monthly manufacturing overhead cost.
y = $80,000 + $12X
where:
y = monthly manufacturing overhead cost
X = machine-hours
The standard error of estimate of the regression is $6,000.
The standard time required to manufacture one six-unit case of Tory’s
single product is four machine-hours. Tory applies manufacturing
overhead to production on the basis of machine-hours, and its normal
annual production is 50,000 cases.
Tory’s estimated variable manufacturing overhead cost for a month in
which scheduled production is 10,000 cases would be
a. $80,000.
b. $480,000. c. $160,000. d. $320,000.
42
Quiz
5. Tory Company derived the following cost relationship from a regression
analysis of its monthly manufacturing overhead cost.
y = $80,000 + $12X
where:
y = monthly manufacturing overhead cost
X = machine-hours
The standard error of estimate of the regression is $6,000.
The standard time required to manufacture one six-unit case of Tory’s
single product is four machine-hours. Tory applies manufacturing
overhead to production on the basis of machine-hours, and its normal
annual production is 50,000 cases.
1. Tory’s predetermined fixed manufacturing overhead rate would be
a. $4.80/MH.
b. $4.00/MH. c. $3.20/MH.
d. $1.60/MH.
43
Quiz
6. Three criteria to use in identifying cost drivers from
the potentially large set of independent variables that can be
included in a regression model are
a. goodness of fit, size of the intercept term, and
specification analysis.
b. independence between independent variables,
economic plausibility, and specification analysis.
c. economic plausibility, goodness of fit, and
significance of independent variable.
d. spurious correlation, expense of gathering data, and
multicollinearity.
44
Quiz
7. Companies that take advantage of quantity
discounts in purchasing their materials have
a.
b.
c.
d.
decreasing cost functions.
linear cost functions.
nonlinear cost functions.
stationary cost functions.
45
Quiz
8. Stone Isle Manufacturing recently completed and sold an
order of 50 units having the following costs:
Direct materials
$ 1,500
Direct labor (1,000 hours @ $8.50)
8,500
Variable overhead (1,000 hours @ $4.00)¹
4,000
Fixed overhead²
1,400
$15,400
¹Allocated on the basis of direct labor-hours.
²Allocated at the rate of 10% of variable cost.
The company has now been requested to prepare a bid for
150 units of the same product.
If an 80% learning curve is applicable, Stone Isle’s
total cost on this order would be estimated at
a. $26,400. b. $31,790. c. $37,950. d. $38,500.
46
Quiz
9. Stone Isle Manufacturing recently completed and sold an order of 50 units
having the following costs:
Direct materials
$ 1,500
Direct labor (1,000 hours @ $8.50)
8,500
Variable overhead (1,000 hours @ $4.00)¹
4,000
Fixed overhead²
1,400
$15,400
¹Allocated on the basis of direct labor-hours.
²Allocated at the rate of 10% of variable cost.
The company has now been requested to prepare a bid for 150 units of the
same product.
If Stone Isle had experienced a 70% learning curve, the bid for the 150 units
would
a. show a 30% reduction in the total direct labor-hours required
with no learning curve.
b. include 6.40 direct labor-hours per unit at $8.50 per hour.
c. include 1,404 total direct labor-hours at $8.50 per hour.
47
d. be 10% lower than the total bid at an 80% learning curve.
Quiz
10.
Which of the following is not a common problem
encountered in collecting data for cost estimation?
a.
b.
c.
d.
Lack of observing extreme values
Missing data
Changes in technology
Distortions resulting from inflation
48