Acc301

College of Administration and Finance Sciences
Assignment (1)
Deadline: 13/07/2024 @ 23:59
Course Name: Cost Accounting
Student’s Name:
Course Code: ACCT 301
Student’s ID Number:
Semester: Summer
CRN:
Academic Year: 1445 H
For Instructor’s Use only
Instructor’s Name:
Students’ Grade:
/15
Level of Marks: High/Middle/Low
Instructions – PLEASE READ THEM CAREFULLY
• The Assignment must be submitted on Blackboard (WORD format only) via allocated
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College of Administration and Finance Sciences
Assignment Question(s):
(Marks 15)
Q1. Abdul Karim Company manufactures a product A. The company estimates the cost
function for the total costs. The cost driver is number of units. The following information were
collected:
Month
Units
January
3,560
SAR 242,400
February
3,800
SAR 252,000
March
4,000
SAR 260,000
April
3,600
SAR 244,000
May
3,200
SAR 228,000
June
3,040
SAR 221,600
Compute a cost function using the high-low method.
Total Costs
(3 Marks)
Answer:
Q2.
Hashim Corporation sells its product for SAR17 per unit. Its variable cost is SAR 10 per
unit, and total fixed costs are SAR 800. Assuming next period’s estimated sales are 300,
calculate the following amounts:
a. Degree of operating leverage
(1Mark)
b. Margin of safety in units
(1Mark)
c. Margin of safety in revenues
(1Mark)
Answer
Restricted – ‫مقيد‬
College of Administration and Finance Sciences
Q3. TTL Corporation is in the manufacturer of several plastic products. TTL sells its one of the
plastic product for SAR 500. The variable costs per unit are SAR 200, and the total fixed costs
are SAR 510,000. Based on cost-volume profit analysis, calculate:
(6 Marks)
a) Contribution margin per unit and contribution margin ratio.
b) Break-even point in units and sales SAR.
c) Pretax profit if the company sells 2,200 units.
d) Profit/loss if the company sells 1,500 units.
e) Units needed to reach target pretax profit of SAR 180,000.
f) Sales SAR needed to reach the target pretax profit of SAR 180,000.
Answer:
Q4. Which types of companies would most likely use the job costing? Provide example of one
Saudi Company. How actual allocation rates and estimated allocation rates are analyzed in
these compagnies?
Answer:
Restricted – ‫مقيد‬
(3 Marks)
Cost Management
Measuring, Monitoring, and Motivating Performance
Chapter 2
The Cost Function
© John Wiley & Sons, 2011
Chapter 2: The Cost Function
Eldenburg & Wolcott’s Cost Management, 2e
Slide # 1
Q1: Different Ways to Describe Costs
• Costs can be defined by how they relate to a cost
object, which is defined as any thing or activity for
which we measure costs.
• Costs can also be categorized as to how they are
used in decision making.
• Costs can also be distinguished by the way they
change as activity or volume levels change.
© John Wiley & Sons, 2011
Chapter 2: The Cost Function
Eldenburg & Wolcott’s Cost Management, 2e
Slide # 3
Q1: Assigning Costs to a Cost Object
Cost Assignment
Determining the costs that should attach to a cost object is
called cost assignment.
cost tracing
Direct
Costs
Cost
Object
Indirect
Costs
Direct costs are
easily traced to the
cost object.
Indirect costs are
not easily traced to
the cost object, and
must be allocated.
cost allocation
© John Wiley & Sons, 2011
Chapter 2: The Cost Function
Eldenburg & Wolcott’s Cost Management, 2e
Slide # 4
Q1: Direct and Indirect Costs
• In manufacturing:
• all materials costs that are easily traced to the product are called
direct material costs
• all labor costs that are easily traced to the product are called direct
labor costs
• all other production costs are called overhead costs
• Whether or not a cost is a direct cost depends upon:
• the definition of the cost object
• the precision of the bookkeeping system that tracks costs
• the technology available to capture cost information
• whether the benefits of tracking the cost as direct exceed the
resources expended to track the cost
• the nature of the operations that produce the product or service
© John Wiley & Sons, 2011
Chapter 2: The Cost Function
Eldenburg & Wolcott’s Cost Management, 2e
Slide # 5
Q1: Linear Cost Behavior Terminology
• Total fixed costs are costs that do not change (in
total) as activity levels change.
• Total variable costs are costs that increase (in total)
in proportion to the increase in activity levels.
• Total costs equal total fixed costs plus total variable
costs.
• The relevant range is the span of activity levels for
which the cost behavior patterns hold.
• A cost driver is a measure of activity or volume
level; increases in a cost driver cause total costs to
increase.
© John Wiley & Sons, 2011
Chapter 2: The Cost Function
Eldenburg & Wolcott’s Cost Management, 2e
Slide # 6
Q1: Behavior of Total (Linear) Costs
$
Total Costs
If costs are linear, then total costs
graphically look like this.
Cost Driver
$
Total Fixed Costs
Total fixed costs do not change as the cost
driver increases.
Higher total fixed costs are higher above
the x axis.
Cost Driver
© John Wiley & Sons, 2011
Chapter 2: The Cost Function
Eldenburg & Wolcott’s Cost Management, 2e
Slide # 7
Q1: Behavior of Total (Linear) Costs
$
Total Costs
If costs are linear, then total costs
graphically look like this.
Cost Driver
$
Total Variable Costs
Total variable costs increase as the cost
driver increases.
A steeper slope represents higher variable
costs per unit of the cost driver.
Cost Driver
© John Wiley & Sons, 2011
Chapter 2: The Cost Function
Eldenburg & Wolcott’s Cost Management, 2e
Slide # 8
Q1: Total Versus Per-unit (Average) Cost Behavior
$
Total Variable Costs
slope = $m/unit
If total variable costs look
like this . . .
Cost Driver
$/unit
Per-Unit Variable Costs
. . . then variable costs per
unit look like this.
m
Cost Driver
© John Wiley & Sons, 2011
Chapter 2: The Cost Function
Eldenburg & Wolcott’s Cost Management, 2e
Slide # 9
Q1: Total Versus Per-Unit (Average) Cost Behavior
$
Total Fixed Costs
If total fixed costs look
like this . . .
Cost Driver
$/unit
Per-Unit Fixed Costs
. . . then fixed costs per
unit look like this.
Cost Driver
© John Wiley & Sons, 2011
Chapter 2: The Cost Function
Eldenburg & Wolcott’s Cost Management, 2e
Slide # 10
Q1: Total Versus Per-Unit (Average) Cost Behavior
Lari’s Leather produces customized motorcycle jackets. The leather for
one jacket costs $50, and Lari rents a shop for $450/month. Compute the
total costs per month and the average cost per jacket if she made only
one jacket per month. What if she made 10 jackets per month?
Average variable costs are constant
1 Jacket Total variable costs go up 10 Jackets
Total Average
Costs/ Cost/
Month Jacket
Total Average
Costs/ Cost/
Month Jacket
Leather
$50
$50
Leather
$500
$50
Rent
$450
$450
Rent
$450
$45
Total
$500
$500
Total
$950
$95
Total fixed costs are constant
© John Wiley & Sons, 2011
Average fixed costs go down
Chapter 2: The Cost Function
Eldenburg & Wolcott’s Cost Management, 2e
Slide # 11
Q1: The Cost Function
When costs are linear, the cost function is:
TC = F + V x Q, where
F = total fixed cost, V = variable cost per unit of the cost
driver, and Q = the quantity of the cost driver.
$
Total Costs
The intercept is the total fixed cost.
The slope is the variable cost per
unit of the cost driver.
slope = $V/unit of cost driver
F
Cost Driver
© John Wiley & Sons, 2011
A cost that includes a fixed cost
element and a variable cost
element is known as a mixed cost.
Chapter 2: The Cost Function
Eldenburg & Wolcott’s Cost Management, 2e
Slide # 12
Q1: Nonlinear Cost Behavior
Sometimes nonlinear costs exhibit linear cost behavior over a
range of the cost driver. This is the relevant range of activity.
intercept = total fixed costs
Total
Costs
slope = variable cost per
unit of cost driver
Cost Driver
Relevant Range
© John Wiley & Sons, 2011
Chapter 2: The Cost Function
Eldenburg & Wolcott’s Cost Management, 2e
Slide # 13
Q1: Stepwise Linear Cost Behavior
Some costs are fixed at one level for one range of activity and
fixed at another level for another range of activity. These are
known as stepwise linear costs.
Total Supervisor Salaries Cost in $1000s
Example: A production
supervisor makes
$40,000 per year and
the factory can produce
100,000 units annually
for each 8-hour shift it
operates.
120
80
40
100
200
300
Number of units produced, in 1000s
© John Wiley & Sons, 2011
Chapter 2: The Cost Function
Eldenburg & Wolcott’s Cost Management, 2e
Slide # 14
Q1: Piecewise Linear Cost Behavior
Some variable costs per unit are constant at one level for one
range of activity and constant at another level for another
range of activity. These are known as piecewise linear costs.
Total Materials Costs
slope=
$9/gallon
slope=
$7.50/gallon
slope=
$8/gallon
1000
© John Wiley & Sons, 2011
Example: A supplier
sells us raw materials
at $9/gallon for the first
1000 gallons, $8/gallon
for the second 1000
gallons, and at
$7.50/gallon for all
gallons purchased over
2000 gallons.
2000
Gallons purchased
Chapter 2: The Cost Function
Eldenburg & Wolcott’s Cost Management, 2e
Slide # 15
Q1: Cost Terms for Decision Making
• In Chapter 1 we learned the distinction between
relevant and irrelevant cash flows.
• Opportunity costs are the benefits of an alternative
one gives up when that alternative is not chosen.
• Opportunity costs are difficult to measure because they
are associated with something that did not occur.
• Opportunity costs are always relevant in decision
making.
• Sunk costs are costs that were incurred in the past.
• Sunk costs are never relevant for decision making.
© John Wiley & Sons, 2011
Chapter 2: The Cost Function
Eldenburg & Wolcott’s Cost Management, 2e
Slide # 16
Q1: Cost Terms for Decision Making
• Discretionary costs are periodic costs incurred for
activities that management may or may not
determine are worthwhile.
• These costs may be variable or fixed costs.
• Discretionary costs are relevant for decision making
only if they vary across the alternatives under
consideration.
• Marginal cost is the incremental cost of producing
the next unit.
• When costs are linear and the level of activity is within
the relevant range, marginal cost is the same as
variable cost per unit.
• Marginal costs are often relevant in decision making.
© John Wiley & Sons, 2011
Chapter 2: The Cost Function
Eldenburg & Wolcott’s Cost Management, 2e
Slide # 17
Q2: What Process is Used to Estimate
Future Costs?
Past costs are often used to estimate future,
non-discretionary, costs. In these instances,
one must also consider:
• whether the past costs are relevant to the
decision at hand
• whether the future cost behavior is likely to
mimic the past cost behavior
• whether the past fixed and variable cost
estimates are likely to hold in the future
© John Wiley & Sons, 2011
Chapter 2: The Cost Function
Eldenburg & Wolcott’s Cost Management, 2e
Slide # 18
Q3: Engineered Estimates of Cost Functions
• Use accountants, engineers, employees, and/or
consultants to analyze the resources used in the
activities required to complete a product, service,
or process.
• For example, a company making inflatable rubber
kayaks would estimate some of the following:
• the amount and cost of the rubber required
• the amount and cost of labor required in the cutting department
•
•
•
•
the amount and cost of labor required in the assembly department
overhead costs and the best cost allocation base to use
the selling costs, including commissions and advertising
the distribution costs
© John Wiley & Sons, 2011
Chapter 2: The Cost Function
Eldenburg & Wolcott’s Cost Management, 2e
Slide # 19
Q3: Account Analysis Method of
Estimating a Cost Function
• Review past costs in the general ledger and past
activity levels to determine each cost’s past
behavior.
• For example, a company producing clay wine
goblets might review its records and find:
• the cost of clay is piecewise linear with respect to the number of
pounds of clay purchased
• skilled production labor is variable with respect to the number of
goblets produced
• unskilled production labor is mixed, and the variable portion varies
with respect to the number of times the kiln is operated
• production supervisors’ salary costs are stepwise linear
• distribution costs are mixed, with the variable portion dependent
upon the number of retailers ordering goblets
© John Wiley & Sons, 2011
Chapter 2: The Cost Function
Eldenburg & Wolcott’s Cost Management, 2e
Slide # 20
Q3: Example – Account Analysis Method of
Estimating a Cost Function
•The table on the right
contains the
expenditures for Scott
Manufacturing during the
last year.
•100,000 units were
produced and sold
•$500,000 of sales
revenue was recorded
Required:
1. Determine the cost
function using units
produced as the
driver
2. Repeat using sales
dollars as the driver
© John Wiley & Sons, 2011
Expense
Amount
Direct Materials
$500,000
Direct Labor
300,000
Rent
25,000
Insurance
15,000
Commissions
200,000
Property Tax
20,000
Telephone
10,000
Depreciation
85,000
Power & Light
30,000
Admin Salaries
100,000
Total
1,285,000
Chapter 2: The Cost Function
Eldenburg & Wolcott’s Cost Management, 2e
Variable
Fixed
Slide # 21
Q3: Example – Account Analysis Method of
Estimating a Cost Function
• Steps in estimating a cost function using account
analysis
– Separate fixed and variable costs
– Total the fixed costs
– Total the variable costs
– Calculate a variable cost per driver
– Write out the cost function
© John Wiley & Sons, 2011
Chapter 2: The Cost Function
Eldenburg & Wolcott’s Cost Management, 2e
Slide # 22
Q3: Solution – Account Analysis Method of
Estimating a Cost Function
Expense
Amount
Variable
Direct Materials
$500,000
500,000
Direct Labor
300,000
300,000
Rent
25,000
25,000
Insurance
15,000
15,000
Commissions
200,000
Property Tax
20,000
Cost Function on Dollars:
20,000
Telephone
10,000
10,000
TC = FC + VC/Sales $ * Sales $
Depreciation
85,000
TC = $285,000 + ($0.20) * Sales $
85,000
Power & Light
30,000
30,000
Admin Salaries
100,000
100,000
Total
1,285,000
1,000,000 285,000
© John Wiley & Sons, 2011
Fixed
Cost Function on Units:
TC = FC + VC/Unit * Qty
TC = $285,000 + ($10/unit) * Qty
200,000
Chapter 2: The Cost Function
Eldenburg & Wolcott’s Cost Management, 2e
Slide # 23
Q3: Two-Point Method of
Estimating a Cost Function
• Use the information contained in two past
observations of cost and activity to separate
mixed and variable costs.
• It is much easier and less costly to use than the
account analysis or engineered estimate of cost
methods, but:
• it estimates only mixed cost functions,
• it is not very accurate, and
• it can grossly misrepresent costs if the data points
come from different relevant ranges of activity
© John Wiley & Sons, 2011
Chapter 2: The Cost Function
Eldenburg & Wolcott’s Cost Management, 2e
Slide # 24
Q3: Example – Two-Point Method of
Estimating a Cost Function
In July the Gibson Co. incurred total overhead costs of $58,000 and
made 6,200 units. In December it produced 3,200 units and total
overhead costs were $40,000. What are the total fixed factory costs per
month and average variable factory costs?
We first need to determine V, using the equation for the slope of a line.
$
rise/run = $58,000 – $40,000
6,200 – 3,200 units
= $18,000/3,000 units
= $6/unit
Then, using TC = F + V x Q, and one
of the data points, determine F.
$58,000
$58,000 = F + $6/unit x 6,200 units
$40,000
$58,000 = F + $37,200
$20,800
$20,800 = F
3,200
© John Wiley & Sons, 2011
6,200
Units
Chapter 2: The Cost Function
Eldenburg & Wolcott’s Cost Management, 2e
Slide # 25
Q3: High-Low Method of
Estimating a Cost Function
• The high-low method is a two-point method
• the two data points used to estimate costs are
observations with the highest and the lowest
activity levels
• The extreme points for activity levels may not
be representative of costs in the relevant
range
• this method may underestimate total fixed costs
and overestimate variable costs per unit,
• or vice versa.
© John Wiley & Sons, 2011
Chapter 2: The Cost Function
Eldenburg & Wolcott’s Cost Management, 2e
Slide # 26
Q4: How Does a Scatterplot
Assist with Categorizing a Cost?
• A scatterplot shows cost observations plotted
against levels of a possible cost driver.
• A scatterplot can assist in determining:
• which cost driver might be the best for
analyzing total costs, and
• the cost behavior of the cost against the
potential cost driver.
© John Wiley & Sons, 2011
Chapter 2: The Cost Function
Eldenburg & Wolcott’s Cost Management, 2e
Slide # 27
Q4: Which Cost Driver Has the Best
Cause & Effect Relationship with Total Cost?
8 observations of total selling expenses plotted against 3 potential cost drivers
$
$
# units sold
$
# customers
The number of salespersons
appears to be the best cost
driver of the 3.
© John Wiley & Sons, 2011
Chapter 2: The Cost Function
Eldenburg & Wolcott’s Cost Management, 2e
# salespersons
Slide # 28
Q4: What is the Underlying Cost Behavior?
$
This cost is probably linear and fixed.
# units sold
$
This cost is
probably linear and
variable.
© John Wiley & Sons, 2011
Chapter 2: The Cost Function
Eldenburg & Wolcott’s Cost Management, 2e
# units sold
Slide # 29
Q4: What is the Underlying Cost Behavior?
$
This cost is probably linear and mixed.
# units sold
$
This is likely a
stepwise linear
cost.
© John Wiley & Sons, 2011
Chapter 2: The Cost Function
Eldenburg & Wolcott’s Cost Management, 2e
# units sold
Slide # 30
Q4: What is the Underlying Cost Behavior?
$
This cost may be piecewise linear.
# units sold
$
This cost appears to
have a nonlinear
relationship with units
sold.
© John Wiley & Sons, 2011
Chapter 2: The Cost Function
Eldenburg & Wolcott’s Cost Management, 2e
# units sold
Slide # 31
Q5: How is Regression Analysis Used to
Estimate a Mixed Cost Function?
• Regression analysis estimates the parameters for a linear
relationship between a dependent variable and one or more
independent (explanatory) variables.
• When there is only one independent variable, it is called
simple regression.
• When there is more than one independent variable, it is
called multiple regression.
Y=α+βX+
dependent
variable
independent
variable
α and β are the parameters;  is the error term (or residual)
© John Wiley & Sons, 2011
Chapter 2: The Cost Function
Eldenburg & Wolcott’s Cost Management, 2e
Slide # 32
Q5: How is Regression Analysis Used to
Estimate a Mixed Cost Function?
We can use regression to separate the fixed and
variable components of a mixed cost.
Yi = α + β Xi + i
the predicted total cost for
Xi and the actual total cost
for observation i
Yi is the
actual total
costs for
data point i
Xi is the actual quantity
of the cost driver for
data point i
the intercept
term is total
fixed costs
© John Wiley & Sons, 2011
i is the difference between
the slope
term is the
variable cost
per unit
Chapter 2: The Cost Function
Eldenburg & Wolcott’s Cost Management, 2e
Slide # 33
Q5: Regression Output Terminology:
Adjusted R-Square
• Goodness of fit
• How well does the line from the regression output fit the
actual data points?
• The adjusted R-square statistic shows the percentage
of variation in the Y variable that is explained by the
regression equation.
• The next slide has an illustration of how a regression
equation can explain the variation in a Y variable.
© John Wiley & Sons, 2011
Chapter 2: The Cost Function
Eldenburg & Wolcott’s Cost Management, 2e
Slide # 34
Q5: Regression Output Terminology:
Adjusted R-Square
100,000
90,000
80,000
70,000
60,000
50,000
40,000
30,000
20,000
10,000
0
Values of Y by Observation #
Observation #
0
5
10
15
20
25
30
• We have 29 observations of a Y variable, and the average of the Y variables is
56,700.
• If we plot them in order of the observation number, there is no discernable pattern.
• We have no explanation as to why the observations vary about the average of
56,700.
© John Wiley & Sons, 2011
Chapter 2: The Cost Function
Eldenburg & Wolcott’s Cost Management, 2e
Slide # 35
Q5: Regression Output Terminology:
Adjusted R-Square
If each Y value had an
associated X value, then we
could reorder the Y
observations along the X axis
according to the value of the
associated X.
100,000 Values of Y by X Value
90,000
80,000
70,000
60,000
50,000
40,000
30,000
20,000
10,000
0
0
1,000
2,000
3,000
Now we can measure how the Y observations vary from the “line of
best fit” instead of from the average of the Y observations. Adjusted RSquare measures the portion of Y’s variation about its mean that is
explained by Y’s relationship to X.
© John Wiley & Sons, 2011
Chapter 2: The Cost Function
Eldenburg & Wolcott’s Cost Management, 2e
Slide # 36
Q5: Regression Output Terminology:
p-value and t-statistic.
• Statistical significance of regression coefficients
• When running a regression we are concerned about
whether the “true” (unknown) coefficients are non-zero.
• Did we get a non-zero intercept (or slope coefficient) in
the regression output only because of the particular
data set we used?
© John Wiley & Sons, 2011
Chapter 2: The Cost Function
Eldenburg & Wolcott’s Cost Management, 2e
Slide # 37
Q5: Regression Output Terminology:
p-value and t-statistic.
• The t-statistic and the p-value both measure our
confidence that the true coefficient is non-zero.
• In general, if the t-statistic for the intercept (slope) term
> 2, we can be about 95% confident (at least) that the
true intercept (slope) term is not zero.
• The p-value is more precise
• it tells us the probability that the true coefficient
being estimated is zero
• if the p-value is less than 5%, we are more than
95% confident that the true coefficient is non-zero.
© John Wiley & Sons, 2011
Chapter 2: The Cost Function
Eldenburg & Wolcott’s Cost Management, 2e
Slide # 38
Q5: Interpreting Regression Output
Suppose we had 16 observations of total costs and activity levels
(measured in machine hours) for each total cost. If we regressed the total
costs against the machine hours, we would get . . .
Regression Statistics
Multiple R
0.885
R Square
0.783
Adjusted R Square 0.768
Standard Error
135.3
Observations
16
Std
Coefficients Error t Stat P-value
Intercept
2937 64.59 45.47 1.31E-16
Machine Hours 5.215 0.734 7.109 5.26E-06
The coefficients give you the parameters of the estimated cost function.
Predicted total costs = $2,937 + ($5.215/mach hr) x (# of mach hrs)
Total fixed costs are
estimated at $2,937.
© John Wiley & Sons, 2011
Variable costs per machine
hour are estimated at $5.215.
Chapter 2: The Cost Function
Eldenburg & Wolcott’s Cost Management, 2e
Slide # 39
Q5: Interpreting Regression Output
Regression Statistics
Multiple R
0.885
R Square
0.783
Adjusted R Square 0.768
Standard Error
135.3
Observations
16
Std
Coefficients Error t Stat P-value
Intercept
2937 64.59 45.47 1.31E-16
Machine Hours 5.215 0.734 7.109 5.26E-06
The regression line explains
76.8% of the variation in the total
cost observations.
(5.26E-06 means 5.26 x 10-6,
or 0.00000526)
© John Wiley & Sons, 2011
The high t-statistics . . .
. . . and the low p-values on
both of the regression
parameters tell us that the
intercept and the slope
coefficient are “statistically
significant”.
Chapter 2: The Cost Function
Eldenburg & Wolcott’s Cost Management, 2e
Slide # 40
Q5: Regression Interpretation Example
Carole’s Coffee asked you to help determine its cost function for its chain
of coffee shops. Carole gave you 16 observations of total monthly costs
and the number of customers served in the month. The data is presented
below, and the a portion of the output from the regression you ran is
presented on the next slide. Help Carole interpret this output.
Costs Customers
$5,100
1,600
$10,800
3,200
$7,300
4,800
$17,050
6,400
$9,900
8,000
$16,800
9,600
$29,400
11,200
$26,900
12,800
$20,000
14,400
$24,700
16,000
$30,800
17,600
$26,300
19,200
$39,600
20,800
$42,000
22,400
$32,000
24,000
$37,500
25,600
© John Wiley & Sons, 2011
$40,000
Carole’s Coffee – Total Monthly Costs
$35,000
$30,000
$25,000
$20,000
$15,000
$10,000
$5,000
Customers Served
$0
0
5,000
10,000
Chapter 2: The Cost Function
Eldenburg & Wolcott’s Cost Management, 2e
15,000
20,000
25,000
Slide # 41
Q5: Regression Interpretation Example
Regression Statistics
Multiple R
0.91
R Square
0.8281
Std
Adjusted R Square 0.8158
Coefficients Error t Stat
P-value
Standard Error
4985.6 Intercept
4634 2614 1.7723 0.0980879
Observations
16 Customers 1.388 0.169 8.2131 1.007E-06
What is Carole’s estimated cost function? In a store that serves 10,000
customers, what would you predict for the store’s total monthly costs?
Predicted total costs = $4,634 + ($1.388/customer) x (# of customers)
Predicted total
costs at 10,000
customers
© John Wiley & Sons, 2011
=
$4,634 + ($1.388/customer) x 10,000 customers
=
$18,514
Chapter 2: The Cost Function
Eldenburg & Wolcott’s Cost Management, 2e
Slide # 42
Q5: Regression Interpretation Example
Regression Statistics
Multiple R
0.91
R Square
0.8281
Std
Adjusted R Square 0.8158
Coefficients Error t Stat
P-value
Standard Error
4985.6 Intercept
4634 2614 1.7723 0.0980879
Observations
16 Customers 1.388 0.169 8.2131 1.007E-06
What is the explanatory power of this model? Are the coefficients
statistically significant or not? What does this mean about the cost function?
The model
The slope coefficient is
explains 81.58%significantly different from zero.
of the variation This means we can be pretty
in total costs, sure that the true cost function
which is pretty includes nonzero variable costs
good.
per customer.
The intercept is not
significantly different
from zero. There’s a
9.8% probability that
the true fixed costs are
zero*.
*(Some would say the intercept is significant as long as the p-value is less than 10%, rather than 5%.)
© John Wiley & Sons, 2011
Chapter 2: The Cost Function
Eldenburg & Wolcott’s Cost Management, 2e
Slide # 43
Q6: Considerations When Using
Estimates of Future Costs
• The future is always unknown, so there are
uncertainties when estimating future costs.
• The estimated cost function may have misspecified the cost behavior.
• The cost function may be using an incorrect cost
driver.
• Future cost behavior may not mimic past cost
behavior.
• Future costs may be different from past costs.
© John Wiley & Sons, 2011
Chapter 2: The Cost Function
Eldenburg & Wolcott’s Cost Management, 2e
Slide # 44
Q6: Considerations When Using
Estimates of Future Costs
• The data used to estimate past costs may not be of
high-quality.
• The accounting system may aggregate costs in a
way that mis-specifies cost behavior.
• Information from outside the accounting system
may not be accurate.
• The true cost function may not be in agreement
with the cost function assumptions.
• For example, if variable costs per unit of the cost
driver are not constant over any reasonable
range of activity, the linearity of total cost
assumption is violated.
© John Wiley & Sons, 2011
Chapter 2: The Cost Function
Eldenburg & Wolcott’s Cost Management, 2e
Slide # 45
Appendix 2A: Multiple Regression Example
We have 10 observations of total project cost, the number of
machine hours used by the projects, and the number of
machine set-ups the projects used.
$10,000 Total Costs
$10,000
$8,000
$8,000
$6,000
$6,000
$4,000
$4,000
$2,000
Number of Set-ups
$0
Total Costs
$2,000
Number of Machine Hours
$0
0
© John Wiley & Sons, 2011
2
4
6
0
10 20 30 40 50 60 70 80 90
Chapter 2: The Cost Function
Eldenburg & Wolcott’s Cost Management, 2e
Slide # 46
Appendix 2A: Multiple Regression Example
Regress total costs on the number of set-ups to get the
following output and estimated cost function:
Regression Statistics
Multiple R
0.788
R Square
0.621
Std
Coefficients Error t Stat P-value
Adjusted R Square 0.574
2925.6 1284 2.278 0.0523
Standard Error
1804 Intercept
Observations
10 # of Set-ups 1225.4 338 3.62 0.0068
Predicted project costs = $2,926 + ($1,225/set-up) x (# set-ups)
The explanatory power is 57.4%. The # of set-ups
is significant, but the intercept is not significant if
we use a 5% limit for the p-value.
© John Wiley & Sons, 2011
Chapter 2: The Cost Function
Eldenburg & Wolcott’s Cost Management, 2e
Slide # 47
Appendix 2A: Multiple Regression Example
Regress total costs on the number of machine hours to get
the following output and estimated cost function:
Regression Statistics
Multiple R
0.814
R Square
0.663
Std
Adjusted R Square 0.621
Coefficients Error t Stat P-value
Standard Error
1701 Intercept
-173.8 1909 -0.09 0.9297
Observations
10 # Mach Hrs 112.65 28.4 3.968 0.0041
Predicted project costs = – $173 + ($113/mach hr) x (# mach hrs)
The explanatory power is 62.1%. The intercept shows up
negative, which is impossible as total fixed costs can not
be negative. However, the p-value on the intercept tells us
that there is a 93% probability that the true intercept is
zero. The # of machine hours is significant.
© John Wiley & Sons, 2011
Chapter 2: The Cost Function
Eldenburg & Wolcott’s Cost Management, 2e
Slide # 48
Appendix 2A: Multiple Regression Example
Regress total costs on the # of set ups and the # of
machine hours to get the following:
Regression Statistics
Multiple R
0.959
Std
Coefficients Error t Stat P-value
R Square
0.919
-1132 1021 -1.11 0.3044
Adjusted R Square 0.896 Intercept
857.4 182.4
4.7 0.0022
Standard Error
891.8 # of Set-ups
Observations
10 # of Mach Hrs 82.31 16.23 5.072 0.0014
Predicted
project = – $1,132 + ($857/set-up) x (# set-ups) + ($82/mach hr) x (# mach hrs)
costs
The explanatory power is now 89.6%. The p-values on both
slope coefficients show that both are significant. Since the
intercept is not significant, project costs can be estimated
based on the project’s usage of set-ups and machine hours.
© John Wiley & Sons, 2011
Chapter 2: The Cost Function
Eldenburg & Wolcott’s Cost Management, 2e
Slide # 49
Appendix 2B: What is a Learning Curve?
A learning curve is
• the rate at which labor hours per unit decrease as the
volume of activity increases
• the relationship between cumulative average hours per
unit and the cumulative number of units produced.
A learning curve can be represented mathematically as:
Y = α Xr, where
Y = cumulative average labor hours,
α = time required for the first unit,
X = cumulative number of units produced,
r = an index for learning = ln(% learning)/ln(2), and
ln is the natural logarithmic function.
© John Wiley & Sons, 2011
Chapter 2: The Cost Function
Eldenburg & Wolcott’s Cost Management, 2e
Slide # 50
Appendix 2B: Learning Curve Example
Deanna’s Designer Desks just designed a new solid wood desk for
executives. The first desk took her workforce 55 labor hours to make, but
she estimates that each desk will require 75% of the time of the prior desk
(i.e. “% learning” = 75%). Compute the cumulative average time to make 7
desks, and draw a learning curve.
First compute r:
r = ln(75%)/ln(2) = -0.2877/0.693 = -0.4152
Then compute the cumulative
average time for 7 desks:
60
x 7(-0.4152) = 25.42 hrs
40
Y = 55
Cumulative Average Hours Per Desk
50
30
In order to draw a learning curve,
you must compute the value of Y for
all X values from 1 to 7. . . .
Hrs
per
Desk
20
10
Cumulative Number of Desks
0
1
© John Wiley & Sons, 2011
2
Chapter 2: The Cost Function
Eldenburg & Wolcott’s Cost Management, 2e
3
4
5
6
7
Slide # 51
Cost Management
Measuring, Monitoring, and Motivating Performance
Chapter 3
Cost-Volume-Profit Analysis
© John Wiley & Sons, 2011
Chapter 3: Cost-Volume-Profit Analysis
Eldenburg & Wolcott’s Cost Management, 2e
Slide # 1
Q1: CVP Analysis and the Breakeven Point
• CVP analysis looks at the relationship between
selling prices, sales volumes, costs, and profits.
• The breakeven point (BEP) is where total revenue
equal total costs.
$
Total Revenue (TR)
BEP in
sales $
Total Costs (TC)
units
BEP in units
© John Wiley & Sons, 2011
Chapter 3: Cost-Volume-Profit Analysis
Eldenburg & Wolcott’s Cost Management, 2e
Slide # 3
Q2: How is CVP Analysis Used?
• CVP analysis can determine, both in units and in
sales dollars:
• the volume required to break even
• the volume required to achieve target profit levels
• the effects of discretionary expenditures
• the selling price or costs required to achieve
target volume levels
• CVP analysis helps analyze the sensitivity of profits
to changes in selling prices, costs, volume and
sales mix.
© John Wiley & Sons, 2011
Chapter 3: Cost-Volume-Profit Analysis
Eldenburg & Wolcott’s Cost Management, 2e
Slide # 4
Q2: CVP Calculations for a Single Product
Units required to
F  Profit
achieve target  Q 
P -V
pretax profit
where F = total fixed costs
P = selling price per unit
V = variable cost per unit
P – V = contribution margin per unit
To find the breakeven point in units, set Profit = 0.
© John Wiley & Sons, 2011
Chapter 3: Cost-Volume-Profit Analysis
Eldenburg & Wolcott’s Cost Management, 2e
Slide # 5
Q2: CVP Calculations for a Single Product
Sales $ required
to achieve target  F  Profit
CMR
pretax profit
where F = total fixed costs
CMR = contribution margin ratio
= (P- V)/P
Note that CMR
can also be
computed as
Total Revenue  Total Variable Costs
CMR 
Total Revenue
To find the breakeven point in sales $, set Profit = 0.
© John Wiley & Sons, 2011
Chapter 3: Cost-Volume-Profit Analysis
Eldenburg & Wolcott’s Cost Management, 2e
Slide # 6
Q2: Breakeven Point Calculations
Bill’s Briefcases makes high quality cases for laptops that sell for $200.
The variable costs per briefcase are $80, and the total fixed costs are
$360,000. Find the BEP in units and in sales $ for this company.
BEP in units 
F 0
$360,000

P  V $200 / unit  $80 / unit
$360,000

 3,000 units
$120 / unit
F
$360,000
F 0 

BEP in sales $ 
(P  V ) / P ($200  $80) / $200
CMR
$360,000

 $600,000
60%
© John Wiley & Sons, 2011
Chapter 3: Cost-Volume-Profit Analysis
Eldenburg & Wolcott’s Cost Management, 2e
Slide # 7
Q2: CVP Graph
Draw a CVP graph for Bill’s Briefcases. What is the pretax profit if Bill
sells 4100 briefcases? If he sells 2200 briefcases? Recall that P =
$200, V = $80, and F = $360,000.
TR
$132,000
$1000s
TC
$600
$360
Profit at 2200 units = $120 x 2200 – $360,000.
More easily: 4100 units is 1100 units past BEP,
so profit = $120 x 1100 units; 2200 units is 800
units before BEP, so loss = $120 x 800 units.
-$96,000
2200
© John Wiley & Sons, 2011
Profit at 4100 units =
$120 x 4100 – $360,000.
3000
4100
Chapter 3: Cost-Volume-Profit Analysis
Eldenburg & Wolcott’s Cost Management, 2e
units
Slide # 8
Q2: CVP Calculations
How many briefcases does Bill need to sell to reach a target pretax
profit of $240,000? What level of sales revenue is this? Recall that P =
$200, V = $80, and F = $360,000.
Units needed to F  Profit $360,000  $240,000

reach target 
$120 / unit
P V
pretax profit
 5,000 units
Sales $ required F  $240,000
F

to reach target 
CMR
(P  V ) / P
pretax profit
$600,000

 $1,000,000
60%
© John Wiley & Sons, 2011
Chapter 3: Cost-Volume-Profit Analysis
Eldenburg & Wolcott’s Cost Management, 2e
Of course, 5,000 units x
$200/unit = $1,000,000,
too.
But sometimes you only
know the CMR and not
the selling price per
unit, so this is still a
valuable formula.
Slide # 9
Q2: CVP Calculations
How many briefcases does Bill need to sell to reach a target after-tax
profit of $319,200 if the tax rate is 30%? What level of sales revenue is
this? Recall that P = $200, V = $80, and F = $360,000.
First convert the target after-tax profit to its target pretax profit:
After-tax profit $319,200
Pretax profit 

 $456,000
(1  Tax rate)
(1  0.3)
Units needed to
$360,000  $456,000

 6,800 units
reach target
$120 / unit
pretax profit
Sales $ needed
to reach target
pretax profit
© John Wiley & Sons, 2011
$360,000  $456,000

 $1,360,000
60%
Chapter 3: Cost-Volume-Profit Analysis
Eldenburg & Wolcott’s Cost Management, 2e
Slide # 10
Q1,2: Using CVP to Determine Target Cost Levels
Suppose that Bill’s marketing department says that he can sell 6,000
briefcases if the selling price is reduced to $170. Bill’s target pretax
profit is $210,000. Determine the highest level that his variable costs
can so that he can make his target. Recall that F = $360,000.
Use the CVP formula for units, but solve for V:
Q = 6,000 units  $360,000  $210,000
$170/unit  V
$170/unit  V 
$360,000  $210,000
 $95/unit
6,000 units
V  $75/unit
If Bill can reduce his variable costs to $75/unit, he can meet his goal.
© John Wiley & Sons, 2011
Chapter 3: Cost-Volume-Profit Analysis
Eldenburg & Wolcott’s Cost Management, 2e
Slide # 11
Q4: Business Risk in Bill’s Decision
• After this analysis, Bill needs to consider several
issues before deciding to lower his price to
$170/unit.
• How reliable are his marketing department’s estimates?
• Is a $5/unit decrease in variable costs feasible?
• Will this decrease in variable costs affect product quality?
• If 6,000 briefcases is within his plant’s capacity but lower
than his current sales level, will the increased production
affect employee morale or productivity?
© John Wiley & Sons, 2011
Chapter 3: Cost-Volume-Profit Analysis
Eldenburg & Wolcott’s Cost Management, 2e
Slide # 12
Q1: Using CVP to Compare Alternatives
• CVP analysis can compare alternative cost
structures or selling prices.
• high salary/low commission vs. lower salary/higher
commission for sales persons
• highly automated production process with low variable
costs per unit vs. lower technology process with higher
variable costs per unit and lower fixed costs.
• broad advertising campaign with higher selling prices vs.
minimal advertising and lower selling prices
• The indifference point between alternatives is the
level of sales (in units or sales $) where the profits of
the alternatives are equal.
© John Wiley & Sons, 2011
Chapter 3: Cost-Volume-Profit Analysis
Eldenburg & Wolcott’s Cost Management, 2e
Slide # 13
Q1,2: Using CVP to Compare Alternatives
Currently Bill’s salespersons have salaries totaling $80,000 (included
in F of $360,000) and earn a 5% commission on each unit ($10 per
briefcase). He is considering an alternative compensation arrangement
where the salaries are decreased to $35,000 and the commission is
increased to 20% ($40 per briefcase). Compute the BEP in units under
the proposed alternative. Recall that P = $200 and V = $80 currently.
First compute F and V under the proposed plan:
F = $360,000 – $45,000 decrease in salaries = $315,000
V = $80 + $30 increase in commission = $110
Then compute Q under the proposed plan:
Units
$315,000
needed to  Q  F  0 
 3,500 units
$200 / unit – $110/unit
P V
breakeven
© John Wiley & Sons, 2011
Chapter 3: Cost-Volume-Profit Analysis
Eldenburg & Wolcott’s Cost Management, 2e
Slide # 14
Q1: Determining the Indifference Point
Compute the volume of sales, in units, for which Bill is indifferent
between the two alternatives.
The indifference point in units is the Q for which the profit equations
of the two alternatives are equal.
Current Plan
Proposed Plan
Contribution margin per unit
$120
$90
Total fixed costs
$360,000
$315,000
Profit (current plan) = $120Q – $360,000
Profit (proposed plan) = $90Q – $315,000
$120Q – $360,000 = $90Q – $315,000
$30Q = $45,000
© John Wiley & Sons, 2011
Q = 1,500 units
Chapter 3: Cost-Volume-Profit Analysis
Eldenburg & Wolcott’s Cost Management, 2e
Slide # 15
Q1,2: CVP Graphs of the Indifference Point
Draw a CVP graph for Bill’s that displays the costs under both
alternatives. Notice that the total revenue line for both alternatives is
the same, but the total cost lines are different.
$1000s
BEP for the
current plan
TR
TC-proposed plan
TC-current plan
$600
BEP for the
proposed plan
$360
$315
indifference point between the plans
1500
© John Wiley & Sons, 2011
3000
3500
Chapter 3: Cost-Volume-Profit Analysis
Eldenburg & Wolcott’s Cost Management, 2e
units
Slide # 16
Q1,2: Comparing Alternatives
The current plan breaks even before the proposed plan.
At 1500 units, the plans have the same total cost.
TR
$1000s
TC-proposed plan
TC-current plan
$600
Each unit sold
provides a larger
contribution to profits
under the current
plan.
$360
$315
1500
© John Wiley & Sons, 2011
3000
3500
Chapter 3: Cost-Volume-Profit Analysis
Eldenburg & Wolcott’s Cost Management, 2e
units
Slide # 17
Q4: Business Risk in Bill’s Decision
• Hopefully Bill is currently selling more than 1500
briefcases, because profits are negative under
BOTH plans at this point.
• The total costs of the current plan are less than the
those of the proposed plan at sales levels past
1500 briefcases.
• Therefore, it seems the current plan is preferable to
the proposed plan.
However, . . .
© John Wiley & Sons, 2011
Chapter 3: Cost-Volume-Profit Analysis
Eldenburg & Wolcott’s Cost Management, 2e
Slide # 18
Q5: Business Risk in Bill’s Decision
. . . this may not be true because the level of future
sales is always uncertain.
• What if the briefcases were a new product line?
• Estimates of sales levels may be highly uncertain.
• The lower fixed costs of the proposed plan may be
safer.
• The plans may create different estimates of the
likelihood of various sales levels.
• Salespersons may have an incentive to sell more
units under the proposed plan.
© John Wiley & Sons, 2011
Chapter 3: Cost-Volume-Profit Analysis
Eldenburg & Wolcott’s Cost Management, 2e
Slide # 19
Q3: CVP Analysis for Multiple Products
When a company sells more than one product the
CVP calculations must be adjusted for the sales
mix. The sales mix should be stated as a proportion
• of total units sold when performing CVP
calculations for in units.
• of total revenues when performing CVP
calculations in sales $.
© John Wiley & Sons, 2011
Chapter 3: Cost-Volume-Profit Analysis
Eldenburg & Wolcott’s Cost Management, 2e
Slide # 20
Q3: Sales Mix Computations
• The weighted average contribution margin is the
weighted sum of the products’ contribution margins:
WACM  ni=1  iCM i
where λi is product i’s % of total sales
in units, CMi is product i’s contribution
margin, and n= the number of
products.
• The weighted average contribution margin ratio is
the weighted sum of the products’ contribution
margin ratios:
where i is product i’s % of total
revenues, CMRi is product i’s
WACMR  ni=1  iCMR i sales
contribution margin ratio, and n=
the number of products.
© John Wiley & Sons, 2011
Chapter 3: Cost-Volume-Profit Analysis
Eldenburg & Wolcott’s Cost Management, 2e
Slide # 21
Q3: Multiple Product Breakeven Point
Peggy’s Kitchen Wares sells three sizes of frying pans. Next year she
hopes to sell a total of 10,000 pans. Peggy’s total fixed costs are
$40,800. Each product’s selling price and variable costs is given
below. Find the BEP in units for this company.
Expected sales in units
Small Medium
2,000
5,000
Selling price per unit
Variable costs per unit
Contribution margin per unit
$10.00
$4.00
$6.00
Large Total
3,000 10,000
$15.00 $18.00
$8.00 $11.00
$7.00 $7.00
First note the sales mix in units is 20%:50%:30%, respectively; then
compute the weighted average contribution margin:
WACM = 20%x$6 + 50%x$7 + 30%x$7 = $6.80
© John Wiley & Sons, 2011
Chapter 3: Cost-Volume-Profit Analysis
Eldenburg & Wolcott’s Cost Management, 2e
Slide # 22
Q3: Multiple Product Breakeven Point
Next, compute the BEP in terms of total units:
Total units
F 0
$40,800
needed to  Q 

 6,000 units
P V
$6.80/unit
breakeven
But 6,000 units is not really the BEP in units; the BEP is only 6,000 units if
the sales mix remains the same.
The BEP should be stated in terms of how many of each unit must be sold:
Units required to break even:
Small pans
20% 1,200
Medium pans
50% 3,000
Large pans
30% 1,800
6,000
© John Wiley & Sons, 2011
Chapter 3: Cost-Volume-Profit Analysis
Eldenburg & Wolcott’s Cost Management, 2e
Slide # 23
Q3: Multiple Product Breakeven Point
Find the BEP in sales $ for Peggy’s Kitchen Wares. The total revenue
and total variable cost information below is based on the expected
sales mix.
Small Medium
2,000 5,000
Expected sales in units
Total revenue
Total variable costs
Total contribution margin
Contribution margin ratio
Large
3,000
Total
10,000
$20,000 $75,000 $54,000 $149,000
$8,000 $40,000 $33,000 $81,000
$12,000 $35,000 $21,000 $68,000
60.0%
46.7%
38.9%
45.6%
First compute the weighted average contribution margin ratio:
WACMR = (20/149)x60% + (75/149)x46.7% + (54/149)x38.9% =
© John Wiley & Sons, 2011
Chapter 3: Cost-Volume-Profit Analysis
Eldenburg & Wolcott’s Cost Management, 2e
Slide # 24
Q3: Multiple Product Breakeven Point
. . . = 45.6%, of course! Depending on how the given
information is structured, it may be easier to compute the
CMR as Total contribution margin/Total revenue.
Next compute the BEP in sales $:
BEP in sales $ 
F  0 $40,800

 $89,474*
0.456
CMR
* If you sum the number of units of each size pan required
at breakeven times its selling price you get $89,400. The
extra $74 in the answer above comes from rounding the
contribution margin ratio to three decimals.
© John Wiley & Sons, 2011
Chapter 3: Cost-Volume-Profit Analysis
Eldenburg & Wolcott’s Cost Management, 2e
Slide # 25
Q4: Assumptions in CVP Analysis
CVP analysis assumes that costs and revenues are
linear within a relevant range of activity.
• Linear total revenues means that selling prices per unit
are constant and the sales mix does not change.
• Offering volume discounts to customers violates this assumption.
• Linear total costs means total fixed costs are constant
and variable costs per unit are constant.
• If volume discounts are received from suppliers, then
variable costs per unit are not constant.
• If worker productivity changes as activity levels change,
then variable costs per unit are not constant.
© John Wiley & Sons, 2011
Chapter 3: Cost-Volume-Profit Analysis
Eldenburg & Wolcott’s Cost Management, 2e
Slide # 26
Q4: Assumptions in CVP Analysis
• These assumptions may induce a small relevant
range.
• Results of CVP calculations must be checked to see if
they fall within the relevant range.
• Linear CVP analysis may be inappropriate if the
linearity assumptions hold only over small ranges
of activity.
• Nonlinear analysis techniques are available.
• For example, regression analysis, along with nonlinear
transformations of the data, can be used to estimate
nonlinear cost and revenue functions.
© John Wiley & Sons, 2011
Chapter 3: Cost-Volume-Profit Analysis
Eldenburg & Wolcott’s Cost Management, 2e
Slide # 27
Q5: Margin of Safety
The margin of safety is a measure of how far past
the breakeven point a company is operating, or
plans to operate. It can be measured 3 ways.
margin of
safety in units
=
actual or estimated units of
activity – BEP in units
margin of
safety in $
=
actual or estimated sales $
– BEP in sales $
margin of
safety
percentage
=
Margin of safety in units
Actual or estimated units
© John Wiley & Sons, 2011
Margin of safety in $

Actual or estimated sales $
Chapter 3: Cost-Volume-Profit Analysis
Eldenburg & Wolcott’s Cost Management, 2e
Slide # 28
Q5: Margin of Safety
Suppose that Bill’s Briefcases has budgeted next year’s sales at 5,000
units. Compute all three measures of the margin of safety for Bill.
Recall that P = $200, V = $80, F = $360,000, the BEP in units = 3,000,
and the BEP in sales $ = $600,000.
margin of safety in units = 5,000 units – 3,000 units = 2,000 units
margin of safety in $ = $200 x 5,000 – $600,000 = $400,000
margin of safety percentage =
2,000 units
$400,000
=
= 40%
5,000 units
$200 x 5,000
The margin of safety tells Bill how far sales can
decrease before profits go to zero.
© John Wiley & Sons, 2011
Chapter 3: Cost-Volume-Profit Analysis
Eldenburg & Wolcott’s Cost Management, 2e
Slide # 29
Q5: Degree of Operating Leverage
• The degree of operating leverage measures the
extent to which the cost function is comprised of
fixed costs.
• A high degree of operating leverage indicates a
high proportion of fixed costs.
• Businesses operating at a high degree of operating
leverage
• face higher risk of loss when sales decrease,
• but enjoy profits that rise more quickly when sales
increase.
© John Wiley & Sons, 2011
Chapter 3: Cost-Volume-Profit Analysis
Eldenburg & Wolcott’s Cost Management, 2e
Slide # 30
Q5: Degree of Operating Leverage
The degree of operating leverage can be computed
3 ways.
Contribution margin
Profit
degree of
operating
=
Fixed costs
+1
Profit
leverage
1
Margin of safety percentage
© John Wiley & Sons, 2011
Chapter 3: Cost-Volume-Profit Analysis
Eldenburg & Wolcott’s Cost Management, 2e
Slide # 31
Q5: Degree of Operating Leverage
Suppose that Bill’s Briefcases has budgeted next year’s sales at 5,000
units. Compute Bill’s degree of operating leverage. Recall that P =
$200, V = $80, F = $360,000, and the margin of safety percentage at
5,000 units is 40%.
First, compute contribution margin and profit at 5,000 units:
Contribution margin = ($200 – $80) x 5,000 = $600,000
Profit = $600,000 – $360,000 = $240,000
Degree of operating leverage =
or, degree of operating leverage =
$600,000
= 2.5
$240,000
$360,000
+ 1 = 2.5
$240,000
or, degree of operating leverage =
© John Wiley & Sons, 2011
Chapter 3: Cost-Volume-Profit Analysis
Eldenburg & Wolcott’s Cost Management, 2e
1
= 2.5
40%
Slide # 32
Q5: Using the Degree of Operating Leverage
• The degree of operating leverage shows the
sensitivity of profits to changes in sales.
• On the prior slide Bill’s degree of operating leverage
was 2.5 and profits were $240,000.
• If expected sales were to increase to 6,000 units,
a 20% increase, then profits would increase by
2.5 x 20%, or 50%, to $360,000.*
• If expected sales were to decrease to 4,500 units,
a 10% decrease, then profits would decrease by
2.5 x 10%, or 25%, to $180,000.**
* $240,000 x 1.5 = $360,000
© John Wiley & Sons, 2011
** $240,000 x 0.75 = $180,000
Chapter 3: Cost-Volume-Profit Analysis
Eldenburg & Wolcott’s Cost Management, 2e
Slide # 33
Cost Management
Measuring, Monitoring, and Motivating Performance
Chapter 4
Relevant Information for Decision Making
© John Wiley & Sons, 2011
Chapter 4: Relevant Costs for Nonroutine Operating Decisions
Eldenburg & Wolcott’s Cost Management, 2e
Slide # 1
Q1: Nonroutine Operating Decisions
• Routine operating decisions are those made on a
regular schedule. Examples include:
• annual budgets and resource allocation decisions
• monthly production planning
• weekly work scheduling issues
• Nonroutine operating decisions are not made on a
regular schedule. Examples include:
• accept or reject a customer’s special order
• keep or drop business segments
• insource or outsource a business activity
• constrained (scarce) resource allocation issues
© John Wiley & Sons, 2011
Chapter 4: Relevant Costs for Nonroutine Operating Decisions
Eldenburg & Wolcott’s Cost Management, 2e
Slide # 3
Q1: Nonroutine Operating Decisions
© John Wiley & Sons, 2011
Chapter 4: Relevant Costs for Nonroutine Operating Decisions
Eldenburg & Wolcott’s Cost Management, 2e
Slide # 4
Q1: Process for Making Nonroutine
Operating Decisions
1. Identify the type of decision to be made.
2. Identify the relevant quantitative analysis
technique(s).
3. Identify and analyze the qualitative factors.
4. Perform quantitative and/or qualitative analyses
5. Prioritize issues and arrive at a decision.
© John Wiley & Sons, 2011
Chapter 4: Relevant Costs for Nonroutine Operating Decisions
Eldenburg & Wolcott’s Cost Management, 2e
Slide # 5
Q1: Identify the Type of Decision
•
•
Special order decisions
•
determine the pricing
•
accept or reject a customer’s proposal for order quantity
and pricing
•
identify if there is sufficient available capacity
Keep or drop business segment decisions
•
•
examples of business segments include product lines,
divisions, services, geographic regions, or other distinct
segments of the business
eliminating segments with operating losses will not
always improve profits
© John Wiley & Sons, 2011
Chapter 4: Relevant Costs for Nonroutine Operating Decisions
Eldenburg & Wolcott’s Cost Management, 2e
Slide # 6
Q1: Identify the Type of Decision
•
•
•
Outsourcing decisions
•
make or buy production components
•
perform business activities “in-house” or pay another
business to perform the activity
Constrained resource allocation decisions
•
determine which products (or business segments)
should receive allocations of scarce resources
•
examples include allocating scarce machine hours or
limited supplies of materials to products
Other decisions may use similar analyses
© John Wiley & Sons, 2011
Chapter 4: Relevant Costs for Nonroutine Operating Decisions
Eldenburg & Wolcott’s Cost Management, 2e
Slide # 7
Q1: Identify and Apply the Relevant
Quantitative Analysis Technique(s)
•
•
Regression, CVP, and linear programming are
examples of quantitative analysis techniques.
Analysis techniques require input data.
•
Data for some input variables will be known and for
other input variables estimates will be required.
•
Many nonroutine decisions have a general
decision rule to apply to the data.
•
The results of the general rule need to be
interpreted.
•
The quality of the information used must be considered
when interpreting the results of the general rule.
© John Wiley & Sons, 2011
Chapter 4: Relevant Costs for Nonroutine Operating Decisions
Eldenburg & Wolcott’s Cost Management, 2e
Slide # 8
Q2-Q5 : Identify and Analyze Qualitative Factors
•
Qualitative information cannot easily be valued in
dollars.
•
•
•
can be difficult to identify
can be every bit as important as the quantitative
information
Examples of qualitative information that may be
relevant in some nonroutine decisions include:
•
quality of inputs available from a supplier
•
effects of decision on regular customers
•
effects of decision on employee morale
•
effects of production on the environment or the
community
© John Wiley & Sons, 2011
Chapter 4: Relevant Costs for Nonroutine Operating Decisions
Eldenburg & Wolcott’s Cost Management, 2e
Slide # 9
Q1: Consider All Information and Make a Decision
•
Before making a decision:
•
Consider all quantitative and qualitative information.
• Judgment is required when interpreting the effects of
qualitative information.
•
Consider the quality of the information.
• Judgment is also required when user lower-quality
information.
© John Wiley & Sons, 2011
Chapter 4: Relevant Costs for Nonroutine Operating Decisions
Eldenburg & Wolcott’s Cost Management, 2e
Slide # 10
Q2: Special Order Decisions
•
•
A new customer (or an existing customer) may
sometimes request a special order with a lower
selling price per unit.
The general rule for special order decisions is:
•
•
accept the order if incremental revenues exceed
incremental costs,
subject to qualitative considerations.
Price >=
•
Relevant
Variable Costs +
Relevant
Fixed Costs +
Opportunity
Cost
If the special order replaces a portion of normal
operations, then the opportunity cost of accepting
the order must be included in incremental costs.
© John Wiley & Sons, 2011
Chapter 4: Relevant Costs for Nonroutine Operating Decisions
Eldenburg & Wolcott’s Cost Management, 2e
Slide # 11
Q2: Special Order Decisions
RobotBits, Inc. makes sensory input devices for robot manufacturers.
The normal selling price is $38.00 per unit. RobotBits was approached
by a large robot manufacturer, U.S. Robots, Inc. USR wants to buy
8,000 units at $24, and USR will pay the shipping costs. The per-unit
costs traceable to the product (based on normal capacity of 94,000
units) are listed below. Which costs are relevant to this decision?
yes$6.20 Relevant?
Direct materials
yes 8.00 Relevant?
Direct labor
Variable mfg. overhead yes 5.80 Relevant?
no 3.50 Relevant?
Fixed mfg. overhead
yes
Shipping/handling
no 2.50 Relevant?
Fixed administrative costs no 0.88 Relevant?
no 0.36 Relevant?
Fixed selling costs
$27.24
© John Wiley & Sons, 2011
Chapter 4: Relevant Costs for Nonroutine Operating Decisions
Eldenburg & Wolcott’s Cost Management, 2e
$20.00
Slide # 12
Q2: Special Order Decisions
Suppose that the capacity of RobotBits is 107,000 units and projected
sales to regular customers this year total 94,000 units. Does the
quantitative analysis suggest that the company should accept the
special order?
First determine if there is sufficient idle capacity to accept this
order without disrupting normal operations:
Projected sales to regular customers
Special order
94,000 units
8,000 units
102,000 units
RobotBits still has 5,000 units of idle capacity if the order is
accepted. Compare incremental revenue to incremental cost:
Incremental profit if accept special order =
($24 selling price – $20 relevant costs) x 8,000 units = $32,000
© John Wiley & Sons, 2011
Chapter 4: Relevant Costs for Nonroutine Operating Decisions
Eldenburg & Wolcott’s Cost Management, 2e
Slide # 13
Q2: Qualitative Factors in
Special Order Decisions
What qualitative issues, in general, might RobotBits consider before
finalizing its decision?
• Will USR expect the same selling price per unit on future
orders?
• Will other regular customers be upset if they discover the
lower selling price to one of their competitors?
• Will employee productivity change with the increase in
production?
• Given the increase in production, will the incremental costs
remain as predicted for this special order?
• Are materials available from its supplier to meet the increase
in production?
© John Wiley & Sons, 2011
Chapter 4: Relevant Costs for Nonroutine Operating Decisions
Eldenburg & Wolcott’s Cost Management, 2e
Slide # 14
Q2: Special Order Decisions and Capacity Issues
Suppose instead that the capacity of RobotBits is 100,000 units and
projected sales to regular customers this year totals 94,000 units.
Should the company accept the special order?
Here the company does not have enough idle
capacity to accept the order:
Projected sales to regular customers
Special order
94,000 units
8,000 units
102,000 units
If USR will not agree to a reduction of the order to 6,000
units, then the offer can only be accepted by denying sales
of 2,000 units to regular customers.
© John Wiley & Sons, 2011
Chapter 4: Relevant Costs for Nonroutine Operating Decisions
Eldenburg & Wolcott’s Cost Management, 2e
Slide # 15
Q2: Special Order Decisions and Capacity Issues
Suppose instead that the capacity of RobotBits is 100,000 units and
projected sales to regular customers this year total 94,000 units. Does
the quantitative analysis suggest that the company should accept the
special order?
Direct materials
Direct labor
Variable mfg. overhead
Fixed mfg. overhead
Shipping/handling
Fixed administrative costs
Fixed selling costs
$6.20
8.00
5.80
3.50
2.50
0.88
0.36
$27.24
Variable cost/unit for
regular sales = $22.50.
CM/unit on regular sales
= $38.00 – $22.50 = $15.50.
The opportunity cost of accepting this
order is the lost contribution margin
on 2,000 units of regular sales.
Incremental profit if accept special order =
$32,000 incremental profit under idle capacity – opportunity cost =
$32,000 – $15.50 x 2,000 = $1,000
© John Wiley & Sons, 2011
Chapter 4: Relevant Costs for Nonroutine Operating Decisions
Eldenburg & Wolcott’s Cost Management, 2e
Slide # 16
Q2: Qualitative Factors in
Special Order Decisions
What additional qualitative issues, in this case of a capacity constraint,
might RobotBits consider before finalizing its decision?
• What will be the effect on the regular customer(s) that do not
receive their order(s) of 2,000 units?
• What is the effect on the company’s reputation of leaving
orders from regular customers of 2,000 units unfilled?
• Will any of the projected costs change if the company
operates at 100% capacity?
• Are there any methods to increase capacity? What effects do
these methods have on employees and on the community?
• Notice that the small incremental profit of $1,000 will probably
be outweighed by the qualitative considerations.
© John Wiley & Sons, 2011
Chapter 4: Relevant Costs for Nonroutine Operating Decisions
Eldenburg & Wolcott’s Cost Management, 2e
Slide # 17
Q3: Keep or Drop Decisions
•
Managers must determine whether to keep or
eliminate business segments that appear to be
unprofitable.
•
The general rule for keep or drop decisions is:
•
•
keep the business segment if its contribution margin
covers its avoidable fixed costs,
subject to qualitative considerations.
Drop if: Contribution < Relevant Margin Fixed Costs • + Opportunity Cost If the business segment’s elimination will affect continuing operations, the opportunity costs of its discontinuation must be included in the analysis. © John Wiley & Sons, 2011 Chapter 4: Relevant Costs for Nonroutine Operating Decisions Eldenburg & Wolcott’s Cost Management, 2e Slide # 18 Q3: Keep or Drop Decisions Starz, Inc. has 3 divisions. The Gibson and Quaid Divisions have recently been operating at a loss. Management is considering the elimination of these divisions. Divisional income statements (in 1000s of dollars) are given below. According to the quantitative analysis, should Starz eliminate Gibson or Quaid or both? Revenues Variable costs Contribution margin Traceable fixed costs Division operating income Unallocated fixed costs Operating income Gibson Quaid Russell $390 $433 $837 247 335 472 143 98 365 166 114 175 ($23) ($16) $190 Breakdown of traceable fixed costs: Avoidable $154 Unavoidable 12 $166 © John Wiley & Sons, 2011 $96 18 $114 Total $1,660 1,054 606 455 151 81 $70 $139 36 $175 Chapter 4: Relevant Costs for Nonroutine Operating Decisions Eldenburg & Wolcott’s Cost Management, 2e Slide # 19 Q3: Keep or Drop Decisions Revenues Variable costs Contribution margin Traceable fixed costs Division operating income Unallocated fixed costs Operating income Gibson Quaid Russell $390 $433 $837 247 335 472 143 98 365 166 114 175 ($23) ($16) $190 Breakdown of traceable fixed costs: Avoidable $154 Unavoidable 12 $166 $96 18 $114 Total $1,660 1,054 606 455 151 81 $70 $139 36 $175 Contribution margin Avoidable fixed costs Effect on profit if keep Use the general rule to determine if Gibson and/or Quaid should be eliminated. Gibson Quaid $143 $98 154 96 ($11) $2 The general rule shows that we should keep Quaid and drop Gibson. © John Wiley & Sons, 2011 Chapter 4: Relevant Costs for Nonroutine Operating Decisions Eldenburg & Wolcott’s Cost Management, 2e Slide # 20 Q3: Keep or Drop Decisions Revenues Variable costs Contribution margin Traceable fixed costs Division operating income Unallocated fixed costs Operating income Gibson Quaid Russell $390 $433 $837 247 335 472 143 98 365 166 114 175 ($23) ($16) $190 Breakdown of traceable fixed costs: Avoidable $154 Unavoidable 12 $166 $96 18 $114 Total $1,660 1,054 606 455 151 81 $70 $139 36 $175 Using the general rule is easier than recasting the income statements: Gibson Quaid Russell Total Revenues $390 $433 $837 $1,270 Variable costs 247 335 472 807 Contribution margin 143 98 365 $463 Traceable fixed costs 166 114 175 289 Division operating income ($23) ($16) $190 $174 Unallocated fixed costs 81 Gibson's unavoidable fixed costs 12 Operating income $81 Quaid & Russell only Profits increase by $11 when Gibson is eliminated. © John Wiley & Sons, 2011 Chapter 4: Relevant Costs for Nonroutine Operating Decisions Eldenburg & Wolcott’s Cost Management, 2e Slide # 21 Q3: Keep or Drop Decisions Suppose that the Gibson & Quaid Divisions use the same supplier for a particular production input. If the Gibson Division is dropped, the decrease in purchases from this supplier means that Quaid will no longer receive volume discounts on this input. This will increase the costs of production for Quaid by $14,000 per year. In this scenario, should Starz still eliminate the Gibson Division? Effect on profit if drop Gibson before considering impact on Quaid's production costs Opportunity cost of eliminating Gibson Revised effect on profit if drop Gibson $11 (14) ($3) Profits decrease by $3 when Gibson is eliminated. © John Wiley & Sons, 2011 Chapter 4: Relevant Costs for Nonroutine Operating Decisions Eldenburg & Wolcott’s Cost Management, 2e Slide # 22 Q3: Qualitative Factors in Keep or Drop Decisions What qualitative issues should Starz consider before finalizing its decision? • What will be the effect on the customers of Gibson if it is eliminated? What is the effect on the company’s reputation? • What will be the effect on the employees of Gibson? Can any of them be reassigned to other divisions? • What will be the effect on the community where Gibson is located if the decision is made to drop Gibson? • What will be the effect on the morale of the employees of the remaining divisions? © John Wiley & Sons, 2011 Chapter 4: Relevant Costs for Nonroutine Operating Decisions Eldenburg & Wolcott’s Cost Management, 2e Slide # 23 • Q4: Insource or Outsource (Make or Buy) Decisions Managers often must determine whether to • • • make or buy a production input keep a business activity in house or outsource the activity The general rule for make or buy decisions is: • • choose the alternative with the lowest relevant (incremental cost), subject to qualitative considerations If the decision will affect other aspects of operations, these costs (or lost revenues) must be included in the analysis. Outsource if: Cost to Outsource < Cost to Insource Where: © John Wiley & Sons, 2011 Cost to Relevant Relevant Opportunity Insource = FC + VC + Cost Chapter 4: Relevant Costs for Nonroutine Operating Decisions Eldenburg & Wolcott’s Cost Management, 2e Slide # 24 Q4: Make or Buy Decisions Graham Co. currently of our main product manufactures a part called a gasker used in the manufacture of its main product. Graham makes and uses 60,000 gaskers per year. The production costs are detailed below. An outside supplier has offered to supply Graham 60,000 gaskers per year at $1.55 each. Fixed production costs of $30,000 associated with the gaskers are unavoidable. Should Graham make or buy the gaskers? The production costs per unit for manufacturing a gasker are: yes $0.65 Relevant? Direct materials yes 0.45 Relevant? Direct labor Variable manufacturing overhead yes 0.40 Relevant? no 0.50 Relevant? Fixed manufacturing overhead* $2.00 *$30,000/60,000 units = $0.50/unit $1.50 Advantage of “make” over “buy” = [$1.55 - $1.50] x 60,000 = $3,000 © John Wiley & Sons, 2011 Chapter 4: Relevant Costs for Nonroutine Operating Decisions Eldenburg & Wolcott’s Cost Management, 2e Slide # 25 Q4: Qualitative Factors in Make or Buy Decisions The quantitative analysis indicates that Graham should continue to make the component. What qualitative issues should Graham consider before finalizing its decision? • Is the quality of the manufactured component superior to the quality of the purchased component? • Will purchasing the component result in more timely availability of the component? • Would a relationship with the potential supplier benefit the company in any way? • Are there any worker productivity issues that affect this decision? © John Wiley & Sons, 2011 Chapter 4: Relevant Costs for Nonroutine Operating Decisions Eldenburg & Wolcott’s Cost Management, 2e Slide # 26 Q3: Make or Buy Decisions Suppose the potential supplier of the gasker offers Graham a discount for a different sub-unit required to manufacture Graham’s main product if Graham purchases 60,000 gaskers annually. This discount is expected to save Graham $15,000 per year. Should Graham consider purchasing the gaskers? Advantage of “make” over “buy” before considering discount (slide 23) $3,000 Discount Advantage of “buy” over “make” 15,000 $12,000 Profits increase by $12,000 when the gasker is purchased instead of manufactured. © John Wiley & Sons, 2011 Chapter 4: Relevant Costs for Nonroutine Operating Decisions Eldenburg & Wolcott’s Cost Management, 2e Slide # 27 Q5: Constrained Resource (Product Emphasis) Decisions • Managers often face constraints such as • • production capacity constraints such as machine hours or limits on availability of material inputs limits on the quantities of outputs that customers demand • Managers need to determine which products should first be allocated the scarce resources. • The general rule for constrained resource allocation decisions with only one constraint is: • allocate scarce resources to products with the highest contribution margin per unit of the constrained resource, • subject to qualitative considerations. © John Wiley & Sons, 2011 Chapter 4: Relevant Costs for Nonroutine Operating Decisions Eldenburg & Wolcott’s Cost Management, 2e Slide # 28 Q5: Constrained Resource Decisions (Two Products; One Scarce Resource) Urban’s Umbrellas makes two types of patio umbrellas, regular and deluxe. Suppose there is unlimited customer demand for each product. The selling prices and variable costs of each product are listed below. Selling price per unit Variable cost per unit Contribution margin per unit Regular $40 20 $20 Deluxe $110 44 $ 66 Contribution margin ratio 50% 60% Required machine hours/unit 0.4 2.0 Urban has only 160,000 machine hours available per year. Write Urban’s machine hour constraint as an inequality. 0.4R + 2D  160,000 machine hours © John Wiley & Sons, 2011 Chapter 4: Relevant Costs for Nonroutine Operating Decisions Eldenburg & Wolcott’s Cost Management, 2e Slide # 29 Q5: Constrained Resource Decisions (Two Products; One Scarce Resource) Suppose that Urban decides to make all Regular umbrellas. What is the total contribution margin? Recall that the CM/unit for R is $20. The machine hour constraint is: 0.4R + 2D  160,000 machine hours If D=0, this constraint becomes 0.4R  160,000 machine hours, or R  400,000 units Total contribution margin = $20*400,000 = $8 million Suppose that Urban decides to make all Deluxe umbrellas. What is the total contribution margin? Recall that the CM/unit for D is $66. If R=0, this constraint becomes 2D  160,000 machine hours, or D  80,000 units Total contribution margin = $66*80,000 = $5.28 million © John Wiley & Sons, 2011 Chapter 4: Relevant Costs for Nonroutine Operating Decisions Eldenburg & Wolcott’s Cost Management, 2e Slide # 30 Q5: Constrained Resource Decisions (Two Products; One Scarce Resource) If the choice is between all Ds or all Rs, then clearly making all Rs is better. But how do we know that some combination of Rs and Ds won’t yield an even higher contribution margin? make all Ds; get $5.28 million make all Rs; get $8 million In a one constraint problem, a combination of Rs and Ds will yield a contribution margin between $5.28 and $8 million. Therefore, Urban will only make one product, and clearly R is the best choice. © John Wiley & Sons, 2011 Chapter 4: Relevant Costs for Nonroutine Operating Decisions Eldenburg & Wolcott’s Cost Management, 2e Slide # 31 Q5: Constrained Resource Decisions (Two Products; One Scarce Resource) The general rule for constrained resource decisions with one scarce resource is to first make only the product with the highest contribution margin per unit of the constrained resource. In Urban’s case, the sole scarce resource was machine hours, so Urban should make only the product with the highest contribution margin per machine hour. R: CM/mach hr = $20/0.4mach hrs = $50/mach hr D: CM/mach hr = $66/2mach hrs = $33/mach hr Notice that the total contribution margin from making all Rs is $50/mach hr x 160,000 machine hours to be used producing Rs = $8 million. © John Wiley & Sons, 2011 Chapter 4: Relevant Costs for Nonroutine Operating Decisions Eldenburg & Wolcott’s Cost Management, 2e Slide # 32 Q5: Constrained Resource Decisions (Multiple Scarce Resources) • Usually managers face more than one constraint. • Multiple constraints are easiest to analyze using a quantitative analysis technique known as linear programming. • A problem formulated as a linear programming problem contains • an algebraic expression of the company’s goal, known as the objective function • • for example “maximize total contribution margin” or “minimize total costs” a list of the constraints written as inequalities © John Wiley & Sons, 2011 Chapter 4: Relevant Costs for Nonroutine Operating Decisions Eldenburg & Wolcott’s Cost Management, 2e Slide # 33 Q5: Constrained Resource Decisions (Two Products; Two Scarce Resources) Suppose Urban also need 2 and 6 hours of direct labor per unit of R and D, respectively. There are only 120,000 direct labor hours available per year. Formulate this as a linear programming problem. Max 20R + 66D R,D subject to: 0.4R+2D  160,000 mach hr constraint 2R+6D  120,000 DL hr constraint nonnegativity constraints R0 (can’t make a negative D0 amount of R or D) objective function R, D are the choice variables constraints © John Wiley & Sons, 2011 Chapter 4: Relevant Costs for Nonroutine Operating Decisions Eldenburg & Wolcott’s Cost Management, 2e Slide # 34 Q5: Constrained Resource Decisions (Two Products; Two Scarce Resources) Draw a graph showing the possible production plans for Urban. Every R, D ordered pair To determine this, graph the is a production plan. constraints as inequalities. But which ones are feasible, 0.4R+2D  160,000 mach hr constraint given the constraints? When D=0, R=400,000 D When R=0, D=80,000 2R+6D  120,000 DL hr constraint When D=0, R=60,000 When R=0, D=20,000 80,000 20,000 60,000 © John Wiley & Sons, 2011 400,000 R Chapter 4: Relevant Costs for Nonroutine Operating Decisions Eldenburg & Wolcott’s Cost Management, 2e Slide # 35 Q5: Constrained Resource Decisions (Two Products; Two Scarce Resources) There are not enough machine hours or enough direct labor hours to produce this production plan. There are enough machine hours, but not enough direct labor hours, to produce this production plan. This production plan is feasible; there are enough machine hours and enough direct labor hours for this plan. D 80,000 The feasible set is the area where all the production constraints are satisfied. 20,000 60,000 © John Wiley & Sons, 2011 400,000 R Chapter 4: Relevant Costs for Nonroutine Operating Decisions Eldenburg & Wolcott’s Cost Management, 2e Slide # 36 Q5: Constrained Resource Decisions (Two Products; Two Scarce Resources) The graph helped us realize an important aspect of this problem – we thought there were 2 constrained resources but in fact there is only one. For every feasible production plan, Urban will never run out of machine hours. D The machine hour constraint is non-binding, or slack, but the direct labor hour constraint is binding. 80,000 We are back to a one-scarceresource problem. 20,000 60,000 © John Wiley & Sons, 2011 400,000 R Chapter 4: Relevant Costs for Nonroutine Operating Decisions Eldenburg & Wolcott’s Cost Management, 2e Slide # 37 Q5: Constrained Resource Decisions (Two Products; One Scarce Resource) Here direct labor hours is the sole scarce resource. We can use the general rule for one-constraint problems. R: CM/DL hr = $20/2DL hrs = $10/DL hr D: CM/DL hr = $66/6DL hrs = $11/DL hr D Urban should make all deluxe umbrellas. 80,000 Optimal plan is R=0, D=20,000. Total contribution margin = $66 x 20,000 = $1,320,000 20,000 60,000 © John Wiley & Sons, 2011 400,000 R Chapter 4: Relevant Costs for Nonroutine Operating Decisions Eldenburg & Wolcott’s Cost Management, 2e Slide # 38 Q5: Constrained Resource Decisions (Two Products; Two Scarce Resources) Suppose Urban has been able to train a new workforce and now there are 600,000 direct labor hours available per year. Formulate this as a linear programming problem, graph it, and find the feasible set. Max 20R + 66D R,D subject to: 0.4R+2D  160,000 mach hr constraint 2R+6D  600,000 DL hr constraint R0 D0 The formulation of the problem is the same as before; the only change is that the right hand side (RHS) of the DL hour constraint is larger. © John Wiley & Sons, 2011 Chapter 4: Relevant Costs for Nonroutine Operating Decisions Eldenburg & Wolcott’s Cost Management, 2e Slide # 39 Q5: Constrained Resource Decisions (Two Products; Two Scarce Resources) The machine hour constraint is the same as before. 0.4R+2D  160,000 mach hr constraint D 100,000 2R+6D  600,000 DL hr constraint When D=0, R=300,000 When R=0, D=100,000 80,000 300,000 © John Wiley & Sons, 2011 400,000 R Chapter 4: Relevant Costs for Nonroutine Operating Decisions Eldenburg & Wolcott’s Cost Management, 2e Slide # 40 Q5: Constrained Resource Decisions (Two Products; Two Scarce Resources) There are not enough machine hours or enough direct labor hours for this production plan. There are enough direct labor hours, but not enough machine hours, for this production plan. There are enough machine hours, but not enough direct labor hours, for this production plan. D 100,000 This production plan is feasible; there are enough machine hours and enough direct labor hours for this plan. 80,000 The feasible set is the area where all the production constraints are satisfied. 300,000 © John Wiley & Sons, 2011 400,000 R Chapter 4: Relevant Costs for Nonroutine Operating Decisions Eldenburg & Wolcott’s Cost Management, 2e Slide # 41 Q5: Constrained Resource Decisions (Two Products; Two Scarce Resources) How do we know which of the feasible plans is optimal? We can’t use the general rule for one-constraint problems. We can graph the total contribution margin line, because its slope will help us determine the optimal production plan. D 100,000 80,000 The objective “maximize total contribution margin” means that we . . . this would be the choose a production plan so that the optimal production plan. contribution margin is a large as possible, without leaving the feasible set. If the slope of the total contribution margin line is lower (in absolute value terms) than the slope of the machine hour constraint, then. . . 300,000 © John Wiley & Sons, 2011 400,000 R Chapter 4: Relevant Costs for Nonroutine Operating Decisions Eldenburg & Wolcott’s Cost Management, 2e Slide # 42 Q5: Constrained Resource Decisions (Two Products; Two Scarce Resources) What if the slope of the total contribution margin line is higher (in absolute value terms) than the slope of the direct labor hour constraint? If the total CM line had this steep slope, . . D 100,000 . . then this would be the optimal production plan. 80,000 300,000 © John Wiley & Sons, 2011 400,000 R Chapter 4: Relevant Costs for Nonroutine Operating Decisions Eldenburg & Wolcott’s Cost Management, 2e Slide # 43 Q5: Constrained Resource Decisions (Two Products; Two Scarce Resources) What if the slope of the total contribution margin line is between the slopes of the two constraints? If the total CM line had this slope, . . D 100,000 . . then this would be the optimal production plan. 80,000 300,000 © John Wiley & Sons, 2011 400,000 R Chapter 4: Relevant Costs for Nonroutine Operating Decisions Eldenburg & Wolcott’s Cost Management, 2e Slide # 44 Q5: Constrained Resource Decisions (Two Products; Two Scarce Resources) The last 3 slides showed that the optimal production plan is always at a corner of the feasible set. This gives us an easy way to solve 2 product, 2 or more scarce resource problems. D 100,000 R=0, D=80,000 The total contribution margin here is 0 x $20 + 80,000 x $66 = $5,280,000. R=?, D=? Find the intersection of the 2 constraints. 80,000 R=300,000, D=0 The total contribution margin here is 300,000 x $20 + 0 x $66 = $6,000,000. 300,000 © John Wiley & Sons, 2011 400,000 R Chapter 4: Relevant Costs for Nonroutine Operating Decisions Eldenburg & Wolcott’s Cost Management, 2e Slide # 45 Q5: Constrained Resource Decisions (Two Products; Two Scarce Resources) To find the intersection of the 2 constraints, use substitution or subtract one constraint from the other. multiply each side by 5 Total CM = $5,280,000. D 100,000 80,000 0.4R+2D = 160,000 2R+10D = 800,000 2R+6D = 600,000 2R+6D = 600,000 subtract 0R+4D = 200,000 D = 50,000 Total CM = $20 x 150,000 + 2R+6(50,000) = 600,000 $66 x 50,000 = $6,300,000. 2R = 300,000 R = 150,000 Total CM = $6,000,000. 300,000 © John Wiley & Sons, 2011 400,000 R Chapter 4: Relevant Costs for Nonroutine Operating Decisions Eldenburg & Wolcott’s Cost Management, 2e Slide # 46 Q5: Constrained Resource Decisions (Two Products; Two Scarce Resources) By checking the total contribution margin at each corner of the feasible set (ignoring the origin), we can see that the optimal production plan is R=150,000, D=50,000. Total CM = $5,280,000. D 100,000 80,000 Knowing how to graph and solve 2 product, 2 scarce resource problems is good for understanding the nature of a linear programming problem (but difficult in more complex problems). Total CM = $6,300,000. 50,000 Total CM = $6,000,000. 150,000 300,000 © John Wiley & Sons, 2011 400,000 R Chapter 4: Relevant Costs for Nonroutine Operating Decisions Eldenburg & Wolcott’s Cost Management, 2e Slide # 47 Q5: Qualitative Factors in Scarce Resource Allocation Decisions The quantitative analysis indicates that Urban should produce 150,000 regular umbrellas and 50,000 deluxe umbrellas. What qualitative issues should Urban consider before finalizing its decision? • The assumption that customer demand is unlimited is unlikely; can this be investigated further? • Are there any long-term strategic implications of minimizing production of the deluxe umbrellas? • What would be the effects of attempting to relax the machine hour or DL hour constraints? • Are there any worker productivity issues that affect this decision? © John Wiley & Sons, 2011 Chapter 4: Relevant Costs for Nonroutine Operating Decisions Eldenburg & Wolcott’s Cost Management, 2e Slide # 48 Q5: Constrained Resource Decisions (Multiple Products; Multiple Constraints) • Problems with multiple products, one scarce resource, and one constraint on customer demand for each product are easy to solve. • The general rule is to make the product with the highest contribution margin per unit of the scarce resource: – until its customer demand is satisfied – then move to the product with the next highest contribution margin per unit of the scarce resource, etc. • Problems with multiple products and multiple scarce resources are too cumbersome to solve by hand – Excel solver is a useful tool here. © John Wiley & Sons, 2011 Chapter 4: Relevant Costs for Nonroutine Operating Decisions Eldenburg & Wolcott’s Cost Management, 2e Slide # 49 Q5: Constrained Resource Decisions (Two Products; One Scarce Resource) Urban’s Umbrellas makes two types of patio umbrellas, regular and deluxe. Suppose customer demand for regular umbrellas is 300,000 units and for deluxe umbrellas customer demand is limited to 60,000. Urban has only 160,000 machine hours available per year. What is his optimal production plan? How much would he pay (above his normal costs) for an extra machine hour? Selling price per unit Variable cost per unit Contribution margin per unit Regular $40 20 $20 Deluxe $110 44 $ 66 Required machine hours/unit 0.4 2.0 CM/machine hour $50 $33 Urban should first concentrate on making Rs. He can make enough to satisfy customer demand for Rs: 300,000 Rs x 0.4 mach hr/R = 120,000 mach hrs. © John Wiley & Sons, 2011 Chapter 4: Relevant Costs for Nonroutine Operating Decisions Eldenburg & Wolcott’s Cost Management, 2e Slide # 50 Q5: Constrained Resource Decisions (Two Products; One Scarce Resource) Selling price per unit Variable cost per unit Contribution margin per unit Regular $40 20 $20 Deluxe $110 44 $ 66 Required machine hours/unit 0.4 2.0 CM/machine hour $50 $33 The 40,000 remaining hours will make 20,000 Ds. The optimal plan is 300,000 Rs and 20,000 Ds. The CM/mach hr shows how much Urban would be willing to pay, above his normal costs, for an additional machine hour. Here Urban will be producing Ds when he runs out of machine hours so he’d be willing to pay up to $33 for an additional machine hour. If customer demand for Rs exceeded 400,000 units, Urban would be willing to pay up to an additional $50 for a machine hour. If customer demand for Rs and Ds could be satisfied with the 160,000 available machine hours, then Urban would not be willing to pay anything to acquire an additional machine hour. © John Wiley & Sons, 2011 Chapter 4: Relevant Costs for Nonroutine Operating Decisions Eldenburg & Wolcott’s Cost Management, 2e Slide # 51 Q5: Constrained Resource Decisions Using Excel Solver To obtain the solver dialog box, choose “Solver” from the Tools pull-down menu. The “target cell” will contain the maximized value for the objective (or “target”) function. Choose “max” for the types of problems in this chapter. Add constraint formulas by clicking “add”. © John Wiley & Sons, 2011 Choose one cell for each choice variable (product). It’s helpful to “name” these cells. Click “solve” to obtain the next dialog box. Chapter 4: Relevant Costs for Nonroutine Operating Decisions Eldenburg & Wolcott’s Cost Management, 2e Slide # 52 Q5: Constrained Resource Decisions Using Excel Solver Cell B2 was named “Regular” and cell C2 was named Deluxe. =20*Regular + 66*Deluxe =0.4*Regular+ 2*Deluxe =2*Regular+ 6*Deluxe =Regular (cell B2) =Deluxe (cell C2) Then click “solve” and choose all 3 reports. © John Wiley & Sons, 2011 Chapter 4: Relevant Costs for Nonroutine Operating Decisions Eldenburg & Wolcott’s Cost Management, 2e Slide # 53 Q5: Excel Solver Answer Report Microsoft Excel 9.0 Answer Report Refer to the problem on Slide #50. Target Cell (Max) Original Cell Name Value 0 $B$3 Regular The total contribution margin for the optimal plan was $6.3 million. Final Value 6,300,000 The optimal production plan was 150,000 Rs and 50,000 Ds. Adjustable Cells Original Cell Name Value 0 $B$2 Regular 0 $C$2 Deluxe Final Value 150,000 50000 The machine and DL hour constraints are binding – the plan uses all available machine and DL hours. Constraints Cell Value Formula Status 600,000 $B$9=$C$11 Binding 50,000 $B$10 R>0
Not
150,000 $B$10>=$C$10 Binding
150,000
Cell
Name
$B$9 DL hr
© John Wiley & Sons, 2011
Slack
The nonnegativity
constraints for R and D
are not binding; the slack
is 50,000 and 150,000
units respectively.
Chapter 4: Relevant Costs for Nonroutine Operating Decisions
Eldenburg & Wolcott’s Cost Management, 2e
Slide # 54
Q5: Excel Solver Sensitivity Report
Microsoft Excel 9.0 Sensitivity Report
Refer to the problem on Slide #50.
Adjustable Cells
Final Reduced Objective Allowable Allowable
Cell Name Value
Cost Coefficient Increase Decrease
$B$2 Regular 150,000
0
20
2
6.8
$C$2 Deluxe
50000
0
66
34
6
Constraints
Final Shadow Constraint Allowable Allowable
Cell Name Value
Price R.H. Side Increase Decrease
$B$9 DL hr
600,000
9
600000
200000
120000
$B$8 mach hr 160,000
8
160000
40000
40000
$B$11 D>0
50,000
0
0
50000
1E+30
$B$10 R>0
150,000
0
0
150000
1E+30
This shows
how much the
slope of the
total CM line
can change
before the
optimal
production
plan will
change.
The CM per unit for Regular can drop to $13.20 or increase to $22 (all else equal)
before the optimal plan will change. The CM per unit for Deluxe can drop to $60 or
increase to $100 (all else equal) before the optimal plan will change.
© John Wiley & Sons, 2011
Chapter 4: Relevant Costs for Nonroutine Operating Decisions
Eldenburg & Wolcott’s Cost Management, 2e
Slide # 55
Q5: Excel Solver Sensitivity Report
Microsoft Excel 9.0 Sensitivity Report
Refer to the problem on Slide #50.
Adjustable Cells
Final Reduced Objective Allowable Allowable
Cell Name Value
Cost Coefficient Increase Decrease
$B$2 Regular 150,000
0
20
2
6.8
$C$2 Deluxe
50000
0
66
34
6
Constraints
Final Shadow Constraint Allowable Allowable
Cell Name Value
Price R.H. Side Increase Decrease
$B$9 DL hr
600,000 8.50
600000
200000
120000
$B$8 mach hr 160,000 7.50
160000
40000
40000
$B$11 D>0
50,000 0.00
0
50000
1E+30
$B$10 R>0
150,000 0.00
0
150000
1E+30
This shows
how much the
RHS of each
constraint can
change
before the
shadow price
will change.
The available DL hours could decrease to 480,000 or increase to 800,000 (all
else equal) before the shadow price for DL would change. The available
machine hours could decrease to 120,000 or increase to 200,000 (all else
equal) before the shadow price for machine hours would change.
© John Wiley & Sons, 2011
Chapter 4: Relevant Costs for Nonroutine Operating Decisions
Eldenburg & Wolcott’s Cost Management, 2e
Slide # 56
Q5: Excel Solver Sensitivity Report
Microsoft Excel 9.0 Sensitivity Report
Refer to the problem on Slide #50.
Adjustable Cells
Final Reduced Objective Allowable Allowable
Cell Name Value
Cost Coefficient Increase Decrease
$B$2 Regular 150,000
0
20
2
6.8
$C$2 Deluxe
50000
0
66
34
6
Constraints
Final Shadow Constraint Allowable Allowable
Cell Name Value
Price R.H. Side Increase Decrease
$B$9 DL hr
600,000 8.50
600000
200000
120000
$B$8 mach hr 160,000 7.50
160000
40000
40000
$B$11 D>0
50,000 0.00
0
50000
1E+30
$B$10 R>0
150,000 0.00
0
150000
1E+30
The shadow
price shows
how much a
one unit
increase in
the RHS of a
constraint will
improve the
total
contribution
margin.
Urban would be willing to pay up to $8.50 to obtain one more DL hour and up
to $7.50 to obtain one more machine hour.
© John Wiley & Sons, 2011
Chapter 4: Relevant Costs for Nonroutine Operating Decisions
Eldenburg & Wolcott’s Cost Management, 2e
Slide # 57
Q7: Impacts to Quality of
Nonroutine Operating Decisions
• The quality of the information used in nonroutine
operating decisions must be assessed.
• There may be more information quality issues (and more
uncertainty) in nonroutine decisions because of the
irregularity of the decisions.
• Three aspects of the quality of information
available can affect decision quality.
• Business risk (changes in economic condition, consumer
demand, regulation, competitors, etc.)
• Information timeliness
• Assumptions in the quantitative and qualitative analyses
© John Wiley & Sons, 2011
Chapter 4: Relevant Costs for Nonroutine Operating Decisions
Eldenburg & Wolcott’s Cost Management, 2e
Slide # 58
Q7: Impacts to Quality of
Nonroutine Operating Decisions
• Short term decision must align to company’s overall
strategic plans
• Must watch for decision maker bias
– Predisposition for specific outcome
– Preference for one type of analysis without considering
other options
• Opportunity costs are often overlooked
• Performing sensitivity analysis can help assess and
minimize business risk
• Established control system incentives (performance
bonuses, etc.) can encourage sub-obtimal decision
making
© John Wiley & Sons, 2011
Chapter 4: Relevant Costs for Nonroutine Operating Decisions
Eldenburg & Wolcott’s Cost Management, 2e
Slide # 59
Cost Management
Measuring, Monitoring, and Motivating Performance
Chapter 5
Job Costing
© John Wiley & Sons, 2011
Chapter 5: Job Costing
Eldenburg & Wolcott’s Cost Management, 2e
Slide # 1
Q1: Job Costing versus Process Costing
Job
Costing
• Used when products can be
distinguished from one
another
Process
Costing
• Used when similar products
are mass produced
Hybrid
Costing
• Includes characteristics of
both job and process costing
© John Wiley & Sons, 2011
Chapter 5: Job Costing
Eldenburg & Wolcott’s Cost Management, 2e
Slide # 3
Q1: Job Costing versus Process Costing
Job Costing
Process Costing
Discrete
Continuous
Product
Fewer units
Many units
Units
Readily identifiable
Fungible
Job or batch
Processing
department
One
Same as the # of
processing
departments
Operations
Cost object
# of WIP
accounts
© John Wiley & Sons, 2011
Chapter 5: Job Costing
Eldenburg & Wolcott’s Cost Management, 2e
Slide # 4
Q1: Assigning Costs to Jobs
Direct
Cost Tracing
Costs
Cost
Cost
Assign-
Object
ment
(Job)
Indirect
Costs
© John Wiley & Sons, 2011
Cost Allocation
Chapter 5: Job Costing
Eldenburg & Wolcott’s Cost Management, 2e
Slide # 5
Q1: Job Cost Records
Each job’s costs are maintained on a job cost record.
The job cost records form the subsidiary ledger for
Work in process inventory.
Date Dir. Materials Dir. Labor Overhead
This information comes
from Materials
Requisition Forms
Total
Overhead costs must be
allocated to each job
This information comes
from Labor Time Reports
© John Wiley & Sons, 2011
Chapter 5: Job Costing
Eldenburg & Wolcott’s Cost Management, 2e
Slide # 6
Q2: Allocating Overhead Costs to Jobs
•
Direct costs are traced to the individual jobs using
source documents.
•
Overhead costs are indirect and cannot be traced
to individual jobs; they must be allocated.
•
An overhead allocation base must be chosen.
•
The overhead allocation base should be some
measure of activity; it should be a reasonably
good cost driver for overhead costs.
© John Wiley & Sons, 2011
Chapter 5: Job Costing
Eldenburg & Wolcott’s Cost Management, 2e
Slide # 7
Q2: Steps in Allocating Overhead
1. Identify the relevant cost object.
2. Identify one or more overhead cost pools and
allocation bases.
3. For each overhead cost pool, calculate an
overhead allocation rate.
4. For each overhead cost pool, allocate costs to the
cost object.
© John Wiley & Sons, 2011
Chapter 5: Job Costing
Eldenburg & Wolcott’s Cost Management, 2e
Slide # 8
Q2: Overhead Allocation Rates
•
Companies may use an actual or an estimated
overhead allocation rate.
Actual allocation rate =
•
Actual overhead cost
Actual quantity of the allocation base
The actual allocation rate cannot be
computed until the accounting period is over.
Estimated allocation rate =
•
Estimated overhead cost
Estimated quantity of the allocation base
The estimated allocation rate can be computed at
the beginning of the accounting period (normal
costing).
© John Wiley & Sons, 2011
Chapter 5: Job Costing
Eldenburg & Wolcott’s Cost Management, 2e
Slide # 9
Q2: Overhead Allocation Rates
Chausse Manufacturing makes road paving equipment. At the
beginning of the year, overhead costs were estimated to be $450,000.
However, actual overhead was $504,000. Chausse uses direct labor
hours as the cost allocation base. At the beginning of the year, total
direct labor hours were estimated at 10,000 hours, but actual direct
labor hours for the year totaled 12,000 hours. Compute the actual
overhead rate and the estimated overhead rate.
Actual allocation rate =
$504,000
 $42/hr
12,000 hours
Estimated allocation rate =
$450,000
 $45/hr
10,000 hours
© John Wiley & Sons, 2011
Chapter 5: Job Costing
Eldenburg & Wolcott’s Cost Management, 2e
Slide # 10
Q2: Actual and Normal Costing
Direct costs
Indirect costs
Actual Costing Normal Costing
Actual costs
Actual costs
Actual rate
Estimated rate
x actual usage x actual usage
of cost
of cost
allocation base allocation base
In normal costing, annual budgeted rates are used
• smoothing effect on numerator
• smoothing effect on denominator
© John Wiley & Sons, 2011
Chapter 5: Job Costing
Eldenburg & Wolcott’s Cost Management, 2e
Slide # 11
Q2: Job Costing Example (Service Sector)
Serena-Sturm is an architectural firm with a professional staff of 5 architects
and a support staff of 7. Some projects are done for a fixed fee, while
others are billed for the actual hours spent on the project. You are given the
following information for Serena-Sturm (SS) for 2005. What is the
estimated indirect cost rate if # of projects is used as the cost allocation
base? Is this a good choice for the cost allocation base?
BUDGETED
ACTUAL
Direct Costs:
Professional labor costs
Professional labor hours
Professional labor rate/hour
$400,000
10,000
$40
$420,000
12,000
$35
Indirect Costs:
Designers, drafters
Office costs
Office salaries & wages
Travel & entertainment
Total indirect costs
$360,000
40,000
45,000
5,000
$450,000
$360,000
80,000
56,800
7,200
$504,000
1,000
3,600
1,200
4,000
Other Information:
Number of projects
Number of blueprints prepared
© John Wiley & Sons, 2011
Estimated indirect cost rate =
$450,000/1,000 projects =
$450/project
Terrible choice for a cost
allocation base; ignores
resource consumption of
the projects.
Chapter 5: Job Costing
Eldenburg & Wolcott’s Cost Management, 2e
Slide # 12
Q2: Job Costing Example (Service Sector)
SS has a costing system with a single direct cost pool. If SS uses a single
indirect cost pool, determine both the estimated and actual indirect cost
rates using (a) number of professional labor hours and (b) number of
blueprints prepared as cost allocation bases.
BUDGETED
ACTUAL
Direct Costs:
Professional labor costs
Professional labor hours
Professional labor rate/hour
$400,000
10,000
$40
$420,000
12,000
$35
Indirect Costs:
Designers, drafters
Office costs
Office salaries & wages
Travel & entertainment
Total indirect costs
$360,000
40,000
45,000
5,000
$450,000
$360,000
80,000
56,800
7,200
$504,000
Other Information:
Number of projects
Number of…