College of Administration and Finance SciencesAssignment (2)

Deadline: Saturday 27/07/2024 @ 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

folder.

• Assignments submitted through email will not be accepted.

• Students are advised to make their work clear and well presented, marks may be

reduced for poor presentation. This includes filling your information on the cover

page.

• Students must mention question number clearly in their answer.

• Late submission will NOT be accepted.

• Avoid plagiarism, the work should be in your own words, copying from students or

other resources without proper referencing will result in ZERO marks. No exceptions.

• All answers must be typed using Times New Roman (size 12, double-spaced) font.

No pictures containing text will be accepted and will be considered plagiarism.

• Submissions without this cover page will NOT be accepted.

Restricted – مقيد

College of Administration and Finance Sciences

Assignment Question(s):

(Marks 15)

Q1. Give example of company using ABC costing and explain the process used in this company to

assign costs in an ABC system?

(3 marks)

Answer:

Q2. Kadhim Co. manufactures product B which is a part of its main product. Kadhim Co makes 50,000

units of product B per year. The production costs are detailed below. An outside supplier has offered

to supply 50,000 units of product B per year at SAR 2.45 each. Should Kadhim Co make or buy the

product B?

(3 marks)

The production cost per unit for manufacturing a unit of product B are:

Direct Materials

0.85

Direct Labor

0.65

Variable Manufacturing Overhead

0.40

Answer:

Q 3. LMN Compagny produces three products K, L and M. During the year, the joint costs of

processing the three products were SAR 480,000.

Production and sales value information were as follows:

Sales Value

Product

Units

at Split-Off

Separable Costs

Selling Price

K

500,000

13 per unit

6.00 per unit

40 per unit

L

300,000

12 per unit

4.00 per unit

37 per unit

M

200,000

8 per unit

3.00 per unit

28 per unit

Allocate the joint costs using the physical output method.

Restricted – مقيد

(3 marks)

College of Administration and Finance Sciences

Answer:

Q4. A company uses a process costing system for its sole processing department. There were 4,000

units in beginning WIP inventory for June and 36,000 units were started in June. The beginning WIP

units were 60% complete and the 3,250 units in ending WIP were 40% complete. All materials are

added at the start of processing.

Required:

a) Compute the no. of units started & completed.

b) Compute the EUP for DM and CC using FIFO and WA methods.

Answer:

Restricted – مقيد

(6 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
R0
(can’t make a negative
D0
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
R0
D0
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 blueprints prepared

© John Wile…

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