### Decision making

```Relevant Costs for Decision
Making
McGraw-Hill/Irwin
13-2
Cost Concepts for Decision Making
Decision making is to choose the best
alternative among many alternatives.
A relevant cost or benefit is a cost or
benefit that differs between alternatives.
McGraw-Hill/Irwin
13-3
Identifying Relevant Costs
Only those costs and benefits that differ between
alternatives are relevant in a decision. All the
other costs and benefits can and should be
ignored.
Two broad categories of costs are never relevant
in any decision. They include:
Sunk costs.
Future costs that do not differ between the
alternatives.
McGraw-Hill/Irwin
13-4
Relevant Cost Analysis: A Two-Step
Process
Step 1 Eliminate costs and benefits that do not differ
between alternatives.
Step 2 Use the remaining costs and benefits that
differ between alternatives in making the
decision. The costs and benefits that remain
are differential costs and benefits.
McGraw-Hill/Irwin
13-5
Sunk Costs
Sunk costs have already been incurred and
cannot be changed now or in the future.
They should be ignored when making
decisions.
Example: You bought an automobile that cost
\$10,000 two years ago. The \$10,000 cost is sunk
because whether you drive it, park it, trade it, or sell
it, you cannot change the \$10,000 cost.
McGraw-Hill/Irwin
13-6
Differential Cost and Revenue
Costs and revenues that differ among
alternatives.
Example: You have a job paying \$1,500 per month in
your hometown. You have a job offer in a neighboring
city that pays \$2,000 per month. The commuting cost
to the city is \$300 per month.
Differential revenue is:
\$2,000 – \$1,500 = \$500
Differential cost is:
\$300
McGraw-Hill/Irwin
13-7
Opportunity Cost
The potential benefit
that is given up when
one alternative is
selected over another.
Example: If you were
not attending college,
you could be earning
\$15,000 per year.
of attending college for
one year is \$15,000.
McGraw-Hill/Irwin
13-8
Different Costs for Different Purposes
Costs that are
relevant in one
decision situation
may not be relevant
in another context.
McGraw-Hill/Irwin
13-9
Total and Differential Cost Approaches
The management of a company is considering a new labor saving
machine that rents for \$3,000 per year. Data about the company’s
annual sales and costs with and without the new machine are:
Sales (5,000 units @ \$40 per unit)
Less variable expenses:
Direct materials (5,000 units @ \$14 per unit)
Direct labor (5,000 units @ \$8 and \$5 per unit)
Variable overhead (5,000 units @ \$2 per unit)
Total variable expenses
Contribution margin
Less fixed expense:
Other
Rent on new machine
Total fixed expenses
Net operating income
McGraw-Hill/Irwin
Current
Situation
\$
200,000
Situation
With New
Machine
\$
200,000
Differential
Costs and
Benefits
-
70,000
40,000
10,000
120,000
80,000
70,000
25,000
10,000
105,000
95,000
15,000
15,000
62,000
62,000
18,000
62,000
3,000
65,000
30,000
(3,000)
(3,000)
12,000
\$
\$
13-10
Total and Differential Cost Approaches
As you can see, the only costs that differ between the alternatives are
the direct labor costs savings and the increase in fixed rental costs.
Current
Situation
\$
200,000
Situation
With New
Machine
\$
200,000
Differential
Costs and
Benefits
-
70,000
40,000
10,000
120,000
80,000
70,000
25,000
10,000
105,000
95,000
15,000
15,000
We can more efficiently analyze the decision 62,000
by
62,000
looking at the different costs and revenues
\$
18,000
and arrive at the same solution.
62,000
3,000
65,000
30,000
(3,000)
(3,000)
12,000
Sales (5,000 units @ \$40 per unit)
Less variable expenses:
Direct materials (5,000 units @ \$14 per unit)
Direct labor (5,000 units @ \$8 and \$5 per unit)
Variable overhead (5,000 units @ \$2 per unit)
Total variable expenses
Contribution margin
Less fixed expense:
Other
Rent on new machine
Total fixed expenses
Net operating income
\$
Net Advantage to Renting the New Machine
Decrease in direct labor costs (5,000 units @ \$3 per unit)
Increase in fixed rental expenses
Net annual cost saving from renting the new machine
McGraw-Hill/Irwin
\$
\$
15,000
(3,000)
12,000
13-11
Learning Objective 2
Prepare an analysis
showing whether a
product line or other
be dropped or retained.
McGraw-Hill/Irwin
13-12
One of the most important decisions
managers make is whether to add or
drop a business segment, such as a
product or a store.
Let’s see how relevant costs should
be used in this type of decision.
McGraw-Hill/Irwin
13-13
Due to the declining popularity of digital
watches, Lovell Company’s digital
watch line has not reported a profit for
several years. Lovell is considering
dropping this product line.
McGraw-Hill/Irwin
13-14
Segment Income Statement
Digital Watches
Sales
Less: variable expenses
Variable manufacturing costs
Variable shipping costs
Commissions
Contribution margin
Less: fixed expenses
Salary of line manager
Depreciation of equipment
Rent - factory space
Net operating loss
McGraw-Hill/Irwin
\$ 500,000
\$ 120,000
5,000
75,000
\$ 60,000
90,000
50,000
100,000
70,000
30,000
200,000
\$ 300,000
400,000
\$ (100,000)
13-15
A Contribution Margin Approach
DECISION RULE
Lovell should drop the digital watch segment only
when doing so increases its profit.
This would only happen if the fixed cost savings
exceed the lost contribution margin.
Let’s look at this solution.
McGraw-Hill/Irwin
13-16
Segment Income Statement
Digital Watches
Sales
Less: variable expenses
Variable manufacturing costs
Variable shipping costs
Commissions
Contribution margin
Less: fixed expenses
Salary of line manager
Depreciation of equipment
Rent - factory space
Net operating loss
McGraw-Hill/Irwin
\$ 500,000
\$ 120,000
5,000
75,000
\$ 60,000
90,000
50,000
100,000
70,000
30,000
200,000
\$ 300,000
400,000
\$ (100,000)
13-17
Segment Income Statement
Digital Watches
Sales
\$ 500,000
Less: variable
expenses has revealed that
Investigation
Variable manufacuring costs \$ 120,000
total
and general
Variable shipping costs
5,000
not be affected
Commissions
200,000
Contribution
margin
if the
digital watch line is dropped.\$ 300,000
Less: fixed expenses
\$ 60,000
The
fixed
general
Salary
of line
manager
90,000and general
to this product
Depreciation of expenses
equipment assigned
50,000
100,000
would be- direct
reallocated to other
product lines.
Rent - factory space
70,000
30,000
400,000
Net operating loss
\$ (100,000)
McGraw-Hill/Irwin
13-18
Segment Income Statement
Digital Watches
Sales
\$ 500,000
Less: variable expenses
Variable
manufacturing
\$ 120,000
The
equipment
usedcosts
to manufacture
Variable
shipping
costshas no resale
5,000
digital
watches
Commissions
75,000
200,000
value
or alternative use.
Contribution
margin
\$ 300,000
Less: fixed expenses
\$ 60,000
Salary of line manager
90,000
Depreciation of equipment
50,000
Should Lovell
retain or drop
100,000
Rent - factory space the digital watch
70,000 segment?
30,000
400,000
Net operating loss
\$ (100,000)
McGraw-Hill/Irwin
13-19
A Contribution Margin Approach
Contribution Margin
Solution
Contribution margin lost if digital
watches are dropped
Less fixed costs that can be avoided
Salary of the line manager
\$
90,000
100,000
Rent - factory space
70,000
McGraw-Hill/Irwin
\$ (300,000)
260,000
\$ (40,000)
13-20
Comparative Income Approach
The Lovell solution can also be obtained by
preparing comparative income statements
showing results with and without the digital
watch segment.
Let’s look at this second approach.
McGraw-Hill/Irwin
13-21
Comparative Income Approach
Solution
Keep
Drop
Digital
Digital
Watches
Watches
Difference
Sales
\$ 500,000
\$
\$ (500,000)
Less variable expenses:
Manufacturing expenses
120,000
120,000
Shipping
5,000
5,000
Commissions
75,000
75,000
Total variable expenses
200,000
200,000
Contribution margin
300,000
(300,000)
Less fixed expenses:
60,000
Salary of line manager
90,000
Depreciation
50,000
If the digital watch
100,000
line is dropped, the
Rent - factory space
70,000
company gives up
30,000
Total fixed expenses
400,000
its contribution
Net operating loss
\$ (100,000)
margin.
McGraw-Hill/Irwin
13-22
Comparative Income Approach
Solution
Keep
Drop
Digital
Digital
Watches
Watches
Difference
Sales
\$ 500,000
\$
\$ (500,000)
Less variable expenses:
Manufacturing expenses
120,000
120,000
Shipping
5,000
5,000
Commissions
75,000
75,000
Total variable expenses
200,000
200,000
Contribution margin
300,000
(300,000)
Less fixed expenses:
60,000
60,000
Salary of line manager
90,000
Depreciation
50,000
On 100,000
the other hand, the general
Rent - factory space
70,000
factory
30,000
same.
So this cost really isn’t
Total fixed expenses
400,000
Net operating loss
\$ (100,000) relevant.
McGraw-Hill/Irwin
13-23
Comparative Income Approach
Solution
Keep
Drop
Digital
Digital
Watches
Watches
Sales
\$ 500,000
\$
Less variable expenses:
But
we
wouldn’t
need
a
Manufacturing expenses
120,000
manager for5,000
the product -line
Shipping
Commissions
75,000
anymore.
Total variable expenses
200,000
Contribution margin
300,000
Less fixed expenses:
60,000
60,000
Salary of line manager
90,000
Depreciation
50,000
100,000
Rent - factory space
70,000
30,000
Total fixed expenses
400,000
Net operating loss
\$ (100,000)
McGraw-Hill/Irwin
Difference
\$ (500,000)
120,000
5,000
75,000
200,000
(300,000)
90,000
13-24
Comparative Income Approach
Solution
Keep
Drop
Digital
Digital
Watches
Watches
Difference
Sales
\$ 500,000
\$
\$ (500,000)
If variable
the digital
watch line is dropped, the net -book value
Less
expenses:
Manufacturing
expenseswould be written
120,000 off. The depreciation
120,000
of
the equipment
Shipping
5,000
5,000
that
would
have
been
taken
will
flow
through
the
Commissions
75,000
75,000
Total variable expenses
200,000
200,000
income statement as
Contribution margin
300,000
(300,000)
Less fixed expenses:
60,000
60,000
Salary of line manager
90,000
90,000
Depreciation
50,000
50,000
100,000
Rent - factory space
70,000
30,000
Total fixed expenses
400,000
Net operating loss
\$ (100,000)
McGraw-Hill/Irwin
13-25
Comparative Income Approach
Solution
Keep
Drop
Digital
Digital
Watches
Watches
Sales
\$ 500,000
\$
Less variable expenses:
Manufacturing expenses
120,000
Shipping
5,000
Commissions
75,000
Total variable expenses
200,000
Contribution margin
300,000
Less fixed expenses:
60,000
60,000
Salary of line manager
90,000
Depreciation
50,000
50,000
100,000
Rent - factory space
70,000
30,000
30,000
Total fixed expenses
400,000
140,000
Net operating loss
\$ (100,000)
\$ (140,000)
McGraw-Hill/Irwin
Difference
\$ (500,000)
120,000
5,000
75,000
200,000
(300,000)
90,000
100,000
70,000
260,000
\$ (40,000)
13-26
Beware of Allocated Fixed Costs
Why should we keep the
digital watch segment
when it’s showing a
\$100,000 loss?
McGraw-Hill/Irwin
13-27
Beware of Allocated Fixed Costs
way we allocate
common fixed costs to
our products.
McGraw-Hill/Irwin
13-28
Beware of Allocated Fixed Costs
Our allocations can
make a segment look
less profitable than it
really is.
McGraw-Hill/Irwin
13-29
Learning Objective 3
analysis.
McGraw-Hill/Irwin
13-30
The Make or Buy Decision: An Example
• Essex Company manufactures part 4A that is
used in one of its products.
• The unit product cost of this part is:
Direct materials
Direct labor
Depreciation of special equip.
Supervisor's salary
Unit product cost
McGraw-Hill/Irwin
\$
9
5
1
3
2
10
\$ 30
13-31
• An outside supplier has offered to provide the
20,000 parts at a cost of \$25 per part.
Should we accept the supplier’s offer?
• The special equipment used to manufacture part 4A
has no resale value.
• The total amount of general factory overhead, which
is allocated on the basis of direct labor hours, would
be unaffected by this decision.
• The \$30 unit product cost is based on 20,000 parts
produced each year.
McGraw-Hill/Irwin
13-32
Cost
Per Unit
Outside purchase price
\$ 25
Direct materials
Direct labor
Depreciation of equip.
Supervisor's salary
Total cost
\$
9
5
1
3
2
10
\$ 30
Cost of 20,000 Units
Make
\$ 500,000
180,000
100,000
20,000
40,000
\$ 340,000
\$ 500,000
20,000 × \$9 per unit = \$180,000
McGraw-Hill/Irwin
13-33
Cost
Per Unit
Outside purchase price
\$ 25
Direct materials
Direct labor
Depreciation of equip.
Supervisor's salary
Total cost
\$
9
5
1
3
2
10
\$ 30
Cost of 20,000 Units
Make
\$ 500,000
180,000
100,000
20,000
40,000
\$ 340,000
\$ 500,000
The special equipment has no resale
value and is a sunk cost.
McGraw-Hill/Irwin
13-34
Cost
Per Unit
Outside purchase price
\$ 25
Direct materials
Direct labor
Depreciation of equip.
Supervisor's salary
Total cost
\$
9
5
1
3
2
10
\$ 30
Cost of 20,000 Units
Make
\$ 500,000
180,000
100,000
20,000
40,000
\$ 340,000
\$ 500,000
Not avoidable; irrelevant. If the product is
dropped, it will be reallocated to other products.
McGraw-Hill/Irwin
13-35
Cost
Per Unit
Outside purchase price
\$ 25
Direct materials
Direct labor
Depreciation of equip.
Supervisor's salary
Total cost
\$
9
5
1
3
2
10
\$ 30
Cost of 20,000 Units
Make
\$ 500,000
180,000
100,000
20,000
40,000
\$ 340,000
\$ 500,000
Should we make or buy part 4A?
McGraw-Hill/Irwin
13-36
Opportunity Cost
An opportunity cost is the benefit that is foregone
(i.e., given up) as a result of pursuing some course of action.
Opportunity costs are not actual dollar outlays and are not
recorded in the formal accounts of an organization.
How would this concept potentially relate to the Essex
Company?
>> Think about the capacity that is no longer used for part 4A.
For example, what if \$200,000 income is generated from
using the facilities for other activities?
McGraw-Hill/Irwin
13-37
Learning Objective 4
Prepare an analysis
showing whether a special
order should be accepted.
McGraw-Hill/Irwin
13-38
Key Terms and Concepts
A special order is a one-time
order that is not considered
part of the company’s normal
When analyzing a special
order, only the incremental
costs and benefits are
relevant.
McGraw-Hill/Irwin
13-39
Special Orders
 Jet, Inc. makes a single product whose normal selling price
is \$20 per unit.
 A foreign distributor offers to purchase 3,000 units for \$10
per unit.
 This is a one-time order that would not affect the
 Annual capacity is 10,000 units, but Jet, Inc. is currently
producing and selling only 5,000 units.
Should Jet accept the offer?
McGraw-Hill/Irwin
13-40
Special Orders
Jet, Inc.
Contribution Income Statement
Revenue (5,000 × \$20)
\$ 100,000
Variable costs:
Direct materials
\$ 20,000
Direct labor
5,000
\$8 unit variable
10,000
Marketing costs
5,000
Total variable costs
40,000
Contribution margin
60,000
Fixed costs:
Marketing costs
20,000
Total fixed costs
48,000
Net operating income
\$ 12,000
McGraw-Hill/Irwin
cost
13-41
Special Orders
If Jet accepts the offer, net operating income will
increase by \$6,000.
Increase in revenue (3,000 × \$10)
Increase in costs (3,000 × \$8 variable cost)
Increase in net income
\$ 30,000
24,000
\$ 6,000
Note: This answer assumes that fixed costs are
unaffected by the order and that all variable costs
are the same for the special order.
McGraw-Hill/Irwin
13-42
Quick Check 
Northern Optical ordinarily sells the X-lens for \$50.
The variable production cost is \$10, the fixed
production cost is \$18 per unit, and the variable
selling cost is \$1. A customer has requested a
special order for 10,000 units of the X-lens to be
imprinted with the customer’s logo. This special
order would not involve any selling costs, but
Northern Optical would have to purchase an
imprinting machine for \$50,000.
(see the next page)
McGraw-Hill/Irwin
13-43
Quick Check 
What is the minimum price below which Northern
Optical should not go in its negotiations with the
customer? In other words, below what price would
Northern Optical actually be losing money on the
sale? There is ample idle capacity to fulfill the order
and the imprinting machine has no further use after
this order.
a. \$50
b. \$10
c. \$15
d. \$29
McGraw-Hill/Irwin
13-44
Quick Check 
What is the rock bottom minimum price below which
Northern Optical should not go in its negotiations
with the customer? In other words, below what
price would Northern Optical actually be losing
money on the sale? There is ample idle capacity to
fulfill the order and the imprinting machine has no
further use after this order.
Variable production cost
\$100,000
a. \$50
+ 50,000
b. \$10
Total relevant cost
\$150,000
c. \$15 Number of units
10,000
d. \$29 Incremental cost per unit =
\$15
McGraw-Hill/Irwin
13-45
Learning Objective 5
Determine the most
profitable use of a
constrained resource and
the value of obtaining
more of the constrained
resource.
McGraw-Hill/Irwin
13-46
Key Terms and Concepts
When a limited resource
of some type restricts
the company’s ability to
satisfy demand, the
company is said to have
a constraint.
The machine or process
that is limiting overall
output is called the
bottleneck – it is the
constraint.
McGraw-Hill/Irwin
13-47
Utilization of a Constrained Resource
•
•
When a constraint exists, a company should not
promote those products that have the highest
unit contribution margin.
Rather, it should promote those products that
earn the highest contribution margin in relation to
the constraining resource.
McGraw-Hill/Irwin
13-48
Utilization of a Constrained Resource: An
Example
Ensign Company produces two products and
selected data are shown below:
Product
1
Selling price per unit
Less variable expenses per unit
Contribution margin per unit
Current demand per week (units)
Contribution margin ratio
Processing time required
on machine A1 per unit
McGraw-Hill/Irwin
2
\$
60
36
\$ 24
2,000
40%
1.00 min.
\$
50
35
\$ 15
2,200
30%
0.50 min.
13-49
Utilization of a Constrained Resource
• Machine A1 is the constrained resource and
is being used at 100% of its capacity.
• There is excess capacity on all other
machines.
• Machine A1 has a capacity of 2,400 minutes
per week.
Should Ensign focus its efforts on
Product 1 or Product 2?
McGraw-Hill/Irwin
13-50
Quick Check 
How many units of each product can be
processed through Machine A1 in one minute?
a.
b.
c.
d.
McGraw-Hill/Irwin
Product 1
1 unit
1 unit
2 units
2 units
Product 2
0.5 unit
2.0 units
1.0 unit
0.5 unit
13-51
Quick Check 
How many units of each product can be
processed through Machine A1 in one minute?
a.
b.
c.
d.
Product 1
1 unit
1 unit
2 units
2 units
Product 2
0.5 unit
2.0 units
1.0 unit
0.5 unit
I was just checking to make sure
you are with us.
McGraw-Hill/Irwin
13-52
Quick Check 
What generates more profit for the company,
using one minute of machine A1 to process
Product 1 or using one minute of machine A1
to process Product 2?
a. Product 1
b. Product 2
c. They both would generate the same profit.
d. Cannot be determined.
McGraw-Hill/Irwin
13-53
Quick Check 
With one minute of machine A1, we could
makegenerates
1 unit of Product
1, with
a contribution
What
more profit
for the
company,
margin
\$24, or
units of A1
Product
2, each
using
oneof
minute
of2machine
to process
contribution
margin
of \$15. A1
Productwith
1 ora using
one minute
of machine
to process Product
2?= \$30 > \$24
2 × \$15
a. Product 1
b. Product 2
c. They both would generate the same profit.
d. Cannot be determined.
McGraw-Hill/Irwin
13-54
Utilization of a Constrained Resource
The key is the contribution margin per unit of the
constrained resource.
Product
1
Contribution margin per unit
Time required to produce one unit
Contribution margin per minute
2
\$
÷
24
\$
15
1.00 min. ÷
0.50 min.
\$
24
\$
30
Product 2 should be emphasized. It provides more
valuable use of the constrained resource machine A1,
yielding a contribution margin of \$30 per minute as
opposed to \$24 for Product 1.
McGraw-Hill/Irwin
13-55
Utilization of a Constrained Resource
The key is the contribution margin per unit of the
constrained resource.
Product
1
Contribution margin per unit
Time required to produce one unit
Contribution margin per minute
2
\$
÷
24
\$
15
1.00 min. ÷
0.50 min.
\$
24
\$
30
If there are no other considerations, the best
plan would be to produce to meet current
demand for Product 2 and then use remaining
capacity to make Product 1.
McGraw-Hill/Irwin
13-56
Utilization of a Constrained Resource
Let’s see how this plan would work.
Alloting Our Constrained Resource (Machine A1)
Weekly demand for Product 2
Time required per unit
Total time required to make
Product 2
McGraw-Hill/Irwin
×
2,200 units
0.50 min.
1,100 min.
13-57
Utilization of a Constrained Resource
Let’s see how this plan would work.
Alloting Our Constrained Resource (Machine A1)
Weekly demand for Product 2
Time required per unit
Total time required to make
Product 2
Total time available
Time used to make Product 2
Time available for Product 1
McGraw-Hill/Irwin
×
2,200 units
0.50 min.
1,100 min.
2,400 min.
1,100 min.
1,300 min.
13-58
Utilization of a Constrained Resource
Let’s see how this plan would work.
Alloting Our Constrained Resource (Machine A1)
Weekly demand for Product 2
Time required per unit
Total time required to make
Product 2
Total time available
Time used to make Product 2
Time available for Product 1
Time required per unit
Production of Product 1
McGraw-Hill/Irwin
×
2,200 units
0.50 min.
1,100 min.
÷
2,400
1,100
1,300
1.00
1,300
min.
min.
min.
min.
units
13-59
Utilization of a Constrained Resource
According to the plan, we will produce 2,200 units
of Product 2 and 1,300 of Product 1. Our
contribution margin looks like this.
Production and sales (units)
Contribution margin per unit
Total contribution margin
Product 1
1,300
\$
24
\$ 31,200
Product 2
2,200
\$
15
\$ 33,000
The total contribution margin for Ensign is \$64,200.
McGraw-Hill/Irwin
13-60
Quick Check 
Colonial Heritage makes reproduction colonial
furniture from select hardwoods.
Chairs
Selling price per unit
\$80
Variable cost per unit
\$30
Board feet per unit
2
Monthly demand
600
Tables
\$400
\$200
10
100
The company’s supplier of hardwood will only be
able to supply 2,000 board feet this month. Is this
enough hardwood to satisfy demand?
a. Yes
b. No
McGraw-Hill/Irwin
13-61
Quick Check 
Colonial Heritage makes reproduction colonial
furniture from select hardwoods.
Chairs
Selling price per unit
\$80
Variable cost per unit
\$30
Board feet per unit
2
Monthly demand
600
Tables
\$400
\$200
10
100
The company’s supplier of hardwood will only be
able to supply 2,000 board feet this month. Is this
enough hardwood to satisfy demand?
a. Yes
b. No
(2  600) + (10  100 ) = 2,200 > 2,000
McGraw-Hill/Irwin
13-62
Quick Check 
Chairs
Selling price per unit
\$80
Variable cost per unit
\$30
Board feet per unit
2
Monthly demand
600
Tables
\$400
\$200
10
100
The company’s supplier of hardwood will only
be able to supply 2,000 board feet this month.
What plan would maximize profits?
a. 500 chairs and 100 tables
b. 600 chairs and 80 tables
c. 500 chairs and 80 tables
d. 600 chairs and 100 tables
McGraw-Hill/Irwin
13-63
Quick Check 
Chairs Tables
Selling price
\$ 80 \$ 400
Chairs Tables
Variable
200
Selling price per
unit cost\$80
\$400 30
Variable cost Contribution
per unit
\$30
margin \$200
\$ 50 \$ 200
Board feet per unit
2
10
Board feet
2
10
Monthly demand
600
100
CM per board foot
\$ 25 \$ 20
The company’s supplier of hardwood will only
of chairs
be able to supplyProduction
2,000 board
feet this 600
month.
feet required
What plan would Board
maximize
profits? 1,200
Board feet remaining
800
a. 500 chairs and 100 tables
Board feet per table
10
b. 600 chairs andProduction
80 tablesof tables
80
c. 500 chairs and 80 tables
d. 600 chairs and 100 tables
McGraw-Hill/Irwin
13-64
Quick Check 
As before, Colonial Heritage’s supplier of hardwood will
only be able to supply 2,000 board feet this month.
Assume the company follows the plan we have
proposed. Up to how much should Colonial Heritage be
willing to pay above the usual price to obtain more
hardwood?
a. \$40 per board foot
b. \$25 per board foot
c. \$20 per board foot
d. Zero
McGraw-Hill/Irwin
13-65
Quick Check 
As before, Colonial Heritage’s supplier of hardwood will
The
wood
would
used
to make
only be
able to supply
2,000
boardbe
feet
this month.
tables.
In this use,
each
board
foot of
Assume
the company
follows
the plan
we have
proposed. Up
to how
should
Heritage
be
wood
willmuch
allow
the Colonial
company
to earn
willing
to pay above
price to obtain
moreand
an
\$20the
of usual
contribution
margin
hardwood?
profit.
a. \$40 per board foot
b. \$25 per board foot
c. \$20 per board foot
d. Zero
McGraw-Hill/Irwin
13-66
Multiple Constraints
• Suppose that you are in charge of producing and
selling two products.
• Product 1 requires 3 hours of machine operation
while Product 2 requires 6 hours. The total available
machine hour is 24000.
• There is also a constraint on labor hours. Each
product requires 2 labor hours, but only 12000 labor
hours are available.
• Assume the following information about the price
and unit variable cost, and the total fixed costs
\$36,000 are unaffected by your decision.
McGraw-Hill/Irwin
13-67
Multiple Constraints
#1
#2
p
10
15
v
4
7
ucm
6
8
MH
3
6
ucm/MH
2
1.333
LH
2
2
ucm/LH
3
4
McGraw-Hill/Irwin
Constraint
24000
12000
13-68
Multiple Constraints
• Checking the ucm per MH, Product 1 is more
profitable.
• Checking the ucm per LH, Product 2 is more
profitable.
• What is then an optimal output choice?
McGraw-Hill/Irwin
13-69
Multiple Constraints
• Max
s.t.
6q1+ 8q2 – 36000
3q1+ 6q2  24000  MH constraint
2q1 + 2q2  12000  LH constraint
q1, q2  0.
• We can solve the problem using Solver in Excel.
• The optimal solution is q1= 4000, q2= 2000 and the
resulting profit equals \$4000.
McGraw-Hill/Irwin
13-70
Learning Objective 6
Prepare an analysis
showing whether joint
products should be sold at
the split-off point or
processed further.
McGraw-Hill/Irwin
13-71
Joint Costs
• In some industries, a number of end
products are produced from a single raw
material input.
• Two or more products produced from a
common input are called joint products.
• The point in the manufacturing process
where each joint product can be
recognized as a separate product is
called the split-off point.
McGraw-Hill/Irwin
13-72
Joint Products
Oil
Joint
Input
Common
Production
Process
Gasoline
Chemicals
Split-Off
Point
McGraw-Hill/Irwin
13-73
Joint Products
Joint
Costs
Joint
Input
Common
Production
Process
Oil
Gasoline
Chemicals
Split-Off
Point
McGraw-Hill/Irwin
Separate
Processing
Final
Sale
Final
Sale
Separate
Processing
Final
Sale
Separate
Product
Costs
13-74
The Pitfalls of Allocation
Joint costs are often
allocated to end products on
the basis of the relative
sales value of each product
or on some other basis.
Although allocation is needed for
some purposes such as balance
sheet inventory valuation,
allocations of this kind are very
dangerous for decision making.
McGraw-Hill/Irwin
13-75
Sell or Process Further
Joint costs are irrelevant in decisions regarding what to
do with a product from the split-off point forward
(i.e., stop or process further).
It will always be profitable to continue processing a
joint product after the split-off point as long as the
incremental revenue exceeds the incremental
processing costs incurred after the split-off point.
McGraw-Hill/Irwin
13-76
Sell or Process Further: An Example
• Sawmill, Inc. cuts logs from which unfinished
lumber and sawdust are the immediate joint
products.
• Unfinished lumber could be sold “as is,” or
processed further into finished lumber.
• Sawdust could also be sold “as is” to gardening
wholesalers, or processed further into “prestologs.”
McGraw-Hill/Irwin
13-77
Sell or Process Further
Data about Sawmill’s joint products includes:
Sales value at the split-off point
Sales value after further processing
Allocated joint product costs
Cost of further processing
McGraw-Hill/Irwin
Per Log
Lumber
Sawdust
\$
140
\$
40
270
176
50
50
24
20
13-78
Sell or Process Further
Analysis of Sell or Process Further
Per Log
Sales value after further processing
Sales value at the split-off point
Incremental revenue
McGraw-Hill/Irwin
Lumber
Sawdust
\$
\$
270
140
130
50
40
10
13-79
Sell or Process Further
Analysis of Sell or Process Further
Per Log
Sales value after further processing
Sales value at the split-off point
Incremental revenue
Cost of further processing
Profit (loss) from further processing
McGraw-Hill/Irwin
Lumber
Sawdust
\$
\$
\$
270
140
130
50
80
\$
50
40
10
20
(10)