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Appendix B - Lecture Notes
AppB-1
Appendix B
Lecture Notes
Main theme: Perhaps more than any other information,
managers would like to know the profitability of their
products, customers, and other business segments.
Accordingly, this appendix provides a coherent
framework for measuring profitability. It distinguishes
between absolute profitability and relative profitability.
I. Absolute profitability
A. Key concepts
i. Absolute profitability measures the impact
on the organization’s overall profits of
adding or dropping a particular segment
such as a product or customer – without
making any other changes. For example:
1. If Coca Cola were considering closing down
its operations in the African country of
Zimbabwe, managers would be interested in
the absolute profitability of those
operations.
ii. Computing absolute profitability
1. For an existing segment, compare the
revenues that would be lost from dropping
the segment to the costs that would be
avoided.
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2. For a potential new segment, compare the
additional revenues from adding the
segment to the additional costs that would
be incurred.
3. In practice, figuring out what costs would
change and what costs would not change if a
segment were dropped or added can be very
difficult.
a. Activity-based costing can be helpful
in this regard, but care must be
exercised to ensure that a given cost
will really change.
4. For examples of the measurement of
absolute profitability see:
a. Segment Reporting in Chapter 6.
b. ABC Action Analysis in Appendix 7A.
c. Adding and Dropping Product Lines
and Other Segments in Chapter 12.
II. Relative profitability
Learning Objective 1: Compute the profitability index
and use it to select from among possible actions.
A. Key concepts
i. Relative profitability is concerned with
ranking products, customers, and other
business segments to determine which should
be emphasized.
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ii. Managers are interested in ranking segments
if a constraint forces them to make trade-
offs among the segments.
1. In the absence of a constraint, all segments
that are absolutely profitable should be
pursued.
iii. In general, the profitability of segments
should be measured by the profitability
index as shown. Notice:
1. The term “incremental profit from the
segment” in the numerator of this equation
is synonymous with the absolute
profitability of the segment.
B. Relative profitability: an example
i. Assume that Segments A and B earn the
incremental profit and have the constraint
requirements as shown.
1. The profitability indexes for Segments A
($1,000 per hour) and B ($500 per hour)
suggest that Segment A makes a more
profitable use of the constraining resource
than Segment B.
C. The project profitability index
i. We have already encountered examples of the
profitability index in previous chapters. For
example, in Chapter 13, the project
profitability index was defined as shown.
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1. The project profitability index is used when
a company has more long-term projects
with positive net present values than it
can fund.
2. The net present value of the project goes in
the numerator since it represents the
incremental profit from the segment.
3. The investment funds are the constraint,
so the amount of investment required by a
project goes in the denominator.
ii. Quality Kitchen Design: an example
1. Assume that management is considering ten
short-term projects with incremental
profits, constraint requirements, and
profitability indexes as shown. Notice:
a. If all ten projects were accepted, they
would require a total of 100 hours.
2. If management only has 46 hours
available, which projects should be
accepted?
a. The projects should be ranked as
shown using the project profitability
index. Notice:
(1). The line drawn beneath
Project A signifies that 46
cumulative constraint hours
have been used.
b. The optimal profit of $32,930 would
be computed as shown.
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III. Volume trade-off decisions
Learning Objective 2: Compute and use the
profitability index in volume trade-off decisions.
A. Key concepts
i. Volume trade-off decisions need to be made
when a company must produce less than the
market demands of some products due to the
existence of a constraint.
ii. In volume trade-off decisions where fixed
costs are irrelevant, the profitability index
takes the special form as shown. Notice:
1. This equation mirrors the “contribution
margin per unit of the constrained
resource” concept that was introduced in
Chapter 12.
B. Volume trade-off decisions: an example
i. Assume that a company makes three
products with unit contribution margins,
weekly demand, and machine constraint
requirements as shown.
ii. Given these assumptions, satisfying demand
for all three products would require 2,700
minutes of constraint time as shown.
iii. If only 2,200 minutes of machine constraint
time are available, which products should
be produced in what quantities?
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1. The first step is to compute the profitability
index for each product as shown. Notice:
a. Product VB30 should be produced first
($5 per minute), followed by SQ500
($4 per minute), and RX200 ($3 per
minute).
2. The second step is to compute the optimal
production plan as shown. Notice:
a. There are only enough minutes
available (e.g., 1,000 minutes) to
make 200 units of RX200 even though
weekly demand is 300 units.
3. The third step is to compute the total
contribution margin earned under the
optimal plan ($8,600) as shown. Notice:
a. There is no other combination of
production that will earn a higher total
contribution.
IV. Managerial implications
Learning Objective 3: Compute and use the
profitability index in other business decisions.
A. Other applications of the profitability index
i. Sales commissions
1. Assume the selling prices, unit contribution
margins, and constraint requirements as
shown for products RX200, VB30, and
SQ500.
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a. If salespersons are paid commissions
based on sales, they will try hardest to
sell RX200 (unit selling price = $40).
b. However, RX200 is the least
profitable product given the current
constraint ($3 per minute).
c. This suggests that salespersons should
be paid commissions based on the
profitability index and the amount
of constraint time sold rather than on
sales revenue.
ii. Pricing new products
1. The price of a new product should at least
cover the variable cost of producing it plus
the opportunity cost of displacing the
production of existing products to make it
(this approach assumes that fixed cost
remain unchanged).
a. In equation form, the minimum
selling price is computed as shown.
2. For purposes of illustration, assume that the
company mentioned in the prior example
has designed a new product, WR6000, with
a variable cost per unit and constraint
requirements as shown. What is the
minimum price that should be charged
for this new product?
a. The first step is to recognize that the
price of WR6000 must cover its $30
variable cost per unit.
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b. The second step is to recognize that
producing WR6000 will require
displacing production of RX200,
VB30, or SQ500.
(1). Since RX200 has the lowest
profitability index of $3 per
minute it should be displaced
first.
c. The third step is to compute the
opportunity cost per unit associated
with displacing production of RX200
($18 per unit).
d. The fourth step is to add the variable
cost per unit ($30) to the opportunity
cost per unit ($18) to arrive at the
minimum selling price ($48).
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