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Appendix B
Profitability Analysis
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B-2
Absolute Profitability
Absolute profitability measures the impact on Absolute profitability measures the impact on the organization’s overall profits of the organization’s overall profits of adding or adding or
droppingdropping a particular segment such as a a particular segment such as a product or customer – without making any product or customer – without making any
other changes.other changes.
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Computing Absolute Profitability
For an Existing SegmentFor an Existing SegmentCompare the revenues that would be lost fromCompare the revenues that would be lost from
dropping that segment to the costs that dropping that segment to the costs that would be avoided.would be avoided.
For an Existing SegmentFor an Existing SegmentCompare the revenues that would be lost fromCompare the revenues that would be lost from
dropping that segment to the costs that dropping that segment to the costs that would be avoided.would be avoided.
For a New SegmentFor a New SegmentCompare the additional revenues from addingCompare the additional revenues from adding
that segment to the costs that would be incurred.that segment to the costs that would be incurred.
For a New SegmentFor a New SegmentCompare the additional revenues from addingCompare the additional revenues from adding
that segment to the costs that would be incurred.that segment to the costs that would be incurred.
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Learning Objective 1
Compute the profitability Compute the profitability index and use it to select index and use it to select
from among possible from among possible actions.actions.
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Relative Profitability
Relative profitability is concerned with ranking products, customers, and other business segments
to determine which should be emphasized in an environment of scarce resources.
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Relative Profitability
Managers are interested in ranking segments if a constraint forces them to make trade-offs among
segments.
In the absence of a constraint, all segments that are absolutely profitable should be pursued.
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B-7
Relative Profitability
ProfitabilityIndex
Incremental profit from the segment
Amount of the constrained resources required by the segment
=
Incremental profit from the segment isIncremental profit from the segment isthe absolute profitability of the segment.the absolute profitability of the segment.Incremental profit from the segment isIncremental profit from the segment is
the absolute profitability of the segment.the absolute profitability of the segment.
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B-8
Profitability Index
Management of Matrix, Inc. developed the following information concerning its two segments:
Management of Matrix, Inc. developed the following information concerning its two segments:
Segment A Segment B
Incremental profit $ 100,000 $ 200,000
Amount of constrained resource required 100 hours 400 hours
Segment A Segment B
Incremental profit $ 100,000 $ 200,000
Amount of constrained resource required 100 hours 400 hours
Profitability index 1,000$ 500$
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Project Profitability Index
ProjectProfitability
Index
Net present value of the project
Amount of investmentrequired by the project
=
The project profitability index is usedThe project profitability index is used when a company has more long-term projects when a company has more long-term projects
with positive net present values than it can fund. with positive net present values than it can fund.
The project profitability index is usedThe project profitability index is used when a company has more long-term projects when a company has more long-term projects
with positive net present values than it can fund. with positive net present values than it can fund.
From Chapter 14
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Project Profitability Index
ProjectProfitability
Index
Net present value of the project
Amount of investmentrequired by the project
=
The net present value of the projectThe net present value of the project goes in the numerator since it represents goes in the numerator since it represents the incremental profit from the segment. the incremental profit from the segment.
The net present value of the projectThe net present value of the project goes in the numerator since it represents goes in the numerator since it represents the incremental profit from the segment. the incremental profit from the segment.
From Chapter 14
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Project Profitability Index
ProjectProfitability
Index
Net present value of the project
Amount of investmentrequired by the project
=
The investment funds are theThe investment funds are theconstraint, so the amount of investmentconstraint, so the amount of investment
required by a project goes in the denominator.required by a project goes in the denominator.
The investment funds are theThe investment funds are theconstraint, so the amount of investmentconstraint, so the amount of investment
required by a project goes in the denominator.required by a project goes in the denominator.
From Chapter 14
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Incremental
Profit
Constrained Resource Required
(a) (b) (a) ÷ (b)
Project A 9,180$ 17 hours 540$ per hour
Project B 7,200 9 hours 800 per hour
Project C 7,040 16 hours 440 per hour
Project D 5,680 8 hours 710 per hour
Project E 5,330 13 hours 410 per hour
Project F 4,280 4 hours 1,070 per hour
Project G 4,160 13 hours 320 per hour
Project H 3,720 12 hours 310 per hour
Project I 3,650 5 hours 730 per hour
Project J 2,940 3 hours 980 per hour
100 hours
Profitability Index
Quality Kitchen Design: An Example
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Incremental
Profit
Constrained Resource Required
(a) (b) (a) ÷ (b)
Project A 9,180$ 17 hours 540$ per hour
Project B 7,200 9 hours 800 per hour
Project C 7,040 16 hours 440 per hour
Project D 5,680 8 hours 710 per hour
Project E 5,330 13 hours 410 per hour
Project F 4,280 4 hours 1,070 per hour
Project G 4,160 13 hours 320 per hour
Project H 3,720 12 hours 310 per hour
Project I 3,650 5 hours 730 per hour
Project J 2,940 3 hours 980 per hour
100 hours
Profitability Index
Quality Kitchen Design: An Example
If managementIf managementonly has 46 hours available,only has 46 hours available,
which projects shouldwhich projects should be accepted? be accepted?
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Ranking Based on Profitability Index
Incremental
Profit
Constrained Resource Required
Profitability Index
Cumulative Hours
Incremental Profit
(a) (b) (a) ÷ (b)
Project F 4,280$ 4 hours 1,070$ 4 hours 4,280$
Project J 2,940 3 hours 980 7 hours 2,940
Project B 7,200 9 hours 800 16 hours 7,200
Project I 3,650 5 hours 730 21 hours 3,650
Project D 5,680 8 hours 710 29 hours 5,680
Project A 9,180 17 hours 540 46 hours 9,180
Project C 7,040 16 hours 440 62 hours
Project E 5,330 13 hours 410 75 hours
Project G 4,160 13 hours 320 88 hours
Project H 3,720 12 hours 310 100 hours
100 hours
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Ranking Based on Profitability Index
Incremental
Profit
Constrained Resource Required
Profitability Index
Cumulative Hours
Incremental Profit
(a) (b) (a) ÷ (b)
Project F 4,280$ 4 hours 1,070$ 4 hours 4,280$
Project J 2,940 3 hours 980 7 hours 2,940
Project B 7,200 9 hours 800 16 hours 7,200
Project I 3,650 5 hours 730 21 hours 3,650
Project D 5,680 8 hours 710 29 hours 5,680
Project A 9,180 17 hours 540 46 hours 9,180
Project C 7,040 16 hours 440 62 hours 32,930$
Project E 5,330 13 hours 410 75 hours
Project G 4,160 13 hours 320 88 hours
Project H 3,720 12 hours 310 100 hours
100 hours
The optimal profitThe optimal profitThe optimal profitThe optimal profit
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Learning Objective 2
Compute and use the Compute and use the profitability index in profitability index in
volume trade-off volume trade-off decisions.decisions.
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Volume Trade-Off Decisions
Volume trade-off decisions need to be made when a company must produce less than the
market demands for some products due to the existence of a constraint.
Volume trade-off decisions need to be made when a company must produce less than the
market demands for some products due to the existence of a constraint.
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Volume Trade-Off Decisions
Profitability indexProfitability indexfor a volumefor a volume
trade-off decisiontrade-off decision
Unit contribution marginUnit contribution marginAmount of the constrained resourceAmount of the constrained resource
required by one unitrequired by one unit=
Volume trade-off decisions need to be made when a company must produce less than the
market demands for some products due to the existence of a constraint.
Volume trade-off decisions need to be made when a company must produce less than the
market demands for some products due to the existence of a constraint.
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Volume Trade-Off Decisions – Example
Matrix, Inc. produces the following three products:
RX200 VB30 SQ500Unit contribution margin 15$ 10$ 16$ Demand per week in units 300 400 100 Contrained resource required per unit 5 minutes 2 minutes 4 minutes
Products
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Volume Trade-Off Decisions – Example
Matrix, Inc. produces the following three products:
RX200 VB30 SQ500Unit contribution margin 15$ 10$ 16$ Demand per week in units 300 400 100 Contrained resource required per unit 5 minutes 2 minutes 4 minutes
Products
RX200 VB30 SQ500Demand per week in units (a) 300 400 100 Contrained resource required per unit (b) 5 minutes 2 minutes 4 minutesTotal time required to meet demand (a) × (b) 1,500 minutes 800 minutes 400 minutes
Products
A total of 2,700 minutes
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Volume Trade-Off Decisions – Example
Matrix, Inc. produces the following three products:
RX200 VB30 SQ500Unit contribution margin 15$ 10$ 16$ Demand per week in units 300 400 100 Contrained resource required per unit 5 minutes 2 minutes 4 minutes
Products
RX200 VB30 SQ500Demand per week in units (a) 300 400 100 Contrained resource required per unit (b) 5 minutes 2 minutes 4 minutesTotal time required to meet demand (a) × (b) 1,500 minutes 800 minutes 400 minutes
Products
A total of 2,700 minutes
If only 2,200 minutes of machine constraintIf only 2,200 minutes of machine constrainttime are available, which products shouldtime are available, which products should
be produced in what quantities?be produced in what quantities?
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First we calculate the profitability index for each product.First we calculate the profitability index for each product.
RX200 VB30 SQ500Contribution margin per unit (a) 15$ 10$ 16$ Contrained resource required per unit (b) 5 minutes 2 minutes 4 minutesProfitabiltiy index (a) ÷ (b) $3 per minute $5 per minute $4 per minute
Products
Most profitableMost profitableMost profitableMost profitableNext mostNext mostprofitableprofitableNext mostNext mostprofitableprofitable
Volume Trade-Off Decisions – Example
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Total minutes of constrained resource 2,200 Less: Minutes needed to produce 400 VB30 800 Available minutes 1,400 Less: Minutes needed to produce 100 SQ500 400 Available minutes 1,000 Less: Minutes needed to produce 200 RX200 1,000 Full utilization of machine time -
Total minutes of constrained resource 2,200 Less: Minutes needed to produce 400 VB30 800 Available minutes 1,400 Less: Minutes needed to produce 100 SQ500 400 Available minutes 1,000 Less: Minutes needed to produce 200 RX200 1,000 Full utilization of machine time -
Volume Trade-Off Decisions – Example
Next we prepare the optimal production plan. Next we prepare the optimal production plan.
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RX200 VB30 SQ500Unit contribution margin 15$ 10$ 16$ Production per week in units 200 400 100 Total contribution 3,000$ 4,000$ 1,600$
Products
Maximum contribution is $8,600 per week.Maximum contribution is $8,600 per week.Maximum contribution is $8,600 per week.Maximum contribution is $8,600 per week.
Volume Trade-Off Decisions – Example
Last, we compute the total contribution marginearned under the optimal production plan.
Last, we compute the total contribution marginearned under the optimal production plan.
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Learning Objective 3
Compute and use the Compute and use the profitability index in other profitability index in other
business decisions.business decisions.
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Sales Commissions
RX200 VB30 SQ500Unit selling price 40$ 30$ 35$ Unit variable cost 25 20 19 Unit contribution margin (a) 15$ 10$ 16$ Contrained resource required per unit (b) 5 minutes 2 minutes 4 minutesProfitability index per minute (a) ÷ (b) 3.00$ 5.00$ 4.00$
Products
Sales commissions are based on gross selling price. If you were a salesperson at Matrix,
which product would you prefer to sell?
RX200RX200
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Sales Commissions
RX200 VB30 SQ500Unit selling price 40$ 30$ 35$ Unit variable cost 25 20 19 Unit contribution margin (a) 15$ 10$ 16$ Contrained resource required per unit (b) 5 minutes 2 minutes 4 minutesProfitability index per minute (a) ÷ (b) 3.00$ 5.00$ 4.00$
Products
However, RX200 is the least profitable product,given the current machine constraint. It might bea better idea to base sales commissions on the
profitability index for each product.
However, RX200 is the least profitable product,given the current machine constraint. It might bea better idea to base sales commissions on the
profitability index for each product.
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Pricing New Products
The price of a new product should cover at least the variable cost of producing it plus the
opportunity cost of displacing the production of existing products to make it.
Selling priceof newproduct
Selling priceof newproduct
Variable costof the new
product
Variable costof the new
product
Opportunity costper unit of theconstrained
resource
Opportunity costper unit of theconstrained
resource
Amount of theconstrained
resource requiredby a unit of the
new product
Amount of theconstrained
resource requiredby a unit of the
new product
≥≥≥≥ ++++ ××××
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Pricing New Products
Matrix, Inc. is planning to introduce a new product – Matrix, Inc. is planning to introduce a new product – WR6000. The variable cost of production is $30 per WR6000. The variable cost of production is $30 per
unit and requires six minutes of constrained machine unit and requires six minutes of constrained machine time per unit.time per unit.
What is the minimum selling price Matrix should What is the minimum selling price Matrix should charge for product WR6000?charge for product WR6000?
Matrix, Inc. is planning to introduce a new product – Matrix, Inc. is planning to introduce a new product – WR6000. The variable cost of production is $30 per WR6000. The variable cost of production is $30 per
unit and requires six minutes of constrained machine unit and requires six minutes of constrained machine time per unit.time per unit.
What is the minimum selling price Matrix should What is the minimum selling price Matrix should charge for product WR6000?charge for product WR6000?
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Pricing New Products
Selling priceof newproduct
Selling priceof newproduct
$30$30Opportunity cost
per unit of theconstrained
resource
Opportunity costper unit of theconstrained
resource
Amount of theconstrained
resource requiredby a unit of the
new product
Amount of theconstrained
resource requiredby a unit of the
new product
≥≥≥≥ ++++ ××××
The first step is to recognize that the price ofWR6000 must cover its $30 variable cost per unit.
The first step is to recognize that the price ofWR6000 must cover its $30 variable cost per unit.
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Pricing New Products
The second step is to recognize that producing WR6000 will require displacing production of
RX200, VB30, or SQ500.
The second step is to recognize that producing WR6000 will require displacing production of
RX200, VB30, or SQ500.
Since RX200 has the lowest profitability indexof $3 per minute it should be displaced first.
Since RX200 has the lowest profitability indexof $3 per minute it should be displaced first.
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Pricing New Products
Selling priceof newproduct
Selling priceof newproduct
$30$30≥≥≥≥ ++++ ××××
The third step is to compute the opportunity cost per unit associated with displacing production of RX200 ($18 per unit).
The third step is to compute the opportunity cost per unit associated with displacing production of RX200 ($18 per unit).
$3per
minute
$3per
minute
6minutesper unit
6minutesper unit
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Pricing New Products
$30$30≥≥≥≥ ++++ ××××
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).
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).
$3per
minute
$3per
minute
6minutesper unit
6minutesper unit
$48$48
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End of Appendix B