978-0078025631 Appendix B Lecture Note

Appendix B – Lecture Notes

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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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