Differential Analysis and Product Pricing

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Differential Analysis and Product Pricing
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After studying this chapter, you should be able
to

• Prepare a differential analysis report for
  decisions involving leasing or selling equipment,
  discontinuing an unprofitable segment,
  manufacturing or purchasing a needed part,
  replacing usable fixed assets, processing further
  or selling an intermediate product, or accepting
  additional business at a special price.

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After studying this chapter, you should be able
to

• Determine the selling price of a product, using
  the total cost, product cost, variable cost, and
  target cost concepts.

• Calculate the relative profitability of products
  in bottleneck production environments.

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Objective 1
Prepare a differential analysis report for
decisions involving leasing or selling equipment,
discontinuing an unprofitable segment,
manufacturing or purchasing a needed part,
replacing usable fixed assets, process further or
selling an intermediate product, or accepting
additional business at a special price.
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Differential Analysis
Relevant revenues and costs focus on the
differences between each alternative. Costs that
have been incurred in the past are not relevant
to the decision. These costs are called sunk
costs.
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Differential revenue is the amount of increase or
decrease in revenue that is expected from a
course of action as compared with an alternative.
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Differential cost is the amount of increase or
decrease in cost that is expected from a course
of action as compared with an alternative.
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Differential income or loss is the difference
between the differential revenue and the
differential costs. Differential income
indicates that a particular decision is expected
to be profitable, while a differential loss
indicates the opposite.
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Differential analysis focuses on the effect of
alternative courses of action on the relevant
revenues and costs.
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Summary
Differential Analysis
Decisions
Alternative A
Differential revenue Differential cost
or
Differential income or loss
Alternative B
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Differential Analysis
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Uses of Differential Analysis
Differential analysis is used for analyzing

• Leasing or selling equipment.
• Discontinuing an unprofitable segment.
• Manufacturing or purchasing a needed part.
• Replacing usable fixed assets.
• Processing further or selling an intermediate
  product.
• Accepting additional business at a special price.

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Lease or Sell
Marcus Company is considering disposing of
equipment that cost 200,000 and that has
120,000 of accumulated depreciation. The
equipment can be sold through a broker for
100,000, less a 6 commission.
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Potamkin Company, the lessee, has offered to
lease the equipment for five years for a total
consideration of 160,000.
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At the end of the fifth year of the lease, the
equipment is expected to have no residual value.
During the period of the lease, Marcus Company
expects to incur repair, insurance, and property
taxes estimated at 35,000.
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Differential Analysis ReportLease or Sell
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Traditional Analysis
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Office space with a cost of 100,000 and
accumulated depreciation of 30,000 can be sold
for 150,000 less a 6 broker commission.
Alternatively, the office space can be leased for
ten years for a total of 170,000 at the end of
which there is no salvage value. In addition,
repair, insurance, and property tax on the rented
office space would total 24,000 over the ten
years. Determine the differential income or loss
from the lease alternative.
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Differential revenue from alternatives Revenue
from lease 170,000 Revenue from sale
150,000 Differential revenue from
lease 20,000 Differential cost of
alternatives Repairs, insurance, and property
tax expense 24,000 Commission expense
9,000 Differential cost of lease
15,000 Net differential income from lease
alternative 5,000
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For Practice PE24-1A, PE24-1B
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Income (Loss) by Product
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Discontinue a Segment or Product
Based on the information contained in the
condensed income statement (Slide 20), management
of Battle Creek Cereal Co. is considering
discontinuing Bran Flakes.
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Differential Analysis ReportDiscontinue an
Unprofitable Segment
Proposal to Discontinue Bran Flakes September 29,
2008
Differential revenue from annual sales of Bran
Flakes Revenue from sales 100,000 Differentia
l cost of annual sales of Bran Flakes Variable
cost goods sold 60,000 Variable operating
expenses 25,000 85,000 Annual differential
income from sales of Bran Flakes 15,000
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Dont discontinue Bran Flakes!
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Traditional Analysis
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Product A has revenue of 65,000, variable cost
of goods sold of 50,000, variable selling
expenses of 12,000, and fixed costs of 25,000,
creating a loss from operations of 22,000. a.
Determine the differential income or loss from
sales of Product A. b. Should Product A be
discontinued?
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Revenue from sales 65,000 Differential costs
of Product A Variable cost of goods
sold 50,000 Variable selling expenses
12,000 62,000 Annual differential income from
Product A 3,000
b. Product A should not be discontinued.
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For Practice PE24-2A, PE24-2B
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Make or Buy
An automobile manufacturer has been purchasing
instrument panels for 240 a unit. The factory
currently operates at 80 of capacity. The cost
per unit is estimated as follows
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Differential Analysis ReportMake or Buy
Proposal to Manufacture Instrument
Panels February 15, 2008
Purchase price of instrument panel 240.00 Differ
ential cost to manufacture Direct
materials 80.00 Direct labor 80.00 Variable
factory overhead 52.00 212.00 Cost savings
from manufacturing instrument panel 28.00
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A company manufactures a subcomponent of an
assembly for 80 per unit, including fixed costs
of 25 per unit. A proposal is offered to
purchase the subcomponent from an outside source
for 60 per unit, plus 5 per unit freight.
Provide a differential analysis of the outside
purchase proposal.
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Differential cost to purchase Purchase price
of the subcomponent 60 Freight for
subcomponent 5 65 Differential cost to
manufacture Variable manufacturing costs (80
25 fixed cost) 55 Cost savings from
manufacturing sub- component 10
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For Practice PE24-3A, PE24-3B
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Replace Equipment
A business is considering the disposal of several
identical machines having a total book value of
100,000 and an estimated remaining life of five
years.
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The old machines can be sold for 25,000. They
can be replaced by a single high-speed machine at
a cost of 250,000. The new machine has an
estimated useful life of five years and no
residual value.
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Differential Analysis ReportReplace Equipment
Proposal to Replace Equipment November 28, 2008

• Annual variable costspresent equipment 225,000
• Annual variable costsnew equipment 150,000
• Annual differential decrease in cost 75,000
• Number of years applicable x 5
• Total differential decrease in cost 375,000
• Proceeds from sale of present equipment
  25,000 400,000
• Cost of new equipment 250,000
• Net differential decrease in cost,
  5-years 150,000
• Annual net differential decrease in costnew
  equipment 30,000

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Opportunity Cost
The amount of income that is foregone from an
alternative use of an asset, such as cash, is
called an opportunity cost.
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A machine with a book value of 32,000 has an
estimated four-year life. A proposal is offered
to sell the old machine for 10,000 and replace
it with a new machine at a cost of 45,000. The
new machine has a four-year life with no salvage
value. The new machine would reduce annual
direct labor costs by 15,000. Provide a
differential analysis on the proposal to replace
the machine.
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Annual direct labor cost reduction 15,000 Number
of years applicable x 4 Total
differential decrease in cost 60,000 Proceeds
from sale of old equipment 10,000 50,000 Cost
of new equipment 45,000 Net differential
decrease in cost from replacing equipment,
4-year total 5,000
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For Practice PE24-4A, PE24-4B
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Process or Sell
A business produces kerosene in batches of 4,000
gallons. Standard quantities of 4,000 gallons of
direct materials are processed, which cost 0.60
per gallon.
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Kerosene can be sold without further processing
for 0.80 per gallon or further processed to
yield gasoline, which can be sold for 1.25 per
gallon. The additional processing costs 650 per
batch, and 20 of the gallons of kerosene will
evaporate during production.
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Differential Analysis ReportProcess or Sell
Proposal to Process Kerosene Further October 1,
2008

• Differential revenue from further
  processing per batch
• Revenue from sale of gasoline (4,000 gallons
  800 gallons evaporation) x 1.25 4,000
• Revenue from sale of kerosene (4,000 gallons x
  0.80) 3,200
• Differential revenue 800
• Differential cost per batch Additional cost of
  producing gasoline 650
• Differential income from further
  processing gasoline per batch 150

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Product T is produced for 2.50 per gallon,
including 1.00 per gallon fixed cost. Product T
can be sold without additional processing for
3.50 per gallon, or processed further into
Product V at an additional cost of 1.60 per
gallon, including 0.90 per gallon fixed cost.
Product V can be sold for 4.00 per gallon.
Provide a differential analysis for further
processing into Product V.
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Differential revenue from further processing
per gallon Revenue per gallon from sale of
Product T 3.50 Revenue per gallon from sale of
Product V 4.00 Differential revenue 0.50 Dif
ferential cost per gallon Additional cost for
producing Product V (1.60 0.90)
0.70 Differential loss from further processing
into Product V 0.20
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For Practice PE24-5A, PE24-5B
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Accept Business at a Special Price
The monthly capacity of a sporting goods business
is 12,500 basketballs. Current sales and
production are averaging 10,000 basketballs per
month. The current manufacturing cost is 20 per
unit (variable, 12.50 fixed, 7.50). The
domestic unit selling price is 30.
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The manufacturer receives an offer from an
exporter for 5,000 basketballs at 18 each.
Production can be spread over three months, so
these basketballs can be manufactured using
normal capacity. Domestic sales would not be
affected.
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Differential Analysis ReportSell at Special
Price
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Product D is normally sold for 4.40 per unit. A
special price of 3.60 is offered for the export
market. The variable production cost is 3.00
per unit. An additional export tariff of 10 of
revenue will be required to be paid for all
export products. Determine the differential
income or loss per unit from selling Product D
for export.
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Differential revenue from export Revenue per
unit from export sale 3.60 Differential
cost from export Variable manufacturing
costs 3.00 Export tariff (10 x 3.60) 0.36
3.36 Differential income from accepting export
sale 0.24
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For Practice PE24-6A, PE24-6B
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Objective 2
Determine the selling price of a product using
the total cost, product cost, variable cost, and
target cost concepts.
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Setting Normal Product Selling Prices
The basic approaches to setting prices are
Market Methods
1. Demand-based methods 2. Competition-based
methods
Cost-Plus Methods
1. Total cost concept 2. Product cost
concept 3. Variable cost concept
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Market Methods

• Demand-based methods set the price according to
  the demand for the product.

• Competition-based methods set the price according
  to the price offered by competitors.

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Markup
Using the cost-plus methods, managers add to the
cost an amount called a markup, so that all costs
plus a profit are included in the selling price.
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Total Cost Concept
Using the total cost concept, all costs of
manufacturing a product...
Manufacturing Cost
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plus the selling and administrative expenses...
Administrative Expenses
Selling Expenses
Manufacturing Cost
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are included in the cost to which the markup is
added.
Administrative Expenses
Selling Expenses
Manufacturing Cost
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The markup is determined by applying the
following formula
Desired Profit
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Digital Solutions Inc.100,000 calculators
Per Unit Total Cost Cost

• Variable Costs
• Direct materials 3.00 300,000
• Direct labor 10.00 1,000,000
• Factory overhead 1.50 150,000
• Selling and admin. exp. 1.50 150,000
• Total variable costs 16.00 1,600,000
• Fixed Costs
• Factory overhead .50 50,000
• Selling and admin. exp. .20 20,000
• Total fixed costs . 70 70,000
• Total costs 16.70 1,670,000

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Markup Percentage
Desired profit Total costs
160,000 1,670,000
9.6

Only the desired profit is covered in the markup.
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Proof That Selling the Calculators at 18.30 Will
Generate the Desired Profit
Digital Solutions Inc. Income Statement For the
Year Ended December 31, 2008
Sales (100,000 units x 18.30) 1,830,000 Expense
s Variable (100,000 units x 16.00) 1,600,000
Fixed (50,000 20,000) 70,000
1,670,000 Income from operations 160,000
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Apex Corporation produces and sells Product Z at
a total cost of 30 per unit. Of this amount,
10 per unit is selling and administrative costs.
The total variable cost is 18 per unit. The
desired profit is 3 per unit. Determine the
markup percentage on total cost.
Markup percentage 3/30 10.0
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For Practice PE24-7A, PE24-7B
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Product Cost Concept
Using the product cost concept, only the costs of
manufacturing the product, termed the product
cost, are included in the cost amount to which
the markup is added.
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Digital Solutions Inc.100,000 calculators
Per Unit Total Cost Cost
Variable Costs Direct materials 3.00
300,000 Direct labor 10.00 1,000,000 Factory
overhead 1.50 150,000 Selling and
administrative 1.50 150,000 Total
variable costs 16.00 1,600,000 Fixed
Costs Factory overhead .50 50,000 Selling
and administrative .20 20,000
Total fixed costs .70 70,000 Total
costs 16.70 1,670,000
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Desired Selling Price
Markup
Manufacturing Cost
Product Cost
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Markup Percentage Formula
The markup percentage for the product cost
concept is determined by applying the following
formula
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Markup Percentage
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Markup Percentage
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Markup Percentage
Markup Percentage
330,000

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1,500,000
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Digital Solutions Inc. would price each
calculator at 18.30 per unit, as shown below
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Apex Corporation produces and sells Product Z at
a total cost of 30 per unit. Of this amount,
10 per unit is selling and administrative costs.
The total variable cost is 18 per unit. The
desired profit is 3 per unit. Determine the
markup percentage on product cost.
Markup percentage (3 10)/20 65.0
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For Practice PE24-8A, PE24-8B
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Variable Cost Concept
The variable cost concept emphasizes the
distinction between variable and fixed costs in
product pricing. Only variable costs are include
in the cost amount to which the markup is added.
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Markup
Total Fixed Costs Desired Profit
Variable Manufacturing Cost Variable
Administrative and Selling Expenses
Product Cost
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Markup Percentage
Total Variable Costs
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Markup Percentage
Total Variable Costs
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Apex Corporation produces and sells Product Z at
a total cost of 30 per unit. Of this amount,
10 per unit is selling and administrative costs.
The total variable cost is 18 per unit. The
desired profit is 3 per unit. Determine the
markup percentage on variable cost, rounded to
one decimal place.
Markup percentage on variable cost (3
12)/18 83.3, rounded to one decimal place
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For Practice PE24-9A, PE24-9B
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Target Costing
Under target costing, a future selling price is
anticipated, using the demand-based methods or
the competition-based methods. The targeted cost
is determined by subtracting a desired profit
from the expected selling price.
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Target Cost Concept
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Future
Present
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Objective 3
Calculate the relative profitability of products
in bottleneck production environments.
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Product Profitability Under Production Bottlenecks
A production bottleneck (or constraint) occurs at
the point in the process where the demand for the
companys product exceeds the ability to produce
the product.
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The theory of constraints (TOC) is a
manufacturing strategy that focuses on reducing
the influence of bottlenecks on a process.
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Pride Craft Tool Co. Example
Small Medium Large Wrench Wrench Wrench
Sales price per unit 130 140 160 Variable
cost per unit 40 40 40
Contribution margin per unit 90 100 120
Heat treatment hours per unit 1 4 8
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Contribution Margin (per unit) per Bottleneck
Hour
Small Medium Large Wrench Wrench Wrench

• Sales price 130 140 160
• Variable cost per unit 40 40 40
• Contribution margin per unit 90 100 120
• Bottleneck (heat treatment) hours per unit
  / 1 / 4 / 8
• Contribution margin (per unit) per bottleneck
  hour 90 25 15

Greatest contribution margin (per unit) per
bottleneck hour
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Product A has a contribution margin of 15 per
unit. Product B has a contribution margin of 20
per unit. Product A requires three furnace
hours, while Product B requires five furnace
hours. Determine the most profitable product
assuming the furnace is a constraint.
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Product A Product B
Contribution margin per unit 15 20 Furnace
hours per unit / 3 / 5 Contribution margin per
bottleneck hour 5 4
Product A is the most profitable in using
bottleneck resources.
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For Practice PE24-10A, PE24-10B
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Product Pricing Under Production Bottlenecks
How much should the firm charge for the large
wrench in order to deliver the same contribution
margin 90 (see Slide 78) as the small wrench?
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Variable Cost per Unit for Large Wrench
Revised Price of Large Wrench
Contribution Margin (per unit) per Bottleneck
Hour for Small Wrench


Bottleneck Hours per Unit for Large Wrench
720 Revised Price of Large Wrench 40
760 Revised Price of Large Wrench
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Proof
Revised price of large wrench (Slide
82) 760 Less Variable cost per unit of large
wrench 40 Contribution margin per unit of
large wrench 720 Bottleneck hours per unit of
large wrench / 8 Revised contribution margin
(per unit) per bottleneck hour 90
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