Differential Analysis
&
Product Pricing
ACG 2071
Chapter 24
Module 11
Fall 2007
Terms
• Costs
– Relevant – estimated costs and revenues that
are important in the decision making process
– Sunk costs – that have been incurred in the
past are not relevant to the decision
Differential Analysis
• Focuses on the effect of alternative courses
of action on the relevant revenues
• Differential revenues
– Is the amount of increases or decreases in
revenue expected from a course of action as
compared with an alternative
Differential Analysis
• Differential cost
– Is the amount of increase or decrease in cost
that is expected from a course of action as
compared with an alternative
• Differential income or loss
– Differential revenue – differential cost
Differential Analysis
Differential Revenue from
alternatives
Revenue from Alternative A
$$$
Revenue from Alternative B
$$$
Differential Revenue
$$$
Differential cost of alternatives
Cost of Alternative A
$$$
Cost of B
$$$
Differential cost
Net differential income or loss from
alternatives
$$$
$$$
Types of Decision Making
• Lease or sell
– Management may have a choice between
leasing or selling a piece of equipment that is
no longer needed in the business.
– The relevant factors to be considered are the
differential revenues and costs associated with
the lease or sell decision
Example 1
• A corporation can sell an asset for
$200,000 less a 6% selling commission.
An alternative would be to lease the asset
for five years at $40,000 per year less
$35,000 in costs over the five years.
Which decision would you make?
Example 1
• Lease:
– Revenue: $40,000 X 5 =
– Cost
– Income
$200,000
35,000
165,000
• Sell
– Revenue
– Cost 6% X $200,000
– Income
$200,000
12,000
188,000
Discontinue a segment or
product
• When a product or a department, branch,
territory, or other segment of a business is
generating losses, management may consider
eliminating the product or segment.
• It is often assumed, sometimes in error, that the
total income from operations of a business would
be increase if the operating loss could be
eliminated
• If contribution margin > 0 then continue with
segment
Example 2
• Should we discontinue the production of
Lotion?
Shampoo
Conditioner
Lotion
Total
Sales
$500,000
$400,000
$100,000
$1,000,000
Cost of goods
sold
Variable
$220,000
$200,000
$60,000
$480,000
Fixed
$120,000
$80,000
$20,000
$220,000
Total CGS
340,000
280,000
80,000
700,000
Gross profit
160,000
$120,000
$20,000
$300,000
Operating
expenses
Variable
$95,000
$60,000
$25,000
$180,000
Fixed
$25,000
$20,000
$6,000
$51,000
Total
$120,000
$80,000
$31,000
$231,000
Income
$40,000
$40,000
$(11,000)
$69,000
Example 2
• Lotion
Sales
Var COGS
Manufacturing margin
Var selling exp
Contribution margin
$
$
$
$
$
100,000.00
60,000.00
40,000.00
25,000.00
15,000.00
Example 3
• A condensed income statement for Fresh
Kola indicated the following
Sales
Cost of goods sold
Gross profit
Operating expenses
Operating income
$
$
$
$
$
250,000.00
175,000.00
50,000.00
60,000.00
(10,000.00)
Variable costs of goods sold is $120,000
Variable operating was $15,000
Should we discontinue Kola?
Example 3
• Result
Sales
Var COGS
Manufacturing margin
Var operating
Contribution margin
$
$
$
$
$
250,000.00
120,000.00
130,000.00
15,000.00
115,000.00
Make or Buy
• The assembly of many parts is often a major
element in manufacturing some products
• The product’s manufacturer may make these
parts or they may be purchased
• Management uses differential cost to decide
whether to make or buy
• MUST HAVE UNUSED CAPACITY
• Only look at variable costs
Example 4
• A factory has unused capacity and is
considering the production of a part of its
product. The cost of making a part in
direct materials is $80, direct labor $70,
variable factory overhead is $52 and fixed
factory overhead is $68. The cost of
purchasing the product is $240 per unit.
Should we make or buy?
Example 4
• Make
• Buy $240
– Unused capacity exists • Since we have unused
– DM $80
capacity, we can make
– DL $70
the product.
– VFO 52
– Total 202
Replace Equipment
• The usefulness of fixed assets may be
reduced long before they are considered to
be worn out
• Equipment may no longer be efficient for
the purposes for which it is used
• On the other hand, the equipment may not
have reached the point of complete
inadequacy
Example 5
• The business is considering the disposal of a
machine with book value of $100,000 and an
estimated remaining live of five years. The old
machine can be sold for $25,000. The new
machine has a cost of $250,000. The new
machine would have a life of five years and no
residual value. Analysis indicates that the
estimated annual reduction in variable
manufacturing costs from $225,000 with the old
machine to $150,000 per year with the new
machine. Should we buy the new machine?
Example 5
•
•
•
•
•
•
•
•
Reduction in cost
$225,000 - $150,000 = $75,000
x 5 yrs
375,000
Selling price of old m/c
25,000
400,000
Cost of new m/c
250,000
Savings
150,000
Example 6
• Francis is considering purchasing a lathe.
The old machine cost $250,000 and has
book value of $50,000 with three years
left. It has a disposal value of $10,000.
The new machine has a cost of $350,000
for five years and no residual value. The
new machine will decrease cost by $75,000
for the next three years. Should we buy the
new machine?
Example 6
•
•
•
•
•
•
Reduction in cost
$75,000 X 3 =
Disposal value
Total
Cost of new machine
Loss
$225,000
10,000
235,000
350,000
(115,000)
Process or Sell
• When a product is manufactured, it
progresses through carious stages of
production
• Often a product can be sold at an
intermediate stage of production, or it can
be processed further and then sold.
Oil Production
• Process
Crude oil
Diesel
Can sell diesel or process
More to make gasoline
Gasoline
Example 7
• A business produces product D in batches of
4,000 gallons. Standard quantities of 4,000
gallons of direct materials are processed which
cost $0.60 per gallon. D can be sold without
further processing for $0.80 per gallon. It can be
processed further to yield G, which can be sold
for $1.25 per gallon. G requires additional
processing costs of $650 per batch and 20% of
the gallons of D will evaporate during
production. Should we sell or process further?
Example 7
• D
– SP: 4,000g x $0.80 = $3,200
– Cost 4,000g X $0.60 = 2,400
– Profit
800
• G
– SP (4,000g X .8) X $1.25 =
– Cost $2,400 + $650
– Profit
• Produce gasoline
$4,000
3,050
950
Example 8
• Environ produces Gecko. Production starts
with 10,000 gallons of direct materials
processed for $2 per gallon. It can be sold
at $3 per gallon. Gecko can be further
processed into Frye for additional costs of
$1.50 per gallon with a cost of 10% of the
product. The selling price of Frye is $4.50
per gallon. Should we process further?
Accept Business at Special Price
• Differential analysis is also useful in deciding whether to
accept additional business at a special rate
• The differential revenue that would be provided from the
additional business is compared to the differential costs of
producing and delivering the product to the customer.
• If the company is operating at full capacity, any
additional production will increase both fixed costs and
variable
• However, the normal production of the company is below
full capacity, additional business may be undertaken
without increasing fixed production costs.
Business at Special Price
• Assume that monthly capacity is 12,500 units.
Current sales and production are 10,000 units.
The current manufacturing costs of $20 per unit
with fixed costs of $7.50. The normal selling
price of the product is $30. The manufacturer
receives from an exporter an offer for 5,000 units
at $18 per unit. The production can be spread
over three months. Should we accept the offer?
Example
• SP 5,000 units X $18 =
• Cost
– $20 - $7.50 = $12.50
– 5,000 units X $12.50 =
• Profit
$90,000
62,500
27,500
Setting Normal Product Selling
Price
• Can be viewed as the target selling price to be
achieved in the long run
• Approaches
Market Methods
Cost-Plus Methods
Demand based methods
Total cost concept
Competition based
methods
Product cost concept
Variable cost concept
Total Cost Concept
• Selling price = Cost + Markup
• Total cost concept
– All costs of manufacturing a product plus the
selling and administrative expenses are
included in the cost amount to which the
markup is added.
– $ amount of markup = profit on the product
Steps to Compute
Steps:
1Determine the total cost of manufacturing the product.
aIncludes the direct materials, direct labor, and factory
overhead
bIncludes the selling and administrative expenses
2Cost per unit is then computed by dividing the total costs by
the total units expected to be produced and sold.
3Markup percentage = Desired profit
Total cost
4Selling price = Cost per unit + ( markup percentage X
cost per unit)
Example
Variable costs
Direct materials
Direct labor
Factory overhead
Selling & administrative
TOTAL Variable
Fixed costs
Factory overhead
Selling & administrative
$3.00
$10.00
$1.50
$1.50
$16.00
$50,000
$20,000
Example (cont’d)
• Desires a profit equal to a 20% rate of
return on assets.
• $800,000 of assets
• Desired profit = 20% X $800,000
Desired profit =$160,000
• 100,000 units are expected to be produced
and sold
•
Example (cont’d)
• Total Cost =
Variable costs
$16 x 100,000 units
Fixed costs
$1,600,000
Factory overhead
$50,000
Selling & Adm
$20,000
Total cost
Per unit
$70,000
$1,670,000
$16.70
Example
• Total Cost Concept
Markup percentage = Desired profit
Total Cost
= $160,000 = 9.6%
$1,670,000
Example
• Selling price
Total cost per unit
Markup ($16.70 X 9.6%)
Selling price
$16.70
1.60
$18.30
Product Cost Concept
Steps:
1Determine the total cost of manufacturing the product include
direct materials, direct labor, and factory overhead.
2Cost per unit is total cost manufacturing divided by the total
units.
3Markup % =
3Desired profit + Total selling & Administrative Expenses
Total Manufacturing Costs
4 Selling price = Cost per unit + (Cost per unit X Markup %)
Example (data from before)
• Manufacturing costs =
Direct materials
Direct labor
Variable Factory overhead
Total
$ 3.00
$10.00
$1.50
$14.50
Example (data from before)
• Total manufacturing costs
Total variable costs
($14.50 x 100,000)
$1,450,000
Fixed manufacturing
50,000
Total manufacturing
1,500,000
Manufacturing costs per unit = $15.00
Example
• Total selling & administrative
Variable
($1.50 x 100,000)
Fixed
Total
$150,000
20,000
$ 170,000
Example (data from before)
• Product Cost Concept
• Markup Percentage =
Desired Profit + Total selling & adm exp
Total manufacturing costs
= $160,000 + $170,000
$1,500,000
= $330,000
$1,500,000
= 22%
Example
• Selling Price
Total manufacturing costs
Markup (22% x $15)
Selling price
$15.00
3.30
$18.30
Variable Cost Concept
Steps:
1Determine the total cost of manufacturing the product
include direct materials, direct labor, variable selling and
administrative expenses, and variable factory overhead.
2Cost per unit is total cost manufacturing divided by the total
units.
3Markup % = Desired profit + Total Fixed Costs
Total Variable Costs
4 Selling price = Cost per unit + (Cost per unit X Markup %)
Example (data from before)
• Variable cost
Variable costs
Direct materials
Direct labor
Factory overhead
Selling & Adm
Total variable cost
Per unit
$300,000
$1,000,000
$150,000
$150,000
$1,600,000
$16.00
Example
• Markup percentage =
Desired profit + Total fixed costs
Total variable costs
= $160,000 + $50,000 + $20,000
$1,600,000
= $230,000
= 14.4%
$1,600,000
Example
Total selling price
Variable cost
Markup ($16 X 14.4%)
Total selling price
$16.00
2.30
$18.30