Chapter: Differential Analysis- Key to
Decision Making
A difference in cost between any two alternatives is known as differential Cost. Differential cost
also referred to as relevant cost or avoidable cost. It is future cost that will differ among the
alternatives.
The main objectives of differential/relevant costs analysis are:

Identify relevant and irrelevant costs , and benefits in a decision.

Analysis showing whether product line or other business segment should be added or
dropped.

Prepare a make or buy analysis.

Whether special order should be accepted.

Determine the most profitable use of constraint resource.

Whether product should be sold at split off point or process further.
 Constraint:
A constraint is anything that prevent you from getting more of what you want.
 Managing Constraint:
When a constraint exists in a production process managers can increase profit by producing the
products with the highest contribution margin per unit of constraint resources . However, they
can also increase profit by increasing the capacity of bottle neck, which is called relaxing or
elevating the constraint.
Capacity of bottleneck can be increased by Working overtime on the bottleneck
 Subcontracting some of the processing at the bottleneck
 Investing in additional machine
 Shifting workers
 Focusing business process improvement
 Reducing defective units.
Math Solutions

Ex: 12-5 [15th Edition, Page- 563]
1. Computation of CM per constraint factor that is time available on the plastic
injection:
Ski guard
a) Selling price per unit
Golf guard
Fishing guard
$200
$300
$255
60
140
55
140
160
200
2
5
4
$32
$50
b) VC
c) CM per unit
d) Plastic injection modeling
machine processing time
required per unit
e) CM per unit of constraint
resource (𝑐 ÷ 𝑑)
$70
Production of Ski guard product would be the most profitable use of constraint
resource that is time and Golf guard is the least profitable.
2. The constraint is the available Pounds of Plastic Pellets:
a) CM per unit
b) Pound of Plastic Pellet
Ski
Golf
Fishing
$140
$160
$200
7
4
8
$20
$40
$25
c) CM per unit of constraint
resource (𝑎 ÷ 𝑏)
In this case Golf guard would be the most profitable use of constraint resources and
Ski would be the least profitable use of constraint resources.
3. The Fishing guard product has the largest unit CM ($200), but it is not the most
profitable use of the constraint resource in either of the cases above. This happens
because the Fishing guard uses more of the constraint resources in proportion to its
CM then the other two products.

Ex: 12-6 [15th Edition, Page- 564]
Portsmouth Company
1. Computation of CM of the constraint factor (hours) of the product Sofa:
Selling price per unit
$ 1800
(-) VC
1200
CM per unit
$ 600
Upholstering Shop, time required to produce one unit of sofa
= 10 hours
CM per unit of constraint factor
= 600 ÷ 10
= 60 per hour
The company should be willing to pay up to $60 per hour to keep the Upholstering
Shop open after normal working hours.
2. Computations of CM of constraint factor of all three products:
Selling price
Recliner
Sofa
$ 1400
$1800
$1500
800
1200
1000
600
600
500
5
(-) VC
CM per unit
Time required per unit
8 hrs.
10
CM per constraint factor
$75
$60
Loveseat
$100 per hour
The offer to Upholster chair for $45 per hour should be accepted. The time would be
used to upholster Loveseats, which will generate ($100-$45) a net gain of $55 per
hour. Based on freed capacity then consider Recliner and Sofa.

Ex: 12-8 [15th Edition, Page- 565]
1.
Computation of CM per Pound of material
A
B
C
i. Contribution margin per unit
$54
$108
$60
ii. Direct material cost per unit
24
72
32
iii. Direct material cost per pound
8
8
8
iv. Pound of material required per unit
3
9
4
$18
$12
$15
v. Contribution margin per pound (𝑖 ÷ 𝑖𝑣)
2. The company should concentrate its available material on Product A:
A
B
C
18
12
15
Pounds material available 5000
5000
5000
$90,000
$60,000
$75,000
CM per pound
Although Product A has the lowest CM per unit and second lowest contribution
margin ratio, it is preferred over the other two products since it has the greater amount
of CM per pound of material and material is the company’s scarce resource.
3. The price Barlow Company would be willing to pay per pound of additional raw
materials depends on how the materials would be used. If there are unfilled orders for all
of the products Barlow would presumably use additional material for A as it generates
$18 CM and willing to pay up to $8+ $18= $26 per pound.
After fulfilling all of the order of A then prefer Product C and willing to pay up to
$8+$15=$23 then Product B and willing to pay original cost + Premium (CM) = 8+12=
$20.