Calculate Point Of Indifference
Between Two Different Cost
Scenarios
Principles of Cost Analysis and
Management
© Dale R. Geiger
1
What would you do for a Klondike Bar?
It’s essentially a Cost/Benefit Analysis!
© Dale R. Geiger
2
Terminal Learning Objective
• Action: Calculate Point Of Indifference Between Two
Different Cost Scenarios That Share A Common
Variable
• Condition: You are a cost analyst with knowledge of
the operating environment and access to all course
materials including handouts and spreadsheet tools
• Standard: With at least 80% accuracy:
1. Describe the concept of indifference point or tradeoff
2. Express cost scenarios in equation form with a common
variable
3. Identify and enter relevant scenario data into macro
enabled templates to calculate Points of Indifference
© Dale R. Geiger
3
What is Tradeoff?
•
•
•
•
Life is full of Tradeoffs
What we give up could be visualized as a “cost”
What we receive could be labeled a “benefit”
The transaction occurs when the benefit
is equal to or greater than the cost
• Point of equilibrium: the point where
cost is equal to benefit received.
© Dale R. Geiger
4
Tradeoff Theory
• Identifies the point of equality between
two differing cost expressions with a
common unknown variable
• “Revenue” and “Total Cost” are cost
expressions with “Number of Units” as the
common variable:
Revenue = $Price/Unit * #Units
Total Cost = ($VC/Unit * #Units) + Fixed Cost
© Dale R. Geiger
5
Tradeoff Theory (cont’d)
• Breakeven Point is the point where:
Revenue – Total Cost = Profit
Revenue – Total Cost = 0
Revenue = Total Cost
• Setting two cost expressions with a common
variable equal to one another will yield the
breakeven or tradeoff point
© Dale R. Geiger
6
What is an Indifference Point?
• The point of equality between two cost
expressions with a common variable
• Represents the “Decision Point” or
“Indifference Point”
• Level of common variable at which two
alternatives are equal
• Above indifference point, one of the alternatives
will yield lower cost
• Below indifference point, the other alternative will
yield lower cost
© Dale R. Geiger
7
Indifference Point Applications
• Evaluating two machines that perform the
same task
• i.e. Laser printer vs. inkjet
• Low usage level favors the inkjet, high usage
favors the laser, but at some point they are equal
• Outsourcing decisions
• What level of activity would make outsourcing
attractive?
• What level would favor insourcing?
• At what level are they equal?
© Dale R. Geiger
8
Check on Learning
• What is an indifference point or tradeoff
point?
• What is an example of an application of
indifference points?
© Dale R. Geiger
9
Indifference Point Applications
• Evaluating two Courses of Action:
•
•
•
•
•
•
Cell phone data plan
Plan A costs $.50 per MB used
Plan B costs $20 per month + $.05 per MB used
Plan A is the obvious choice if usage is low
Plan B is the obvious choice if usage is high
What is the Indifference Point?
• The number of MB used above which Plan B costs less,
below which Plan A costs less?
© Dale R. Geiger
10
Plan A vs. Plan B
• What is the cost expression for Plan A?
• $.50 * # MB
• What is the cost expression for Plan B?
• $20 + $.05 *# MB
• What is the common variable?
• # MB used
© Dale R. Geiger
11
Plan A vs. Plan B
• What is the cost expression for Plan A?
• $.50 * # MB
• What is the cost expression for Plan B?
• $20 + $.05 *# MB
• What is the common variable?
• # MB used
© Dale R. Geiger
12
Plan A vs. Plan B
• What is the cost expression for Plan A?
• $.50 * # MB
• What is the cost expression for Plan B?
• $20 + $.05 *# MB
• What is the common variable?
• # MB used
© Dale R. Geiger
13
Plan A vs. Plan B
• What is the cost expression for Plan A?
• $.50 * # MB
• What is the cost expression for Plan B?
• $20 + $.05 *# MB
• What is the common variable?
• # MB used
© Dale R. Geiger
14
Solving for Indifference Point
• Set the cost expressions equal to each other:
$.50 * # MB = $20 + $.05 *# MB
$.50 * # MB - $.05 *# MB = $20
$.45 * # MB = $20
# MB = $20/$.45
# MB = $20/$.45
# MB = 20/.45
# MB = 44.4
© Dale R. Geiger
15
Solving for Indifference Point
• Set the cost expressions equal to each other:
$.50 * # MB = $20 + $.05 *# MB
$.50 * # MB - $.05 *# MB = $20
$.45 * # MB = $20
# MB = $20/$.45
# MB = $20/$.45
# MB = 20/.45
# MB = 44.4
© Dale R. Geiger
16
Solving for Indifference Point
• Set the cost expressions equal to each other:
$.50 * # MB = $20 + $.05 *# MB
$.50 * # MB - $.05 *# MB = $20
$.45 * # MB = $20
# MB = $20/$.45
# MB = $20/$.45
# MB = 20/.45
# MB = 44.4
© Dale R. Geiger
17
Solving for Indifference Point
• Set the cost expressions equal to each other:
$.50 * # MB = $20 + $.05 *# MB
$.50 * # MB - $.05 *# MB = $20
$.45 * # MB = $20
# MB = $20/$.45
# MB = $20/$.45
# MB = 20/.45
# MB = 44.4
© Dale R. Geiger
18
Solving for Indifference Point
• Set the cost expressions equal to each other:
$.50 * # MB = $20 + $.05 *# MB
$.50 * # MB - $.05 *# MB = $20
$.45 * # MB = $20
# MB = $20/$.45
# MB = $20/$.45
# MB = 20/.45
# MB = 44.4
© Dale R. Geiger
19
Plan A vs. Plan B
$ 35
30
Cost of Plan A is zero when usage is zero, but
increases rapidly with usage
Cost of Plan B starts at $20 but increases
slowly with usage
25
20
Plan A
15
Plan B
10
5
0
0
20
40
X Axis = Number of MB Used
44.4
Cost of both plans increases as # MB increases
© Dale R. Geiger
60
20
Proof
• Plug the solution into the original equation:
$.50 * # MB = $20 + $.05 * # MB
$.50 * 44.4 MB = $20 + $.05 * 44.4 MB
$.50 * 44.4 MB = $20 + $.05 * 44.4 MB
$22.20 = $20 + $2.22
$22.20 = $22.22
(rounding error)
© Dale R. Geiger
21
Interpreting the Results
• Decision: Will you use more or less than 44.4
MB per month?
• Using less than 44.4 MB per month makes Plan A
the better deal
• Using more than 44.4 MB per month makes Plan B
the better deal
• What other factors might you consider when
making the decision?
© Dale R. Geiger
22
Indifference Points Spreadsheet
Enter data to compare two multivariate cost scenarios
i.e. Cell phone data plans
Solve for Breakeven level of Usage
© Dale R. Geiger
23
Indifference Points Spreadsheet
Enter different quantities to compare the
cost of both options for various levels of usage
See which option is more favorable at a given level
© Dale R. Geiger
24
Check on Learning
• How would you find the indifference point
between two cost options with a common
variable?
• You are taking your children to the zoo. You
can purchase individual tickets ($15 for one
adult and $5 per child) or you can purchase
the family ticket for $30. What common
variable will allow you to calculate an
indifference point?
© Dale R. Geiger
25
Indifference Point Example
• A six-pack of soda costs $2.52 and contains 72
ounces of soda
• A two-liter bottle of the same soda contains
67.2 ounces of soda
• What price for the two-liter bottle gives an
equal value?
• The common variable is cost per ounce
© Dale R. Geiger
26
Indifference Point Example
• What is the expression for cost per ounce for
the six pack?
• $2.52/72 oz.
• What is the expression for cost per ounce for
the two-liter bottle?
• $Price/67.2 oz.
© Dale R. Geiger
27
Indifference Point Example
• What is the expression for cost per ounce for
the six pack?
• $2.52/72 oz.
• What is the expression for cost per ounce for
the two-liter bottle?
• $Price/67.2 oz.
© Dale R. Geiger
28
Indifference Point Example
• What is the expression for cost per ounce for
the six pack?
• $2.52/72 oz.
• What is the expression for cost per ounce for
the two-liter bottle?
• $Price/67.2 oz.
© Dale R. Geiger
29
Solving for Breakeven Price
• Set the two cost expressions equal to one
another:
Cost per oz. of two-liter = Cost per oz. of six-pack
$Price/67.2 oz. = $2.52/72 oz.
$Price/67.2 oz. = $.035/oz.
$Price = $.035/oz. * 67.2 oz.
$Price = $.035/oz. * 67.2 oz.
$Price = $.035 * 67.2
$Price = approximately $2.35
© Dale R. Geiger
30
Solving for Breakeven Price
• Set the two cost expressions equal to one
another:
Cost per oz. of two-liter = Cost per oz. of six-pack
$Price/67.2 oz. = $2.52/72 oz.
$Price/67.2 oz. = $.035/oz.
$Price = $.035/oz. * 67.2 oz.
$Price = $.035/oz. * 67.2 oz.
$Price = $.035 * 67.2
$Price = approximately $2.35
© Dale R. Geiger
31
Solving for Breakeven Price
• Set the two cost expressions equal to one
another:
Cost per oz. of two-liter = Cost per oz. of six-pack
$Price/67.2 oz. = $2.52/72 oz.
$Price/67.2 oz. = $.035/oz.
$Price = $.035/oz. * 67.2 oz.
$Price = $.035/oz. * 67.2 oz.
$Price = $.035 * 67.2
$Price = approximately $2.35
© Dale R. Geiger
32
Solving for Breakeven Price
• Set the two cost expressions equal to one
another:
Cost per oz. of two-liter = Cost per oz. of six-pack
$Price/67.2 oz. = $2.52/72 oz.
$Price/67.2 oz. = $.035/oz.
$Price = $.035/oz. * 67.2 oz.
$Price = $.035 /oz. * 67.2 oz.
$Price = $.035 * 67.2
$Price = approximately $2.35
© Dale R. Geiger
33
Solving for Breakeven Price
• Set the two cost expressions equal to one
another:
Cost per oz. of two-liter = Cost per oz. of six-pack
$Price/67.2 oz. = $2.52/72 oz.
$Price/67.2 oz. = $.035/oz.
$Price = $.035/oz. * 67.2 oz.
$Price = $.035 /oz. * 67.2 oz.
$Price = $.035 * 67.2
$Price = approximately $2.35
© Dale R. Geiger
34
Six-Pack vs. Two-Liter
$0.06
Cost Per Ounce
$0.05
Cost of 6-pack is known so
Cost per oz. is constant
$0.04
6-pack $2.52
$0.03
2-Liter (67.2 oz.)
$0.02
$0.01
$$0
$1
$2
$3
$2.35
X Axis = Unknown Price of 2-Liter
As Price of 2-liter increases, cost per oz. increases
© Dale R. Geiger
$4
35
Interpreting the Results
• If the price of the two-liter is less than $2.35,
it is a better deal than the six-pack
• What other factors might you consider when
making your decision?
© Dale R. Geiger
36
Indifference Points Spreadsheet
Enter Data for two different cost per unit options,
i.e. cost per ounce of soda
Enter cost of six-pack
and number of ounces
Enter number ounces in a 2-liter
Solve for breakeven price
© Dale R. Geiger
37
Check on Learning
• When solving for an indifference point, what
two questions should you ask yourself first?
© Dale R. Geiger
38
Tradeoffs Under Uncertainty
• Review: Expected Value =
Probability of Outcome1 * Dollar Value of Outcome1
+
Probability of Outcome2 * Dollar Value of Outcome2
+
Probability of Outcome3 * Dollar Value of Outcome3
etc.
• Assumes probabilities and dollar value of
outcomes are known or can be estimated
© Dale R. Geiger
39
What if Probability is Unknown?
• Solve for Breakeven Probability
• Look for what IS known and what
relationships exist
• Compare two alternatives:
• One has a known expected value
• Example: Only one outcome with a known dollar
value and probability of 100%
• The other has two possible outcomes with
unknown probability
© Dale R. Geiger
40
Solving for Breakeven Probability
• Subscribe to automatic online hard drive
backup service for $100 per year
-OR• Do not subscribe to the backup service
• Pay $0 if your hard drive does not fail
• Pay $1000 to recover your hard drive if it
does fail.
© Dale R. Geiger
41
Solving for Breakeven Probability
• What is the cost expression for the expected
value of the backup service?
• What is the outcome or dollar value?
$100
• What is the probability of that outcome?
100%
• So, the cost expression is:
$100*100%
© Dale R. Geiger
42
Solving for Breakeven Probability
• What is the cost expression for the online
backup service?
• What is the outcome or dollar value?
$100
• What is the probability of that outcome?
100%
• So, the cost expression is:
$100*100%
© Dale R. Geiger
43
Solving for Breakeven Probability
• What is the cost expression for not subscribing to the
online backup service?
• What are the outcomes and dollar values?
• Hard drive failure = $1000
• No hard drive failure = $0
• How would you express the unknown probability of
each outcome?
• Probability% of hard drive failure = P
• Probability% of no hard drive failure = 100% - P
• So, the cost expression is:
$1000*P + $0*(100% - P)
© Dale R. Geiger
44
Solving for Breakeven Probability
• What is the cost expression for not subscribing to the
online backup service?
• What are the outcomes and dollar values?
• Hard drive failure = $1000
• No hard drive failure = $0
• How would you express the unknown probability of
each outcome?
• Probability% of hard drive failure = P
• Probability% of no hard drive failure = 100% - P
• So, the cost expression is:
$1000*P + $0*(100% - P)
© Dale R. Geiger
45
Solving for Breakeven Probability
• Set the two expressions equal to one another:
EV of not subscribing = EV of subscribing
$1000*P + $0*(100% - P) = $100*100%
$1000*P + $0*(100% - P) = $100*100%
$1000*P = -$100*100%
$1000*P = -$100
P = $100/$1000
P = $100/$1000
P = .1 or 10%
© Dale R. Geiger
46
Graphic Solution
$160
Cost of subscription is known so
Expected Value is constant
$140
$120
$100
EV of Subscription
$80
EV of no subscription
$60
$40
$20
$0
0%
5%
10%
15%
X Axis = Probability of hard drive failure
As probability increases, expected value (cost) increases
© Dale R. Geiger
47
Interpreting the Results
• If the probability of hard drive failure is
greater than 10%, then the backup service is a
good deal
• If the probability of hard drive failure is less
than 10%, then the backup service may be
overpriced
• What other factors might you consider in this
case?
© Dale R. Geiger
48
Indifference Points Spreadsheet
Solve for breakeven Probability
Define the two options you are comparing
© Dale R. Geiger
49
Indifference Points Spreadsheet
Enter known data for both options
Solve for unknown probability
See how expected value changes
as probability changes
© Dale R. Geiger
50
What If?
• What if the cost of recovering the hard drive is
$2000? What is the breakeven probability?
• What if the cost of the backup service is $50?
$500?
© Dale R. Geiger
51
Check on Learning
• What is the equation for expected value?
• Which value is represented by a horizontal line
on the graph of breakeven probability?
© Dale R. Geiger
52
Practical Exercises
© Dale R. Geiger
53