### Calculate Point of Indifference between Two Cost Scenarios

```Calculate Point Of Indifference
Between Two Different Cost
Scenarios
Principles of Cost Analysis and
Management
1
What would you do for a Klondike Bar?
It’s essentially a Cost/Benefit Analysis!
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
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
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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.
4
• 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
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• 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
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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
7
Indifference Point Applications
• Evaluating two machines that perform the
• 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?
8
Check on Learning
• What is an indifference point or tradeoff
point?
• What is an example of an application of
indifference points?
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?
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
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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
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
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
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
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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
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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
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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
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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
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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
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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
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)
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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?
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Enter data to compare two multivariate cost scenarios
i.e. Cell phone data plans
Solve for Breakeven level of Usage
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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
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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?
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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
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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.
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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.
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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.
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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
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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
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
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
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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
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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
\$4
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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
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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
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Check on Learning
• When solving for an indifference point, what
two questions should you ask yourself first?
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• 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
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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
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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.
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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%
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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%
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)
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)
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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%
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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
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?
48
Solve for breakeven Probability
Define the two options you are comparing
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Enter known data for both options
Solve for unknown probability
See how expected value changes
as probability changes
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?