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Calculate Point Of Indifference Between Two Different Cost Scenarios © Dale R. Geiger1

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What would you do for a Klondike Bar? It’s essentially a Cost/Benefit Analysis! © Dale R. Geiger2

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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. Geiger3

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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. Will Work for Food © Dale R. Geiger4

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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. Geiger5

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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. Geiger6

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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 © Dale R. Geiger7

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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. Geiger8

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Check on Learning What is an indifference point or tradeoff point? What is an example of an application of indifference points? © Dale R. Geiger9

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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. Geiger10

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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 © Dale R. Geiger11

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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 © Dale R. Geiger12

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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 © Dale R. Geiger13

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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 © Dale R. Geiger14

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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 = 44.4 © Dale R. Geiger15

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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 = 44.4 © Dale R. Geiger16

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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 = 44.4 © Dale R. Geiger17

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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 = 44.4 © Dale R. Geiger18

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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 = 44.4 © Dale R. Geiger19

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Plan A vs. Plan B $ 44.4 X Axis = Number of MB Used Cost of both plans increases as # MB increases 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 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 © Dale R. Geiger 20

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Proof © Dale R. Geiger21

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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? © Dale R. Geiger22

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Indifference Points Spreadsheet Enter data to compare two multivariate cost scenarios i.e. Cell phone data plans Enter data to compare two multivariate cost scenarios i.e. Cell phone data plans Solve for Breakeven level of Usage © Dale R. Geiger23

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Indifference Points Spreadsheet Enter different quantities to compare the cost of both options for various levels of usage 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. Geiger24

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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? © Dale R. Geiger25

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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 © Dale R. Geiger26

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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. © Dale R. Geiger27

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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. © Dale R. Geiger28

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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. © Dale R. Geiger29

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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 * 67.2 $Price = approximately $2.35 © Dale R. Geiger30

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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 * 67.2 $Price = approximately $2.35 © Dale R. Geiger31

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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 * 67.2 $Price = approximately $2.35 © Dale R. Geiger32

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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 * 67.2 $Price = approximately $2.35 © Dale R. Geiger33

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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 * 67.2 $Price = approximately $2.35 © Dale R. Geiger34

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Six-Pack vs. Two-Liter X Axis = Unknown Price of 2-Liter As Price of 2-liter increases, cost per oz. increases Cost Per Ounce $2.35 Cost of 6-pack is known so Cost per oz. is constant Cost of 6-pack is known so Cost per oz. is constant © Dale R. Geiger 35

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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 making your decision? © Dale R. Geiger36

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Indifference Points Spreadsheet Enter Data for two different cost per unit options, i.e. cost per ounce of soda 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 Enter number ounces in a 2-liter Solve for breakeven price © Dale R. Geiger37

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Check on Learning When solving for an indifference point, what two questions should you ask yourself first? © Dale R. Geiger38

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Tradeoffs Under Uncertainty Review: Expected Value = Probability of Outcome 1 * Dollar Value of Outcome 1 + Probability of Outcome 2 * Dollar Value of Outcome 2 + Probability of Outcome 3 * Dollar Value of Outcome 3 etc. Assumes probabilities and dollar value of outcomes are known or can be estimated © Dale R. Geiger39

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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 © Dale R. Geiger40

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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. © Dale R. Geiger41

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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% © Dale R. Geiger42

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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% © Dale R. Geiger43

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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. Geiger44

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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. Geiger45

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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 = -$100*100% $1000*P = -$100 P = $100/$1000 P =.1 or 10% © Dale R. Geiger46

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Graphic Solution X Axis = Probability of hard drive failure As probability increases, expected value (cost) increases Cost of subscription is known so Expected Value is constant Cost of subscription is known so Expected Value is constant © Dale R. Geiger 47

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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. Geiger48

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Indifference Points Spreadsheet Solve for breakeven Probability Define the two options you are comparing © Dale R. Geiger49

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Indifference Points Spreadsheet Enter known data for both options Solve for unknown probability Enter known data for both options Solve for unknown probability See how expected value changes as probability changes See how expected value changes as probability changes © Dale R. Geiger50

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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. Geiger51

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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. Geiger52

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Practical Exercises © Dale R. Geiger53

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