Calculate Point Of Indifference Between Two Different Cost

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 Will Work cost is equal to benefit received. for Food • • © 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 = $20/$. 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 = $20/$. 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 = $20/$. 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 = $20/$. 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 = $20/$. 45 # MB = 20/. 45 # MB = 44. 4 © Dale R. Geiger 19

Plan A vs. Plan B $ 35 30 25 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 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 $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 * 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 * 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 * 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 * 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 * 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 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. 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 = -$100*100% $1000*P = -$100 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