#### Transcript Calculate Point of Indifference between Two Cost Scenarios

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

© 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 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 15 10 5 0 0 20 40

**X Axis = Number of MB Used Cost of both plans increases as # MB increases**

© Dale R. Geiger 44.4

60 Plan A Plan B 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 $0,05 $0,04 $0,03

**Cost of 6-pack is known so Cost per oz. is constant**

$0,02 $0,01 $ $0 $1 $2 $2.35

**X Axis = Unknown Price of 2-Liter As Price of 2-liter increases, cost per oz. increases**

$3 © Dale R. Geiger $4 6-pack $2.52

2-Liter (67.2 oz.) 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 © Dale R. Geiger Enter number ounces in a 2-liter Solve for breakeven price 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 + $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 $140 $120

**Cost of subscription is known so Expected Value is constant**

$100 $80 $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 EV of Subscription EV of no subscription 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