#### 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!

### 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

• • • • • 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

• • 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

(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?

### Check on Learning

• • What is an indifference point or tradeoff point?

What is an example of an application of indifference points?

### 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?

### 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

### 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

### 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

### 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

### 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

### 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

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?

Enter data to compare two multivariate cost scenarios i.e. Cell phone data plans Solve for Breakeven level of Usage © Dale R. Geiger 23

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?

### 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.

### 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.

### 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.

### 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

### 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

### 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

### 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

### 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

### 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?

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?

• • 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?

Solve for breakeven Probability Define the two options you are comparing © Dale R. Geiger 49

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?