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

© Dale R. Geiger 1

Calculate Point Of Indifference Between Two Different Cost Scenarios

Principles of Cost Analysis and Management

© Dale R. Geiger 2

What would you do for a Klondike Bar?It’s essentially a Cost/Benefit Analysis!

© Dale R. Geiger 3

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 tradeoff2. Express cost scenarios in equation form with a common

variable3. Identify and enter relevant scenario data into macro

enabled templates to calculate Points of Indifference

© Dale R. Geiger 4

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. Geiger 5

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 = $Price/Unit * #UnitsTotal Cost = ($VC/Unit * #Units) + Fixed Cost

© Dale R. Geiger 6

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 7

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 8

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 9

Check on Learning

• What is an indifference point or tradeoff point?

• What is an example of an application of indifference points?

© Dale R. Geiger 10

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


Plan A vs. Plan B





Plan A vs. Plan B





Plan A vs. Plan B





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




$.45 * # MB = $20# MB = $20/$.45 # MB = $20/$.45

# MB = 20/.45 # MB = 44.4




$.45 * # MB = $20# MB = $20/$.45 # MB = $20/$.45

# MB = 20/.45 # MB = 44.4




$.45 * # MB = $20# MB = $20/$.45 # MB = $20/$.45

# MB = 20/.45 # MB = 44.4




$.45 * # MB = $20# MB = $20/$.45 # MB = $20/$.45

# MB = 20/.45 # MB = 44.4

20

Plan A vs. Plan B

0 20 40 600

5

10

15

20

25

30

35

Plan APlan B

$

44.4X Axis = Number of MB UsedCost 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

© Dale R. Geiger


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)


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?


Indifference Points SpreadsheetEnter data to compare two multivariate cost scenariosi.e. Cell phone data plans

Solve for Breakeven level of Usage


Indifference Points SpreadsheetEnter different quantities to compare the cost of both options for various levels of usage

See which option is more favorable at a given level


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



• 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

















$Price = $.035/oz. * 67.2 oz. $Price = $.035 /oz. * 67.2 oz.






$Price = $.035/oz. * 67.2 oz. $Price = $.035 /oz. * 67.2 oz.


35

Six-Pack vs. Two-Liter

$0 $1 $2 $3 $4

$(0.01)

$0.00

$0.01

$0.02

$0.03

$0.04

$0.05

$0.06

6-pack $2.522-Liter (67.2 oz.)

X Axis = Unknown Price of 2-LiterAs Price of 2-liter increases, cost per oz. increases

Cost

Per

Oun

ce

$2.35

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

© Dale R. Geiger



• 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?


Indifference Points SpreadsheetEnter 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-literSolve for breakeven price


Check on Learning

• When solving for an indifference point, what two questions should you ask yourself first?


Tradeoffs Under Uncertainty

• 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


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


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.



• 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%



• 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%



• 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)



• 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)



• 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 = -$100P = $100/$1000P = $100/$1000

P = .1 or 10%

47

Graphic Solution

0% 5% 10% 15%$0

$20

$40

$60

$80

$100

$120

$140

$160

EV of SubscriptionEV of no subscription

X Axis = Probability of hard drive failureAs probability increases, expected value (cost) increases

Cost of subscription is known so Expected Value is constant

© Dale R. Geiger



• 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?


Indifference Points SpreadsheetSolve for breakeven Probability

Define the two options you are comparing


Indifference Points SpreadsheetEnter known data for both optionsSolve for unknown probability

See how expected value changes as probability changes


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?


Check on Learning

• What is the equation for expected value? • Which value is represented by a horizontal line

on the graph of breakeven probability?


Practical Exercises

Documents

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