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Modeling Economic Modeling Economic Life…Life…

Modeling Economic Modeling Economic Life…Life…Total EAC = EAC of

Ownership + EAC of Operation

Objective is to determine the optimum number of years to own an asset that minimizes the Total EAC.

This is called the Economic Service Life of the asset.

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Conceptually…Conceptually…Conceptually…Conceptually…

Over time…

Cost of ownership typically decreases.

Cost of operation typically increases.

ESL is the lifetime with minimum EAC!

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ESL ExampleESL ExampleESL ExampleESL ExampleAn existing process has a market value of

$15 000, but to provide the required physical service level for the next 5 years will require an immediate overhaul for $4 000. The salvage value at the end of the current year is estimated to be $1 100, and that will decrease by $100/year thereafter.

Operating and Maintenance costs are currently $4 000 yearly, but these costs will increase by $2 100/year after this year.

Determine the economic service life and resultant total EAC of the asset if the MARR is 8%, compounded annually.

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01 2 3

n = 1, 2, … 5 yrs

$4 000

DIAGRAM: $1 100 – $100(n-1)

$2 100$15 000

$4 000

EAC1=(4000+15000)(A/P,8%,1)+4000+2100(A/G,8%,1) -1100(A/F,8%,1) =$23 420

EAC2=(19 000)(A/P,8%,2)+4000+2100(A/G,8%,2) -1000(A/F,8%,2)

EAC3=(19 000)(A/P,8%,3)+4000+2100(A/G,8%,3) -900(A/F,8%,3)

EAC4=(19 000)(A/P,8%,4)+4000+2100(A/G,8%,4) -800(A/F,8%,4)

EAC5=(19 000)(A/P,8%,5)+4000+2100(A/G,8%,5) -700(A/F,8%,5)

(19 000) (1.0800) (0) (1.0000)=$15 184

(.5608) (.4808) (.4808)

=$13 087(.3880) (.9487) (.3080)

=$12 507(.3019) (1.4040) (.2219)

=$12 518(.2505) (1.8465) (.1705)

ESL = 4 yrs, this is the EACDefender if used through the end of the 4th year!

Finding EAC for lifetimes of 1 through 5 years:

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ESL Example w/ ESL Example w/ ChallengerChallenger

ESL Example w/ ESL Example w/ ChallengerChallengerThe Best Challenger process to replace

the Defender has a 1st cost of $65 000, and an expected physical lifetime of 15 years. The same MARR of 8% (compounded annually) has been used to run an ESL study on the Challenger using the best data available today, and it looks like the ESL is 8 years.

For the 8 year Challenger ESL, the operating and maintenance costs are expected to be $3 500 yearly; and the salvage value at the end of the 8 years is estimated to be $5 000. Determine how to replace the existing process.

Comparing Best ChallengerComparing Best ChallengerComparing Best ChallengerComparing Best Challenger

Opportunity Cost View for “Outsider”:

01 2 3

n = 4 yrs

$4 000

Defender: $800

$2 100$15 000

$4 000

01 2 3

n = 8 yrs

$3 500

Challenger: $5 000

$65 000

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EACChallenger 8=(65 000)(A/P,8%,8) + 3 500 - 5 000(A/F,8%,8) =$14 340(.1740) (.0940)

Finding EAC for Challenger w/ lifetime of 8 years:

01 2 3

n = 8 yrs

$3 500

Challenger: $5 000

$65 000

Lifetime EACDefender

1 $23 420

2 $15 184

3 $13 087

4 $12 507

5 $12 518

Minimum

EACDefender

Choose to keep Defender today, plan to replace defender at start of year 6

(but recheck next year to see if anything has changed!)

Ownership Life – b/c less than EACChallenger

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Questions?

For online Replacement HW problem: Assume all equipment may be salvaged at

10% of first cost, including existing system.