1. Engineering Economics in Canada
Chapter 7
Replacement Decisions

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Introduction
Long-lived assets require regular evaluation as they age.
When they are evaluated, one of four choices can be made:
Keep the asset in use without major change (do nothing)
Overhaul the asset to improve its performance
Remove it from use without replacement
Replace the current asset with another asset
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Introduction (con’t)
Chapter 7 is concerned with replacement decisions for long-lived assets.
Why a special chapter?
The relevant costs for making such decisions are not always obvious.
The service live has been assumed in earlier chapters – Chapter 7 shows how the service life of an asset is calculated.
Assumptions about how an asset may be replaced in the future can affect a current decision.
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4. Reasons for Depreciation
Recall from Chapter 6 – Assets lose value, or depreciate, for a variety of reasons:
Use related physical loss: Measured as a function of units of production, miles driven, or other measures of use
Time related physical loss: Measured in units of time
Functional loss: Measured in terms of the function lost
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7.2 A Replacement Example
How long should you keep a car before replacing it?
Assume that you have an ongoing need for a car.
The equivalent annual capital costs of replacing the car every N years can be found from the capital recovery formula
EAC(capital) = A = (P – S)(A/P, i, N) + Si
The longer the time between replacements, the lower the EAC(capital).
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7.2 A Replacement Example
equivalent annual capital costs
EAC(capital) = A = (P – S)(A/P, i, N) + Si
EAC: Annualized Capital Cost
P: Purchase Value
S: Salvage Value
i: Interest Rate
N: N-year replacement Period
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7. 7.2 A Replacement Example (con’t)
The replacement decision also depends on operating and maintenance costs
These costs tend to increase the longer you keep a car
The EAC of operating and maintaining a car can be computed assuming the car is kept for N years, N=1,2,…
The economic life is the number of years that minimizes:
EAC(total) = EAC(capital) + EAC(op. & maint.)
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A Replacement Example
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9. 7.3 Reasons for Replacement or Retirement
If there is an ongoing need for the service an asset provides…
Replacement becomes necessary if there is a less expensive means of getting the service it provides, or if the service provided is no longer adequate.
If there is no longer a need for the service an asset provides, an asset may be retired – removed from service without replacement.
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10. 7.4 Capital Costs and Other Costs
What are the relevant costs associated with owning and assets?
Purchasing an asset is a decision to acquire capacity, or the ability to produce a good or service. Relevant costs are:
1. Capital costs:
The difference between the price paid and what it can be sold for some time after purchase, usually expressed as EAC.
The largest portion of capital costs of an asset typically occurs early in its life.
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11. Capital Costs and Other Costs (con’t)
2. Installation costs:
Installation costs occur at the beginning of the life of new assets and are not reversible once the capacity is put in place
E.g. lost production time, lost output due to learning a new system
3. Operating and maintenance costs
the cost of using the asset to produce goods or services
Most replacement decisions are made on the basis of total Equivalent Annual Costs (EAC)
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12. Equivalent Annual Costs (EAC)
P = first cost I = installation cost
S = salvage value N = number of years asset kept
EAC(capital) = (P + I – S)(A/P, i, N) + S i
EAC(op & maint):
Treat as an arithmetic or gradient series if applicable, or
Convert each cash flow to PW, then convert to annuity over N periods
EAC(total) = EAC(capital) + EAC(op & maint)
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13. Replacement Scenarios
Defender – an existing asset
Challenger – a potential replacement
We will look at three situations:
1. The Defender and Challenger are identical and the need for the asset continues indefinitely.
2. The Defender is different from the Challenger; the challenger repeats indefinitely.
3. The Defender and Challenger are different, and successive Challengers are not identical.
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14. 7.5 Defender and Challenger are Identical
All long-lived assets will need to be replaced eventually.
We consider the situation where there is an ongoing need for an asset and the technology is not changing rapidly.
We model the replacement decision as if it were to take place an indefinitely large number of times i.e. cyclic replacement
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15. Economic Life of an Asset
Cyclic replacement: When technology, prices and interest rates are not changing quickly, an assumption can be made that an asset will be replaced with the same type of asset over and over
EAC(capital) usually decrease over time
EAC(op&maint) usually increase over time
Hence, there usually is a lifetime that will minimize EAC(total): this is the economic life of the asset
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16. Economic Life Illustrated
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17. Example 7-1(very important)
A new bottle capping machine costs $40 000, plus $5000 for installation.
The machine is expected to have a useful life of 8 years with no salvage value at that time (assume straight line depreciation).
Operating and maintenance costs are expected to be $3000 for the first year, increasing by $1000 each year thereafter.
Interest is 12%. What is the economic life of a bottle capper?
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Replacement Analysis
The minimum Total EAC occurs when replacement occurs every six years.
The economic life of a bottle capper is 6 years
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19. 7.6 Challenger is Different from Defender; Challenger repeats
Decision Rule:
Determine the Economic Life of the challenger and its associated EAC
Determine the remaining Economic Life of the defender and its associated EAC
If the EAC(defender) > EAC(challenger), replace now. Otherwise, do not replace now.
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Example 7-2
Brockville Brackets (BB) has a 3 year old robot and its Challenger is an upgraded used robot.
Defender Challenger
Price (when new) $ $
Installation $ $10 000
Useful life 12 years 9 years
Annual depr. rate 20% 20%
The annual maintenance costs for the upgraded robot are $ the first year and will increase by 10% per year thereafter.
The current robot's maintenance costs are expected to be $ next year, also increasing at 10% per year.
MARR is 15%. Should BB replace the current robot? If yes, when?
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21. Replacement Analysis (a)
The Economic life of challenger robots is 9 years. The EAC of this replacement interval is $ per year.
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22. Replacement Analysis (b)
The remaining economic life of the defender is 5 years. The EAC of keeping the defender this additional time is $97 808
The EAC(defender) > EAC(challenger)  replace now.
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One Year Principle
In some cases, the computations for the Defender can be simplified
For assets that have been in place several years, the annual capital costs will often be low in comparison to operating and maintenance costs and the EAC(total) will be increasing in N
 One year principle: if the cost of keeping the defender one more year exceeds the EAC of the challenger at its economic life, then the defender should be replaced immediately.
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24. Cost Components for Certain Older Assets
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25. 7.7 Challenger is Different from Defender; Challenger Does not Repeat
Normally we expect the future challengers to be better than the current challenger
Do we skip over the current challenger and wait for the next “new and improved” challenger?
We must enumerate all possible combinations of replacement options and evaluate all to make a choice
EAC for each combination must be calculated
Number of combinations increases quickly
Typically, very little information is available on the costs and benefits of future challengers
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Example 7-2 (revisited)
In example 7-2, Brockville Brackets (BB) may use the current robot for its remaining life of 9 years, and replace it with a stream of new robots.
BB may replace the current robot with an upgraded used robot, with a remaining life also of 9 years, followed by a stream of new robots.
… and so on
BB can list all the possible options as Mutually Exclusive projects and select the best based on PW, AW (EAC) or IRR.
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Project #
Keep Current
Robot for
Keep Upgrade
Start stream of
New Robots in 1
0 years 2
1 year 3
2 years … 10
9 years 11 12 13
3 years 19
8 years 55
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Summary
Reasons for Replacement or Retirement of an asset
Costs relevant to replacement decisions
Replacement analysis
Defender and Challenger are Identical
Economic life; cyclic replacement.
Challenger is different from Defender; Challenger repeats Indefinitely
Challenger is different from Defender; Challenger does not repeat
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