Transcript Engineering Economics in Canada

Engineering Economics in Canada
Chapter 7
Replacement Decisions
Introduction
•
•
Long-lived assets require regular evaluation as
they age.
When they are evaluated, one of four choices
can be made:
1. Keep the asset in use without major change (do
nothing)
2. Overhaul the asset to improve its performance
3. Remove it from use without replacement
4. 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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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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7.2 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
20,000
18,000
Economic Life = 5 yrs
16,000
EAC(Total)
14,000
EAC
12,000
10,000
EAC(capital)
8,000
6,000
EAC(op. and maint.)
4,000
2,000
0
0
2
4
6
8
10
Years between replacement, N
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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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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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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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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):
(1)Treat as an arithmetic or gradient series if
applicable, or
(2) Convert each cash flow to PW, then convert
to annuity over N periods
EAC(total) = EAC(capital) + EAC(op & maint)
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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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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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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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Economic Life Illustrated
20,000
18,000
Economic Life = 5 yrs
16,000
EAC(Total)
14,000
EAC
12,000
10,000
EAC(capital)
8,000
6,000
EAC(op. and maint.)
4,000
2,000
0
0
2
4
6
8
10
Years between replacement, N
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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
Years
kept
0
1
2
3
4
5
6
7
8
Salvage
Value
$40,000
$35,000
$30,000
$25,000
$20,000
$15,000
$10,000
$5,000
$0
O&M
Costs
EAC
Capital
EAC
O&M
$3,000
$4,000
$5,000
$6,000
$7,000
$8,000
$9,000
$10,000
$15,400
$12,475
$11,327
$10,631
$10,122
$9,713
$9,365
$9,059
$3,000
$3,472
$3,925
$4,359
$4,775
$5,172
$5,551
$5,913
EAC
Total
$18,400
$15,947
$15,252
$14,990
$14,897
$14,885
$14,916
$14,972
• 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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7.6 Challenger is Different from
Defender; Challenger repeats
Decision Rule:
1. Determine the Economic Life of the challenger
and its associated EAC
2. Determine the remaining Economic Life of the
defender and its associated EAC
3. 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)
$300 000
$175 000
Installation
$50 000
$10 000
Useful life
12 years
9 years
Annual depr. rate
20%
20%
• The annual maintenance costs for the upgraded robot are
$40 000 the first year and will increase by 10% per year
thereafter.
• The current robot's maintenance costs are expected to be
$50 000 next year, also increasing at 10% per year.
• MARR is 15%. Should BB replace the current robot? If yes,
when?
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Replacement Analysis (a)
(a) Challenger - Used Robot
Years
Kept
Salvage
Maint
0
175,000
1
140,000 40,000
2
112,000 44,000
3
89,600 48,400
4
71,680 53,240
5
57,344 58,564
6
45,875 64,420
7
36,700 70,862
8
29,360 77,949
9
23,488 85,744
•
EAC
Capital
72,750
61,703
55,223
50,444
46,683
43,643
41,150
39,088
37,372
EAC
Maint
EAC
Total
40,000
41,860
43,744
45,645
47,561
49,487
51,419
53,352
55,281
112,750
103,564
98,967
96,090
94,245
93,131
92,569
92,440
92,653
The Economic life of challenger robots is 9 years. The EAC of
this replacement interval is $92 440 per year.
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Replacement Analysis (b)
(b) Defender - Current Robot
Years
Kept
Salvage
Maint
0
153,600
1
122,880 50,000
2
98,304 55,000
3
78,643 60,500
4
62,915 66,550
5
50,332 73,205
6
40,265 80,526
7
32,212 88,578
8
25,770 97,436
9
20,616 107,179
•
•
EAC
Capital
53,760
48,759
44,626
41,201
38,356
35,987
34,009
32,352
30,962
EAC
Maint
EAC
Total
50,000
52,326
54,680
57,057
59,452
61,859
64,274
66,689
69,102
103,760
101,085
99,305
98,258
97,808
97,846
98,282
99,042
100,064
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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Cost Components for Certain Older
Assets
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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 Keep Upgrade
#
Robot for
Robot for
Start stream of
New Robots in
1
0 years
0 years
0 years
2
1 year
0 years
1 year
3
2 years
0 years
2 years
…
…
…
…
10
9 years
0 years
9 years
11
0 years
1 year
1 year
12
1 year
1 year
2 years
13
2 years
1 year
3 years
…
…
…
…
19
8 years
1 year
9 years
…
…
…
…
55
0 years
9 years
9 years
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Summary
•
•
•
Reasons for Replacement or Retirement of an
asset
Costs relevant to replacement decisions
Replacement analysis
1. Defender and Challenger are Identical
• Economic life; cyclic replacement.
2. Challenger is different from Defender;
Challenger repeats Indefinitely
3. Challenger is different from Defender;
Challenger does not repeat
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