Matakuliah : D 0094 Ekonomi Teknik
Tahun : 2007
Machine Replacement or
Retention
Pertemuan 21 s.d 22
Replacement Decisions
• Replacement Analysis
Fundamentals
• Economic Service Life
• Replacement Analysis When
Required Service is Long
• Replacement Analysis with
Tax Consideration
Bina Nusantara
Replacement Terminology
• Defender: an old machine
• Challenger: new machine
• Current market value:
selling price of the
defender in the market
place
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• Sunk cost: any past cost
unaffected by any future
decisions
• Trade-in allowance: value
offered by the vendor to
reduce the price of a new
equipment
Sunk Cost associated with an Asset’s Disposal
Original investment
$20,000
Market value
Lost investment
(economic depreciation)
$10,000
Repair cost
$5000
$10,000
Sunk costs = $15,000
$0
Bina Nusantara
$5000
$10,000
$15,000
$20,000
$25,000
$30,000
Replacement Decisions
•
Cash Flow Approach
–
Bina Nusantara
Treat the proceeds from
sale of the old machine
as down payment toward
purchasing the new
machine.
• Opportunity Cost Approach
– Treat the proceeds from
sale of the old machine as
the investment required to
keep the old machine.
Replacement Analysis – Cash Flow Approach
Sales proceeds
from defender
0
1
2
$2500
3
$10,000
$5500
0
Bina Nusantara
2
$6000
$8000
(a) Defender
1
$15,000
(b) Challenger
3
Annual Equivalent Cost - Cash Flow Approach
 Defender:
PW(12%)D = $2,500 (P/F, 12%, 3) - $8,000 (P/A, 12%, 3)
= - $17,434.90
AE(12%)D = PW(12%)D(A/P, 12%, 3)
= -$7,259.10
 Challenger:
Replace
PW(12%)C = $5,500 (P/F, 12%, 3) - $5,000
the
- $6,000 (P/A, 12%, 3)
defender
= -$15,495.90
now!
AE(12%)C = PW(12%)C(A/P, 12%, 3)
= -$6,451.79
Bina Nusantara
Opportunity Cost Approach
0
Defender
$2500
1
3
2
Challenger
0
$10,000
Bina Nusantara
2
$6000
$8000
Proceeds from sale viewed as
an opportunity cost of keeping
the asset
1
$15,000
$5500
3
Opportunity Cost Approach
 Defender:
PW(12%)D = -$10,000 - $8,000(P/A, 12%, 3) + $2,500(P/F, 12%, 3)
= -$27,434.90
AE(12%)D = PW(12%)D(A/P, 12%, 3)
= -$11,422.64
 Challenger:
PW(12%)C = -$15,000 - $6,000(P/A, 12%, 3) + $5,500(P/F, 12%, 3)
= -$25,495.90
AE(12%)C = PW(12%)C(A/P, 12%, 3)
= -$10,615.33
Bina Nusantara
Replace the
defender now!
Economic Service Life
• Def:Economic service life is
the useful life of a defender,
or a challenger, that results in
the minimum equivalent
annual cost
• Why do we need it?: We
should use the respective
economic service lives of the
defender and the challenger
when conducting a
replacement analysis.
Bina Nusantara
Minimize
Ownership (Capital)
cost
+
Operating
cost
Mathematical Relationship
• Capital Cost:
CR(i )  I ( A / P, i , N )  S N ( A / F , i , N )
AEC
• Operating Cost:
N
OC(i )   OCn ( P / F , i , n) ( A / P, i , N )
OC(i)
n 1
• Total Cost:
CR(i)
AEC  CR(i)  OC(i)
• Objective: Find n* that
minimizes AEC
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n*
Economic Service Life for a Lift Truck
Bina Nusantara
Economic Service Life Calculation (Example 15.4)
•
Bina Nusantara
N=1
AEC1 = $18,000(A/P, 15%, 1) + $1,000 - $10,000
= $11,700
• N=2
AEC2 = [$18,000 + $1,000(P/A, 15%, 2)](A/P, 15%, 2)
- $7,500 (A/F, 15%, 2)
= $8,653
Bina Nusantara
N = 3, AEC3 = $7,406
N = 4, AEC4 = $6,678
N = 5, AEC5 = $6,642
N = 6, AEC6 = $6,258
N = 7, AEC7 = $6,394
Economic Service Life
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Minimum cost
Required Assumptions and Decision
Frameworks
•
•
•
•
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Planning horizon (study period)
Technology
Relevant cash flow information
Decision Frameworks
Replacement Strategies under the
Infinite Planning Horizon
Replace the defender now: The cash flows of the challenger
will be used from today and will be repeated because an
identical challenger will be used if replacement becomes
necessary again in the future. This stream of cash flows
is equivalent to a cash flow of AEC* each year for an
infinite number of years.
Replace the defender, say, x years later: The cash flows of the
defender will be used in the first x years. Starting in year
x+1,the cash flows of the challenger will be used
indefinitely.
Bina Nusantara
Example 15.5
• Defender: Find the
remaining useful
(economic) service life.
N  1: AE (15%)  $5,130
N  2: AE (15%)  $5,116
N  3: AE (15%)  $5,500
N D*  2 years
AE D*  $5,116
Bina Nusantara
N  4: AE (15%)  $5,961
N  5: AE (15%)  $6,434
• Challenger: find the
economic service life.
NC*=4 years
AEC*=$5,826
Bina Nusantara
N
N
N
N
N
=
=
=
=
=
1
2
3
4
5
year:
years:
years:
years:
years:
AE(15%) = $7,500
AE(15%) = $6,151
AE(15%) = $5,847
AE(15%) = $5,826
AE(15%) = $5,897
Replacement Decisions
N D*  2 years
AED*  $5,116
NC*=4 years
AEC*=$5,826
Bina Nusantara
• Should replace the
defender now? No,
because AED < AEC
• If not, when is the best
time to replace the
defender? Need to
conduct marginal analysis.
Marginal Analysis
Question: What is the additional (incremental)
cost for keeping the defender one more year
from the end of its economic service life, from
Year 2 to Year 3?
Financial Data:
• Opportunity cost at the end of year 2: Equal to the market
value of $3,000
• Operating cost for the 3rd year: $5,000
• Salvage value of the defender at the end of year 3: $2,000
Bina Nusantara
•
Step 1: Calculate the
equivalent cost of retaining the
defender one more from the
end of its economic service life,
say 2 to 3.
$3,000(F/P,15%,1) + $5,000
- $2,000 = $6,450
•
Step 2: Compare this cost with
AEC = $5,826 of the challenger.
•
Conclusion: Since keeping the
defender for the 3rd year is
more expensive than replacing
it with the challenger, DO NOT
keep the defender beyond its
economic service life.
Bina Nusantara
$2000
2
$3000
2
3
$5000
3
$6,450
Replacement Analysis under the Finite
Planning Horizon
Annual Equivalent Cost ($)
N
Defender
Challenger
1
5,130
7,500
2
5,116
6,151
3
5,500
5,857
4
5,961
5,826
5
Bina Nusantara
6,434
5,897
Some likely replacement patterns
under a finite planning horizon of
8 years
Example 15.6 Replacement Analysis under the Finite Planning
Horizon (PW Approach)
•
Option 1:
• Option 2:
Bina Nusantara
(j0, 0), (j, 4), (j, 4)
PW(15%)1=$5,826(P/A, 15%, 8)
=$26,143
(j0, 1), (j, 4), (j, 3)
PW(15%)2=$5,130(P/F, 15%, 1)
+$5,826(P/A, 15%, 4)(P/F, 15%, 1)
+$5,857(P/A, 15%, 3)(P/F, 15%, 5)
=$25,573
Example 15.6 continued
• Option 3
• Option 4
Bina Nusantara
(j0, 2), (j, 4), (j, 2)
PW(15%)3=$5,116(P/A, 15%, 4)(P/F, 15%, 2)
+$5,826(P/A, 15%, 4)(P/F, 15%, 2)
+$6,151(P/A, 15%, 2)(P/F, 15%, 6)
= $25,217
minimum cost
(j0, 3), (j, 5)
PW(15%)4= $5,500(P/A, 15%, 3)
+$5,897(P/A, 15%, 5)(P/F, 15%, 3)
=$25,555
Example 15.6 continued
• Option 5:
• Option 6:
Bina Nusantara
(j0, 3), (j, 4), (j, 1)
PW(15%)5= $5,500(P/A, 15%, 3)
+ $5,826(P/A, 15%, 4)(P/F, 15%, 3)
+ $7,500(P/F, 15%, 8)
= $25,946
(j0, 4), (j, 4)
PW(15%)6= $5,826(P/A, 15%, 4)(P/F, 15%, 4)
+ $5,826(P/A, 15%, 4)(P/F, 15%, 4)
= $26,529
Planning horizon = 8 years
(j0, 0), (j, 4), (j, 4),
Option 1
(j0, 1), (j, 4), (j, 3),
Option2
(j0, 2), (j, 4), (j, 2),
Option 3
(j0, 3), (j, 5),
Option 4
(j0, 3), (j, 4), (j, 1),
Option 5
(j0, 4), (j, 4),
Option 6
0
1
2
3
4
5
Years in service
6
7
8
Replacement Analysis with Tax Consideration
• Whenever possible, replacement decisions should be based
on the cash flows after taxes. (Example 15.8)
• When computing the net proceeds from sale of the old
asset, any gains or losses must be identified to determine
the correct amount of the opportunity cost. (Example 15.7)
• All basic replacement decision rules including the way of
computing economic service life remain unchanged.
(Example 15.10)
Bina Nusantara
Depreciation basis
$20,000
$20,000
Total
depreciation
Book value
$14,693
$5307
Market value
Book loss
$10,000
$4693
Market value
Loss
tax credit
$4693  40%  $1877
$10,000
Net proceeds from disposal ($11,877)
$0
$4000
$8000
$12,000
$16,000
$20,000
Summary
• In replacement analysis, the defender is an existing
asset; the challenger is the best available replacement
candidate.
• The current market value is the value to use in
preparing a defender’s economic analysis. Sunk
costs—past costs that cannot be changed by any future
investment decision—should not be considered in a
defender’s economic analysis.
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• Two basic approaches to analyzing replacement
problems are the cash flow approach and the
opportunity cost approach.
– The cash flow approach explicitly considers the
actual cash flow consequences for each replacement
alternative as they occur.
– The opportunity cost approach views the net
proceeds from sale of the defender as an opportunity
cost of keeping the defender.
Bina Nusantara
• Economic service life is the remaining useful life of a
defender, or a challenger, that results in the minimum
equivalent annual cost or maximum annual equivalent
revenue. We should use the respective economic service lives
of the defender and the challenger when conducting a
replacement analysis.
• Ultimately, in replacement analysis, the question is not
whether to replace the defender, but when to do so.
• The AE method provides a marginal basis on which to make a
year-by-year decision about the best time to replace the
defender.
• As a general decision criterion, the PW method provides a
more direct solution to a variety of replacement problems,
with either an infinite or a finite planning horizon, or a
technological change in a future challenger.
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• The role of technological change in asset improvement
should be weighed in making long-term replacement plans
• Whenever possible, all replacement decisions should be based
on the cash flows after taxes.
Bina Nusantara