Chapter 12 - Replacement
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EGR 403 Capital Allocation Theory
Dr. Phillip R. Rosenkrantz
Industrial & Manufacturing Engineering Department
Cal Poly Pomona
EGR 403 - The Big Picture
• Framework: Accounting & Breakeven Analysis
• “Time-value of money” concepts - Ch. 3, 4
• Analysis methods
–
–
–
–
Ch. 5 - Present Worth
Ch. 6 - Annual Worth
Ch. 7,7A,8 - Rate of Return (incremental analysis)
Ch. 9 - Benefit Cost Ratio & other methods
• Refining the analysis
– Ch. 10, 11 - Depreciation & Taxes
– Ch. 12 - Replacement Analysis
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Replacement Analysis
• When should a new truck replace the
existing truck?
• When should a process be redesigned?
• When should a product be redesigned?
The most common question asked in industry is
when should the existing be replaced?
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Replacement Analysis Terms
• Defender - the existing equipment or
building previously implemented.
• Challenger - the proposed replacement
currently under consideration.
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Aspects of Replacement Analysis
•
Using available data to determine the analysis
technique.
Determining the base comparison between
alternatives.
Using analysis techniques when:
•
•
•
•
•
•
•
Defender marginal cost can be computed and is
increasing.
Defender marginal cost can be computed and is not
increasing.
Defender marginal cost is not available.
Considering possible future challengers.
After-tax analysis.
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The Replacement Problem
• Engineers replace the existing due to:
– Obsolescence - technological change.
– Depletion - loss of market value.
– Deterioration - wear that is overly expensive to
repair.
Shall the defender be replaced now or be
maintained for one or more periods.
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Issues (Consider Before Starting)
• Is it morally or ethically right to do this project?
• If a unit fails, must it be removed permanently
from service? Or repaired? Are standby units
available if the system should fail?
• Do components or units fail independently of the
failure of other components?
• Is there a budget constraint?
• In the event that the unit can be repaired after
failure is their a constraint on the capacity of the
repair facility?
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Issues (Continued)
• Is there only one replacement allowed over the
planning horizon? Are subsequent replacements
allowed at any time during the study period?
• Is their more than one replacement unit (price and
quality combination) available at a given point in
time?
• Do future replacement units differ over time? Are
technological improvements considered?
• Is preventative maintenance included in the
model?
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Issues (Continued)
• Are periodic operating and maintenance costs
constant or variable over time?
• Is the planning horizon finite or infinite?
• Are consequences other than economic impacts,
i.e., sociotechnical issues considered?
• Are income tax consequences considered?
• Is “inflation” considered?
• Does replacement occur simultaneously with
retirement, or are there nonzero lead times?
• Are cash flow estimates deterministic or
stochastic?
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Replacement Analysis Decision Chart
Where
Compare
Defender
Marginal Cost
Defender
Marginal Cost
Defender
Best
Challenger
1
Available
Increasing
Next-year
Marginal Cost
EUAC at
Minimum
Cost Life
2
Available
Not increasing
EUAC at
Minimum
Cost Life
EUAC at
Minimum
Cost Life
3
Not available
EUAC over
Remaining
Useful Life
EUAC at
Minimum
Cost Life
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What Is the Basic Comparison?
• Identify the defender and the best challenger.
–
–
–
–
–
Product.
Machine.
Process.
Personnel.
Mix.
Decision Criteria leads to one of the following:
If the defender is more economical, it should be retained.
If the challenger is more economical, it should be installed.
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Minimum Cost Life of the Challenger
• Calculate the EUAC for each value of the
useful life (e.g., n = 1, n = 2, n = 3, etc.)
• The number of years at which the EUAC is
minimized is the minimum cost life (economic
useful life)
• Consider Example 12 - 1
– $7500 initial cost (P)
– $900 arithmetic gradient maintenance cost (G)
– $500 uniform cost (A) and 400 arithmetic gradient
operating cost (G)
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EUAC calculations for increasing values of useful life
Year
EUAC of
Capital
Recovery
Costs
EUAC of
Maintenance
and Repair
Costs
EUAC of
Operating
Costs
Initial year
-7500
0
-500
Arithmetic
gradient
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
EUAC Total
Interest
rate
8%
-900
$8,100.00
$4,205.77
$2,910.25
$2,264.41
$1,878.42
$1,622.37
$1,440.54
$1,305.11
$1,200.60
$1,117.72
$1,050.57
$995.21
$948.91
$909.73
$876.22
-400
$0.00
$500.00
$432.69
$692.31
$853.87
$879.50
$1,263.56
$1,061.58
$1,661.82
$1,238.59
$2,048.71
$1,410.54
$2,424.30
$1,577.47
$2,788.67
$1,739.41
$3,141.93
$1,896.41
$3,484.18
$2,048.53
$3,815.55
$2,195.80
$4,136.17
$2,338.30
$4,446.19
$2,476.08
$4,745.75
$2,609.22
$5,035.01
$2,737.78
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$8,600.00
$5,330.77
$4,643.62
$4,589.55
$4,778.84
$5,081.62
$5,442.31
$5,833.19
$6,238.94
$6,650.43
$7,061.93
$7,469.68
$7,871.18
$8,264.69
$8,649.02
<-----MIN
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Graph of EUAC by n.
Economic Useful Life is where Total EUAC is minimized
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Marginal Costs
• Marginal Costs are the year by year costs for
keeping an asset. Example 12-2 illustrates the
calculation of the marginal costs for a new item.
• Marginal Cost includes:
– Loss in value of the asset by retaining it for one more
year
– Lost interest on the money tied up in the asset
– Costs and expenses directly related to the project or
asset (e.g., insurance, operating and maintenance)
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Marginal Cost for a New Item: Example 12-2
Expense
Cost
Investment Cost $25,000.00
Annual O&M
$ 2,000.00
Cost
Annual Insurance
$ 5,000.00
Cost
Useful Life
7
(years)
MARR
15%
Year
0
1
2
3
4
5
6
7
Loss in
Market
Value
Market Value
$
$
$
$
$
$
$
$
25,000.00
18,000.00
13,000.00
9,000.00
6,000.00
4,000.00
3,000.00
2,500.00
$
$
$
$
$
$
$
0
Incremental
cost
thereafter
$
-
1
$ 500.00
3
$ 1,500.00
Years
Foregone
Interest
O&M Cost
7,000.00 $3,750.00 $ 2,000.00
5,000.00 $2,700.00 $ 2,500.00
4,000.00 $1,950.00 $ 3,000.00
3,000.00 $1,350.00 $ 3,500.00
2,000.00 $ 900.00 $ 4,000.00
1,000.00 $ 600.00 $ 4,500.00
500.00 $ 450.00 $ 5,000.00
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Insurance
Cost
$ 5,000.00
$ 5,000.00
$ 5,000.00
$ 6,500.00
$ 8,000.00
$ 9,500.00
$11,000.00
Total
Marginal
Cost
$17,750.00
$15,200.00
$13,950.00
$14,350.00
$14,900.00
$15,600.00
$16,950.00
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Marginal Cost Data Defender
Year
0
1
2
3
4
5
6
7
Expense
Cost
Years
Investment Cost
Annual O&M
Cost
Annual Insurance
Cost
Useful Life
(years)
MARR
$15,000.00
0
Incremental
cost
thereafter
$
-
$10,000.00
1
$ 1,500.00
$
15,000.00
14,000.00
13,000.00
12,000.00
11,000.00
10,000.00
$
Is the marginal cost of
defender increasing?
-
Here the marginal
costs are increasing.
5
15%
Loss in
Market
Value
Market Value
$
$
$
$
$
$
-
Example 12-3
$
$
$
$
$
1,000.00
1,000.00
1,000.00
1,000.00
1,000.00
Foregone
Interest
O&M Cost
Insurance
Cost
$2,250.00
$2,100.00
$1,950.00
$1,800.00
$1,650.00
$10,000.00
$11,500.00
$13,000.00
$14,500.00
$16,000.00
$
$
$
$
$
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Total
Marginal
Cost
$13,250.00
$14,600.00
$15,950.00
$17,300.00
$18,650.00
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Replacement Analysis Technique #1
Defender Marginal costs are increasing
• Replace when the marginal cost of ownership of
the defender is more than the EUAC of the
challenger.
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Analysis Technique # 1
Is Appropriate When
Replacement Repeatability Assumptions Hold
• The best challenger is available in all subsequent
years and will be unchanged in economic cost.
• The period of needed service is infinitely long.
These assumptions appear to be rather
restrictive.
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Relaxing the Restrictions
• This spreadsheet considers that:
– The best challenger is available in subsequent years at
the same economic cost.
– The project life is known and limited.
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Replacement Analysis Technique #2
• If the replacement repeatability assumption holds,
compare EUAC of the defender asset at its
minimum cost life against the EUAC of the
challenger at its minimum cost life.
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Replacement Analysis Technique #3
• Compare the EUAC of the defender over its stated
life against the minimum EUAC of the challenger.
•Here defining defender and challenger first costs can be an issue.
–Trade-in value is not a suitable value.
–Appropriate value is the market value.
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After Tax Replacement Analysis
• Adds expanded perspective as changes occur in:
– Remaining economic life of defender.
– Economic life of challenger.
– Defender vs. Challenger comparisons.
• Affected by:
– Depreciation MACRS.
– Assets market value over time.
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