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Chapter 15
Replacement Decisions
• Replacement Analysis
Fundamentals
• Economic Service Life
• Replacement Analysis
When Required
Service is Long
• Replacement Analysis
with Tax
Consideration
(c) 2001 Contemporary Engineering
Economics

1

Replacement Terminology
• Defender: an old
machine
• Challenger: new
machine
• Current market value:
selling price of the
defender in the market
place

• 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
• Operating Cost

(c) 2001 Contemporary Engineering
Economics

2

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

$5000

$10,000

$15,000

$20,000

(c) 2001 Contemporary Engineering
Economics

$25,000

$30,000
3

Replacement Decisions
•

Cash Flow Approach
–

–
–

Treat the proceeds from
sale of the old machine as
down payment toward
purchasing the new
machine
...

Use NPW or AE analysis
to decide

• Opportunity Cost Approach
– Treat the proceeds from sale
of the old machine as the
investment required to keep
the old machine
...
90
AE(12%)D = PW(12%)D(A/P, 12%, 3)
= -$7,259
...
90
now!
AE(12%)C = PW(12%)C(A/P, 12%, 3)
= -$6,451
...
90
AE(12%)D = PW(12%)D(A/P, 12%, 3)
= -$11,422
...
90
AE(12%)C = PW(12%)C(A/P, 12%, 3)

Replace the
defender now!

= -$10,615
...


Minimize

Ownership (Capital)
Cost (init
...
)

+
Operating
cost
CR(i )  I ( A / P, i , N )  S N ( A / F , i , N )

(c) 2001 Contemporary Engineering
Economics

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Mathematical Relationship
• Capital Recov
...

CR(i )  I ( A / P, i , N )  S N ( A / F , i , N )

AEC

• Operating Cost:

OC(i)

N

OC (i )   OCn ( P / F , i , n) ( A / P, i , N )
n 1

CR(i)

• Total Cost:
AEC  CR(i )  OC(i )

• Objective: Find n*
that minimizes AEC
(c) 2001 Contemporary Engineering
Economics

n*

10

Economic Service Life for a Lift Truck

(c) 2001 Contemporary Engineering
Economics

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Economic Service Life Calculation (Example 15
...


2
...
This
stream of cash flows is equivalent to a cash flow of AE C*
each year for an infinite number of years
...
Starting
in year x+1,the cash flows of the challenger will be used
indefinitely
...
5
• Defender: Find the
remaining useful
(economic) service
life
...


N = 1 year:
N = 2 years:
N = 3 years:
N = 4 years:
N = 5 years:

AE(15%) = $7,500
AE(15%) = $6,151
AE(15%) = $5,847
AE(15%) = $5,826
AE(15%) = $5,897

NC*=4 years
AEC*=$5,826

(c) 2001 Contemporary Engineering
Economics

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Replacement Decisions

N D*  2 years
AED*  $5,116
NC*=4 years
AEC*=$5,826

• 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
...


$2000
2

3

$3,000(F/P,15%,1) + $5,000
$3000

- $2,000 = $6,450
• Step 2: Compare this cost with
AEC = $5,826 of the challenger
...


(c) 2001 Contemporary Engineering
Economics

2

$5000

3

$6,450

21

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

6,434

5,897

Some likely replacement patterns
under a finite planning horizon of
8 years

(c) 2001 Contemporary Engineering
Economics

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Example 15
...
6 continued
• Option 3

• Option 4

(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

(c) 2001 Contemporary Engineering
Economics

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Example 15
...
(Example
15
...
(Example 15
...
(Example 15
...

• The current market value is the value to use in
preparing a defender’s economic analysis
...

(c) 2001 Contemporary Engineering
Economics

29

• Two basic approaches to analyzing replacement
problems are the cash flow approach and the
opportunity cost approach
...

– The opportunity cost approach views the net
proceeds from sale of the defender as an
opportunity cost of keeping the defender
...
We should use the respective economic service
lives of the defender and the challenger when conducting a
replacement analysis
...

• The AE method provides a marginal basis on which to
make a year-by-year decision about the best time to replace
the defender
...

(c) 2001 Contemporary Engineering
Economics

31

• 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

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