Lecture no17 variations in PW
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Variations in Present Worth
Analysis
Lecture No. 17
Chapter 5
Contemporary Engineering Economics
Copyright © 2016
Contemporary Engineering Economics, 6 th edition
Park
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Future Worth Criterion
Given
$47,309
Cash flows and MARR (i)
Find
The net equivalent worth at
a specified period other
than the “present,”
commonly at the end of the
project life
$35,560 $37,360 $31,850 $34,400
0
1
Decision Rule
Accept the project if the
equivalent worth is
positive.
2
3
$76,000
Project life
Contemporary Engineering Economics, 6 th edition
Park
Copyright © 2016 by Pearson Education, Inc.
All Rights Reserved
Excel Solution
1
2
3
4
5
6
7
8
A
Period
0
1
2
3
4
PW(12%)
FW(12%)
B
Cash Flow
($76,000)
$35,650
$37,360
$31,850
$34,400
$30,145
$47,434
Contemporary Engineering Economics, 6 th edition
Park
C
=FV(12%,4,0,-B7)
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FW Calculation with the Cash Flow
Analyzer
Payback
Period
Project
Cash
Flows
Net
Present
Worth
Net
Future
Worth
Contemporary Engineering Economics, 6 th edition
Park
Copyright © 2016 by Pearson Education, Inc.
All Rights Reserved
Example 5.6: Future Equivalent at an
Intermediate Time
Contemporary Engineering Economics, 6 th edition
Park
Copyright © 2016 by Pearson Education, Inc.
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Example 5.8:
Project’s Service Life •
Built a hyd
roelectric
is Extremely Long
plant u
pers
o
Q1: Was Bracewell's
$800,000 investment a
wise one?
o
Q2: How long does he
have to wait to recover
his initial investment,
onal savin
sing his
gs of $800
,000
• Powe
r generati
ng capacit
kwhs
y of 6 mill
ion
• Estim
ated annu
al power s
taxes − $1
ales afer
20,000
• Expec
ted serv
ice life of
5
0 years
and will he ever
make a profit?
Contemporary Engineering Economics, 6 th edition
Park
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Mr. Bracewell’s Hydroelectric Project
V1 V2 $1,101K $1, 468K
$367 K 0
V2 120 K ( P / A,8%,50)
$1, 468 K
V1 $50 K ( F / P,8%,9) $50 K ( F / P,8%,8)
L $100 K ( F / P,8%,1) 60 K
$1,101K
Contemporary Engineering Economics, 6 th edition
Park
Copyright © 2016 by Pearson Education, Inc.
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Find P for a Perpetual Cash Flow
Series, A
Contemporary Engineering Economics, 6 th edition
Park
Copyright © 2016 by Pearson Education, Inc.
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Capitalized Equivalent Worth
A
Principle: PW for a
project with an
annual receipt of A
over infinite service
life
0
n
Equation
CE(i) = A(P/A, i, )
= A/i
Contemporary Engineering Economics, 6 th edition
Park
P
=CE(i
)
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Practice Problem
Given: i = 10%, N = ∞
Find: P or CE (10%)
$2,000
$1,000
0
10
∞
P = CE (10%) = ?
Contemporary Engineering Economics, 6 th edition
Park
Copyright © 2016 by Pearson Education, Inc.
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Solution
$2,000
$1,000
0
10
∞
$1,000 $1,000
(P / F ,10%,10)
0.10
0.10
$10,000(1 0.3855)
CE(10%)
P = CE (10%) = ?
$13,855
Contemporary Engineering Economics, 6 th edition
Park
Copyright © 2016 by Pearson Education, Inc.
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A Bridge Construction Project
•
•
•
•
•
Construction cost = $2,000,000
Annual maintenance cost = $50,000
Renovation cost = $500,000 every 15 years
Planning horizon = infinite period
Interest rate = 5%
Contemporary Engineering Economics, 6 th edition
Park
Copyright © 2016 by Pearson Education, Inc.
All Rights Reserved
Cash Flow Diagram for the Bridge
Construction Project
15
Years
30
45
60
$500,000
$500,000
$500,000
$500,000
0
$50,000
$2,000,000
Contemporary Engineering Economics, 6 th edition
Park
Copyright © 2016 by Pearson Education, Inc.
All Rights Reserved
Solution
•
•
•
Construction Cost
P1 = $2,000,000
Maintenance Costs
P2 = $50,000/0.05 =
$1,000,000
• Total Present Worth
Renovation Costs
P = P1 + P2 + P3
P3 = $500,000(P/F, 5%,
= $3,463,423
15)
+ $500,000(P/F, 5%,
30)
+ $500,000(P/F, 5%,
45)
+ $500,000(P/F, 5%,
60)
:
Contemporary Engineering Economics, 6 th edition
Park
Copyright © 2016 by Pearson Education, Inc.
All Rights Reserved
Alternate Way to Calculate P3
o Concept: Find the
effective interest rate per
payment period.
o Interest rate: Find the
effective interest rate for
a 15-year cycle.
Effective interest rate
for a 15-year period
0
30
15
45
60
i = (1 + 0.05)15 − 1
= 107.893%
$500,000
$500,000
$500,000 $500,000
o Capitalized equivalent
worth
P3 = $500,000/1.0789
= $463,423
Contemporary Engineering Economics, 6 th edition
Park
Copyright © 2016 by Pearson Education, Inc.
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