1
Slide #1
ECE 4001
L15
T. Michaels
© 2011
Lecture 15
Engineering Economics:
Applications and Examples
Slide #2
ECE 4001
L15
T. Michaels
© 2011
F/P
P/F
A/F
F/A
A/P
P/A
Gradient
Factors
Slide #3
ECE 4001
L15
T. Michaels
© 2011
All Factors Obey Rules of Algebra
( / )
A
P
A P
=
⋅
1
( / )
( /
)
F P
P F

=
1
1
P = (P/F ) F
⋅
1
1
F = (F/P)
(P/F )
F
ETC.
..
⋅
⋅
Slide #4
ECE 4001
L15
T. Michaels
© 2011
Cash Flow Diagrams
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Slide #5
ECE 4001
L15
T. Michaels
© 2011
Arithmetic Gradient Series
Payment
End of Year
$0
1
$1000
2
$2000
3
$3000
4
$4000
5
Compute present value for above payments for an
interest rate of 4% (note payment total is $10,000 and
G is the payment made at the end of year 2)
Slide #6
ECE 4001
L15
T. Michaels
© 2011
Present Value of Arithmetic Gradient Series
(assume interest rate of 4%, G = $1000, 4 payments with n = 5)
( / , %, )
( / ,4%,5) 1000
P
P G i
n
G
P G
=
⋅
=
⋅
Slide #7
ECE 4001
L15
T. Michaels
© 2011
Present Value of Arithmetic Gradient Series
(assume interest rate of 4%, G = $1000, 5 yrs of payments)
5
2
5
( / , %, )
( / ,4%,5) 1000
[(1.04)
(0.04) 5 1]
1000
8,554.67
(0.04) (1.04)
P
P G i
n
G
P G
P
=
⋅
=
⋅

⋅ 
=
⋅
=
Note payment total = $10,000
Slide #8
ECE 4001
L15
T. Michaels
© 2011
Arithmetic Gradient Series Plus Annualized Series
Payment
End of Year
$1000
$1000 $0
1
$1500
$1000 $500
2
$2000
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 Spring '09
 FRAZIER
 Time Value Of Money, Net Present Value, T. Michaels, L15 T. Michaels

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