Civil Engineering Reference
In-Depth Information
A general expression for PW is
þ
f
Þ
j
C
pel
Q
el
j
þ
C
p
th
Q
th
j
C
pa
Q
a
j
ð
1
X
n
1
j
PW
¼
I
p
Þ
j
Þ
j
ð
1
þ
r
ð
1
þ
f
C
pel
Q
el
j
þ
C
p
th
Q
th
j
C
pa
Q
a
j
X
n
1
j
¼
I
p
Þ
j
ð
1
þ
i
where
i ¼ r
+
f f
* for small values of
r
,
f
,
f
*.
In order to obtain a simpler expression, annual energy saving in physical units is
assumed constant during the life of the investment, and so are other savings and
additional expenditures. In addition, the present investment
I
p
is assumed to be equal
to the total investment
I
, which is taken to occur wholly in the present year (year zero).
The simplified PW expression becomes as follows:
X
n
1
j
1
PW
¼
C
pel
Q
el
þ
C
p
th
Q
th
C
pa
Q
a
Þ
j
I
ð
1
þ
i
¼
C
pel
Q
el
þ
C
pth
Q
th
C
pa
Q
a
PAF
I
¼
NACF
PAF
I
annual amount of revenues in physical units assumed
constant throughout the life of the investment. They start to become effective in
year 1;
n
where
Q
el
,
Q
th
, and
Q
a
¼
¼
years of investment life,
i
¼
r
+
f
f
*(
i
¼
r
,if
f
¼
f
*), and
I
¼
total
investment concentrated in the year zero (see Payback):
X
n
1
j
j
¼
Present annuity factor PAF
ð
Þ
ð
þ
i
Þ
1
1
NACF
¼
Net annual cash flow (see Payback).
If PW is greater than zero, the project is valid since the revenues are
enough to pay the interest and to recover the initial capital cost
before the end of the life of the investment. If PW equals zero, the
balance occurs at the end of the life, but the investment is scarcely
attractive. PW less than zero means that the project is a bad one.
Projects can conveniently be compared by taking as a parameter the
ratio between the present worth of the project and the related investment
(PW/
I
).
