The general format to determine the PW is
P
PV(
i
%,
n
,
A
,
F
)
[4.4]
It is important to pay attention to the sign placed on the PV function in order to
get the correct answer for the alternative’s PW value. Excel returns the opposite sign
of the
A
series because it interprets cash flows in the manner explained in Chapter
1, that is, costs are negative and the PV function value is a positive equivalent at
time 0. Therefore, to retain the negative sense of a cost series
A
, place a minus sign
immediately in front of the PV function. This is illustrated in the next example.
b.
Use the steps for a budget-constrained selection with b
$15,000.
1
and
2.
Of the 2
4
16 possible bundles, Table 4.1 indicates that 6 are
acceptable. These bundles involve all four projects plus do-nothing
with PW
DN
$0.
3.
The PW value for a bundle is obtained by adding the respective project
PW values. For example, PW
5
6646
973
$7619.
4.
Select projects F and H, since their PW is the largest and both projects
exceed the MARR, as indicated by PW
0 at
i
15%.
Comment:
Budget-constrained selection from independent projects is commonly
called the capital rationing or capital budgeting problem. It may be worked effi-
ciently using a variety of techniques, one being the integer linear programming tech-
nique. Excel and its optimizing tool SOLVER handle this type of problem rather
nicely.
TABLE 4.1
Present Worth Analysis of Independent Projects with
Investment Limited to $15,000, Example 4.7
Total Initial
PW of Bundle
Bundle
Projects
Investment
at 15%
1
F
$
8,000
$
6646
2
G
15,000
1019
3
H
6,000
973
4
J
10,000
1553
5
FH
14,000
7619
6
Do-nothing
0
0
bLa01293_ch04_080-106
8/24/07
1:01 PM
Page 96

4.6
Using Spreadsheets for PW Analysis
97
FIGURE 4.4
Equal-life alternatives evaluated using the PV function,
Example 4.8.
Cesar, a petroleum engineer, has identified two equivalent diesel-powered genera-
tors to be purchased for an offshore platform. Use
i
12% per year to determine
which is the more economic.
Generator 1
Generator 2
P
, $
80,000
120,000
S
, $
15,000
40,000
n
, years
3
3
AOC, $/year
30,000
8,000
Solution
Follow the format in Equation [4.4] in a single cell for each alternative. Figure
4.4 cell tags show the details. Note the use of minus signs on
P
, the PV func-
tion, and AOC value. Generator 2 is selected with the smaller PW of costs
(numerically larger value).
EXAMPLE
4.8
Continuing with the previous example, once Cesar had selected generator 2 to
purchase, he approached the manufacturer with the concerns that the first cost
was too high and the expected life was too short. He was offered a lease arrange-
ment for 6 years with a $20,000 annual cost and an extra $20,000 payment in
the first and last years to cover installation and removal costs. Determine if
generator 2 or the lease arrangement is better at 12% per year.
EXAMPLE
4.9
When different-life alternatives are evaluated, using the LCM basis, it is neces-
sary to input all the cash flows for the LCM of the lives to ensure an equal-service
evaluation. Develop the NPV function to find PW. If cash flow is identified by CF,
the general format is
[4.5]
It is very important that the
initial cost P not be included
in the cash flow series
identified in the NPV function. Unlike the PV function, the NPV function returns

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