12model
10/6/2009 8:15
1/13/2003
Chapter 12.
Spreadsheet Model for Analyzing Unequal Lives and Real Options
PROJECTS WITH UNEQUAL LIVES
If two mutually exclusive projects have different lives, and if the projects can be repeated, then it is necessary to deal explicitly
with those unequal lives.
We use the replacement chain (or common life) approach. This procedure compares projects of
unequal lives by equalizing their lives by assuming that each project can be repeated as many times as necessary to reach a
common life span.
The NPVs over this life span are then compared, and the project with the higher common life NPV is chosen.
To illustrate, suppose a firm is considering two mutually exclusive projects, either a conveyor system (Project C) or a fleet of
forklift trucks (Project F) for moving materials.
The firm's cost of capital is 12%. The cash flow time lines are shown below,
along with the NPV and IRR for each project.
Project C
WACC:
12%
End of Period:
0
1
2
3
4
5
6
($40,000)
$8,000
$14,000
$13,000
$12,000
$11,000
$10,000
NPV
$6,491
IRR
17.47%
Project F
End of Period:
0
1
2
3
($20,000)
$7,000
$13,000
$12,000
NPV
$5,155
IRR
25.20%
Initially, it would appear that Project C is the better investment, based upon its higher NPV.
However, if the firm chooses Projec
F, it would have the opportunity to make the same investment three years from now. Therefore, we must reevaluate Project F
using an extended common life of 6 years.
The time lines are shown below. Note that only F's is changed.
Project C
End of Period:
0
1
2
3
4
5
6
($40,000)
$8,000
$14,000
$13,000
$12,000
$11,000
$10,000
NPV
$6,491
Use function wizard,
IRR
17.47%
Financial, NPV and IRR.
Recall that the cost must
Project F
be input separately for
NPV because Excel
0
1
2
3
4
5
6
assumes that CFs occur at
($20,000)
$7,000
$13,000
$12,000
end of periods.
($20,000)
$7,000
$13,000
$12,000
($20,000)
$7,000
$13,000
($8,000)
$7,000
$13,000
$12,000
NPV
$8,824
IRR
25.20%
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