**Unformatted text preview: **00 3
4
300
100
330.0
4 84 .0
665.5
Terminal Value: 1,579.5 -$1,000.00
$1,078.82 $ 78.82 Reinvestment at WACC = 10% T hus, we see that the NPV is consistent with reinvestment at WACC. Now repeat the process using the IRR, which is G118 as the discount rate.
Project S
IRR = 14 .4 9%
0
(1,000) P V outflows
P V of TV
NPV 1
500 2
4 00 3
4
300
100
34 3.5
5 24 .3
750.3
Terminal Value: 1,718.1 -$1,000.00
$1,000.00 Reinvestment at IRR = 14 .4 9% $0.00 T hus, if compounding is at the IRR, NPV is zero. Since the
definition of IRR is the rate at which NPV = 0, this demonstrates
that the IRR assumes reinvestment at the IRR. Profitability Index (PI)
The profitability index is the present value of all future cash flows divided by the intial cost. It measures
the PV per dollar of investment.
For project S:
PI(S) = PV of future cash flows
PI(S) = $ 1,078.82
P I(S) =
1.079 ÷
÷ Initial cost PI(L) = PV of future cash flows
PI(L) = $ 1,04 9.18
P I(L) =
1.04 9 ÷
÷ Initial cost $ 1,000.00 For project L:
$ 1,000.00 P ROJECTS 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 timelines are shown below,
'along with the NPV and IRR for each project.
Project C WACC: 11.5%
End of Period: 0
($4 0,000) 1
$8,000 NPV
I RR 2
$ 14 ,000 3
$ 13,000 4
$ 12,000 5
$ 11,000 $7,165
17.5% 6
$ 10,000 Project F
End of Period:
0
($20,000) 1
$7,000 NPV
I RR 2
$ 13,000 $5,391
25.2% 3
$ 1...

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