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**Unformatted text preview: **it is possible for some (but not all) projects that have more than one change of signs in the
set of cash flows to have more than one IRR. If you attempted to find the IRR with such a project using a financial calculator,
you would get an error message. The HP-10B says "Error - Soln", the HP-17B says '"Many/No Solutions, and the HP12C says
Error 3; Key in Guess" when such a project is evaluated. The procedure for correcting the problem isto store in a guess for the
IRR, and then the calculator will report the IRR that is closest to your guess. You can then use a different "guess" value, and
you should be able to find the other IRR. However, the nature of the mathematics creates a scenario in which one IRR is quite
extraordinary (often, a few hundred percent).
Consider the case of Project M.
Project M: 0
(1.6) 1
10 2
(10) We will solve this IRR twice, the first time using the default guess of 10%, and the second time we will enter a guess
of 300%. Notice, that the first IRR calculation is exactly as it was above.
IRR M 1 = 25.0% IRR M 2 = 4 00% The two solutions to this problem tell us that this project will have a positive NPV for all costs of capital between
'25% and 400%. We illustrate this point by creating a data table and a graph of the project NPVs.
Project M: 0
(1.6) r=
NPV = 1
10 2
(10) 25.0%
0.00
NPV
$0.0
(1.60)
0.00
0.62
0.85
0.90
0.87
0.80
0.71
0.62
0.53
0.4 4
0.36
0.28
0.20
0.13
0.06
0.00
(0.06)
(0.11)
(0.16)
(0.21)
(0.26)
(0.30) r
0%
25%
5 0%
7 5%
100%
125%
150%
175%
2 00%
2 25%
2 50%
2 75%
300%
325%
350%
375%
4 00%
4 25%
4 50%
4 75%
500%
525%
550% Multiple Rates of Return
$ 1.00
$ 0.90
$ 0.80 Max. $ 0.70
$ 0.60
$ 0.50
$ 0.40
$ 0.30
$ 0.20
$ 0.10
$ 0.00
-100% 0% 100% 200% 300% 400% 500% NPV Profiles
NPV profiles graph the relationship between projects' NPVs and the cost of capital. To create NPV profiles for
P rojects S and L, we create data tables of NPV at different costs of capital.
Net Cash Flows
Project S Project L
-$1,000
-$1...

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