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Lecture III: Finish Discounted Value Formulation
I.
Internal Rate of Return
A. Formally defined: Internal Rate of Return is that interest rate which
reduces the net present value of an investment to zero.
1.
Finding the internal rate of return
:
The solution of the internal rate of
return does not analytically exist.
Methods for finding the internal
rate of return are, thus, numerical search techniques or iterative
processes.
a.
Simple approach: Numeric gradient
(i.)
Compute the NPV of an investment at two points, or for
two interest rates. {The solution technique works best if
one point has a positive NPV and the other a negative
NPV}.
(ii.)
Compute the line between the two points and find where
the line equals zero.
Assume
i
2
>
i
1
and NPV
1
>NPV
2
.
12
311
322
or
NP
V
NPV
iii
ii
NP
V
NPV

=



NPV
i
i
2
i
1
i
3
(iii.)
Decide whether the NPV is close enough to zeroStop if
yes, go back to step (ii) if no.
{If the NPV at
i
3
is positive
replace
i
1
, if it is negative, replace
i
2
}.
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View Full DocumentAEB 6145 Lecture III
Professor Charles B. Moss
2
(iv.)
Problems:
The procedure does not have a good
convergence {it may take a long time}.
It may be
difficult to find a good starting placeyou need two
interest rates that bound the zero (one positive NPV and
another with a negative NPV).
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 Spring '11
 Moss

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