LectureIII - Lecture III: Finish Discounted Value...

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1 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 zero-Stop 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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AEB 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 place-you need two interest rates that bound the zero (one positive NPV and another with a negative NPV).
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LectureIII - Lecture III: Finish Discounted Value...

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