Principles of Finance/Section 1/Chapter 6/Corp/Computation

IRR, computation, Newton's Method
Project valuation may require finding the Internal Rate of Return, or the discount rate at which a project's present value of future cash flows equals to zero. This is the maximum rate of return achievable, and should be greater than the inflation rate. a simple converging guessing method has been illustrated under the Project Valuation chapter. The use of Newton's method was left as an exercise, and a possible solution is shown below. Newton's method finds the x-axis intersection of the gradient line found at an approximate IRR, which will give a better rate to try for IRR, and iterations will find an acceptable IRR where the NPV is small enough to be equal to zero.

background for derivative function of npv: Axiom: for bxa , d ( bxa)  / dx  =  ab xa-1

Hence, if, npv = CF0 / R0 + CF1 / R1 + .. + CFn / Rn, or npv = CF0 + CF1 x R-1 + CF2 x R-2 + .. + CFn x R-n, then , d(npv)/dR = 0 x CF0 x R -1 + - CF1x R -2 + - 2 CF2x R -3 ... + -n x CFn x R-n - 1.