light sweet petroleum, inc. is trying to evaluate a generation project with the

Question

light sweet petroleum, inc. is trying to evaluate a generation project with the following cash flows: -$45,000,000

Explanation / Answer

IRR using a guess rate of 10% is 40.56% IRR using a guess rate of 200% is -43.86% Newton Raphson Method IRR Calculation with NPV equation = 0 f(x) = -34000000(1+i)^0 +66878000(1+i)^-1 -26829531(1+i)^-2 f'(x) = -66878000(1+i)^-2 +53659062(1+i)^-3 x0 = 0.1 f(x0) = 4625015.7025 f'(x0) = -14956226.8971 x1 = 0.1 - 4625015.7025/-14956226.8971 = 0.409236797109 Error Bound = 0.409236797109 - 0.1 = 0.309237 > 0.000001 x1 = 0.409236797109 f(x1) = -52789.0839 f'(x1) = -14502551.1664 x2 = 0.409236797109 - -52789.0839/-14502551.1664 = 0.405596811063 Error Bound = 0.405596811063 - 0.409236797109 = 0.00364 > 0.000001 x2 = 0.405596811063 f(x2) = 46.1057 f'(x2) = -14527852.3896 x3 = 0.405596811063 - 46.1057/-14527852.3896 = 0.405599984668 Error Bound = 0.405599984668 - 0.405596811063 = 3.0E-6 > 0.000001 x3 = 0.405599984668 f(x3) = 0 f'(x3) = -14527830.4133 x4 = 0.405599984668 - 0/-14527830.4133 = 0.40559998467 Error Bound = 0.40559998467 - 0.405599984668 = 0 < 0.000001 IRR = x4 = 0.40559998467 or 40.56% Newton Raphson Method IRR Calculation with NPV equation = 0 f(x) = -34000000(1+i)^0 +66878000(1+i)^-1 -26829531(1+i)^-2 f'(x) = -66878000(1+i)^-2 +53659062(1+i)^-3 x0 = 2 f(x0) = -14688392.3333 f'(x0) = -5443516.2222 x1 = 2 - -14688392.3333/-5443516.2222 = -0.698328016985 Error Bound = -0.698328016985 - 2 = 2.698328 > 0.000001 x1 = -0.698328016985 f(x1) = -107119499.727 f'(x1) = 1219636362.92 x2 = -0.698328016985 - -107119499.727/1219636362.92 = -0.610498969751 Error Bound = -0.610498969751 - -0.698328016985 = 0.087829 > 0.000001 x2 = -0.610498969751 f(x2) = -39144523.6574 f'(x2) = 467240806.328 x3 = -0.610498969751 - -39144523.6574/467240806.328 = -0.526720919702 Error Bound = -0.526720919702 - -0.610498969751 = 0.083778 > 0.000001 x3 = -0.526720919702 f(x3) = -12470642.2038 f'(x3) = 207592167.832 x4 = -0.526720919702 - -12470642.2038/207592167.832 = -0.466648122477 Error Bound = -0.466648122477 - -0.526720919702 = 0.060073 > 0.000001 x4 = -0.466648122477 f(x4) = -2924120.9259 f'(x4) = 118571124.611 x5 = -0.466648122477 - -2924120.9259/118571124.611 = -0.441986798436 Error Bound = -0.441986798436 - -0.466648122477 = 0.024661 > 0.000001 x5 = -0.441986798436 f(x5) = -313447.9702 f'(x5) = 94042769.7517 x6 = -0.441986798436 - -313447.9702/94042769.7517 = -0.438653762084 Error Bound = -0.438653762084 - -0.441986798436 = 0.003333 > 0.000001 x6 = -0.438653762084 f(x6) = -4898.8054 f'(x6) = 91117362.9143 x7 = -0.438653762084 - -4898.8054/91117362.9143 = -0.438599998396 Error Bound = -0.438599998396 - -0.438653762084 = 5.4E-5 > 0.000001 x7 = -0.438599998396 f(x7) = -1.25 f'(x7) = 91070865.7973 x8 = -0.438599998396 - -1.25/91070865.7973 = -0.43859998467 Error Bound = -0.43859998467 - -0.438599998396 = 0 < 0.000001 IRR = x8 = -0.43859998467 or -43.86% Since you have three cash flows, we can use Quadratic formula to find IRR using this online tool at http://finance.thinkanddone.com/online-i

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