A project is estimated to cost $188,454 and provide annual net cash flows of $42

Question

A project is estimated to cost $188,454 and provide annual net cash flows of $42,000 for eight years.

Determine the internal rate of return for this project, using the Present Value of an Annuity of $1 at Compound Interest table shown above.
%

Present Value of an Annuity of $1 at Compound Interest Year 6% 10% 12% 15% 20% 1 0.943 0.909 0.893 0.870 0.833 2 1.833 1.736 1.690 1.626 1.528 3 2.673 2.487 2.402 2.283 2.106 4 3.465 3.170 3.037 2.855 2.589 5 4.212 3.791 3.605 3.352 2.991 6 4.917 4.355 4.111 3.784 3.326 7 5.582 4.868 4.564 4.160 3.605 8 6.210 5.335 4.968 4.487 3.837 9 6.802 5.759 5.328 4.772 4.031 10 7.360 6.145 5.650 5.019 4.192

Explanation / Answer

Calculation of Internal Rate of Return Let the Rate be 10% Year Cash Flow Discount Total 0 -188454 1 -188454 1 42000 0.909091 38181.82 2 42000 0.826446 34710.74 3 42000 0.751315 31555.22 4 42000 0.683013 28686.57 5 42000 0.620921 26078.70 6 42000 0.564474 23707.91 7 42000 0.513158 21552.64 8 42000 0.466507 19593.31 NPV 35612.90 20% Year Cash Flow Discount Total 0 -188454 1 -188454 1 42000 0.833333 35000.00 2 42000 0.694444 29166.67 3 42000 0.578704 24305.56 4 42000 0.482253 20254.63 5 42000 0.401878 16878.86 6 42000 0.334898 14065.72 7 42000 0.279082 11721.43 8 42000 0.232568 9767.86 NPV -27293.29 IRR = Lower Rate+ NPV at lower Rate/ NPV at lower rate+ NPV at higher Rate ( HR-LR) IRR = 10+ 35613/35613+27294 ( 20-10) IRR = 10+5.67 IRR = 15.67% Internal Rate of return is 15.67% approximately

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