Question

Internal Rate of Return A project is estimated to cost $180,116 and provide annual net cash flows of $37,000 for seven years. Present Value of an Annuity of $1 at Compound Interest Year 6% 10% 12% 15% 20% 0.943 0.909 0.893 0.870 0.833 1.833 1.736 1.690 1.626 1.528 2.673 2.487 2.402 2.283 2.106 3.465 3.170 3.037 2.855 2.589 4.212 3.791 3.605 3.352 2.991 4.917 4.355 4.111 3.784 3.326 5.582 4.868 4.564 4.160 3.605 6.210 5.335 4.968 4.487 3.837 6.802 5.759 5.328 4.772 4.031 10 7.360 6.145 5.650 5.019 4.192 Determine the internal rate of return for this project, using the Present Value of an Annuity of $1 at Compound Interest table shown above.

Answer 1

Let irr be x%
At irr,present value of inflows=present value of outflows.

180116=37000/1.0x+37000/1.0x^2+37000/1.0x^3+37000/1.0x^4+37000/1.0x^5+37000/1.0x^6+37000/1.0x^7

180116=37000[1/1.0x+1/1.0x^2+1/1.0x^3+1/1.0x^4+1/1.0x^5+1/1.0x^6+1/1.0x^7]

180116/37000=[1/1.0x+1/1.0x^2+1/1.0x^3+1/1.0x^4+1/1.0x^5+1/1.0x^6+1/1.0x^7]

[1/1.0x+1/1.0x^2+1/1.0x^3+1/1.0x^4+1/1.0x^5+1/1.0x^6+1/1.0x^7]=4.868

Hence looking at present value of annuity factor(10%,7 years);we get irr=10%