The internal rate of return method is used by King Bros Cons

The internal rate of return method is used by King Bros. Construction Co. in analyzing a capital expenditure proposal that involves an investment of $102,030 and annual net cash flows of $15,000 for each of the nine years of its useful life. 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 a. Determine a present value factor for an annuity of $1 which can be used in determining the internal rate of return. If required, round your answer to three decimal places. b. Using the factor determined in part (a) and the present value of an annuity of $1 table above, determine the internal rate of return for the proposal. %

Solution

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

102030=15000/1.0x+15000/1.0x^2+...........+15000/1.0x^9

102030=15000[1/1.0x+1/1.0x^2+...........+1/1.0x^9]

[1/1.0x+1/1.0x^2+...........+1/1.0x^9]=(102030/15000)

[1/1.0x+1/1.0x^2+...........+1/1.0x^9]=6.802

1.Present value factor =6.802

2.Looking at present value factor of 6.802 for 9 years;we get irr=6%