Question

1. The internal rate of return method is used by Leach Construction Co. in analyzing a capital expenditure proposal that involves an investment of $400,125 and annual net cash flows of $75,000 for each of the eight 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	3.353	2.991
   6	4.917	4.355	4.111	3.785	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. 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.
   %

Answer 1

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

400,125=75,000/1.0x+75,000/1.0x^2+.................+75,000/1.0x^8

400,125=75,000[1/1.0x+1/1.0x^2+................+1/1.0x^8]

400,125/75,000=[1/1.0x+1/1.0x^2+................+1/1.0x^8]

[1/1.0x+1/1.0x^2+................+1/1.0x^8]=5.335

Hence present value factor=5.335

b.Hence looking at present value of annuity factor(10%,8 years);we get irr=10%