Question

The internal rate of return method is used by Testerman Construction Co. in analyzing a capital expenditure proposal that involves an investment of $69,264 and annual net cash flows of $13,000 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.

Answer 1

• The annuity amount is that amount which when multiplied by annual cash inflow equals the amount of initial investment.
• Internal Rate of Return is that of return rate that will lead to ‘zero’ Net Present Value when future cash inflows are discounted using this rate.
• Requirement ‘a’

à annuity figure of $1 calculation will be as follows:

$ 69,264 = $ 13,000 x $ 1 Annuity factor for 9^th year

69,264 / 13,000 = $ 1 Annuity factor for 9^th year

$ 1 Annuity factor for 9^th year = 5.328

• Requirement ‘b’

$ 1 Annuity factor for 9^th year calculated above = 5.328.

If you look closely as to where this figure (5.328) is falling in the table of annuities provided in the question, you’ll see that it falls under 12%, for 9^th year.

Hence, the Internal rate of Return = 12%