Question

The internal rate of return method is used by Royston Construction Co. in analyzing a capital expenditure proposal that involves an investment of $52,492 and annual net cash flows of $11,000 for each of the 9 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. If required, round your answer to three decimal places.
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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.
fill in the blank 1 of 1
%

Answer 1

The present value factor for an annuity of $1 for Royston Construction Co.'s proposal is 4.772. By comparing this factor to a present value of an annuity table, the estimated internal rate of return is approximately 15%.

Step-by-step explanation:

To determine the internal rate of return (IRR) for Royston Construction Co.'s capital expenditure proposal, we need to calculate the present value factor for an annuity of $1 and then use this factor to estimate the IRR using the provided present value of an annuity table.

a. The present value factor for an annuity of $1 can be found by dividing the total investment by the annual net cash flow. Therefore, the present value factor is:

Present Value Factor = Investment / Annual Net Cash Flows = $52,492 / $11,000 ≈ 4.772

b. To find the internal rate of return, we look at the present value of an annuity table and find the closest factor to our calculated present value factor of 4.772, which occurs under the 9-year annuity at the 15% interest rate. Hence, the internal rate of return is approximately 15%.