Question
King’s Department Store is contemplating the purchase of a new machine at a cost of $19,169. The machine will provide $4,200 per year in cash flow for seven years. King’s has a cost of capital of 9 percent. Use Appendix D for an approximate answer but calculate your final answer using the financial calculator method.
a. What is the internal rate of return? (Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places.)
b. Should the project be undertaken?
Appendix D Present value of an annuity of $1, PVIEA PVA A Period 2% 9 15.562 14.292 13.166 12.166 11.274 10.477 18.046 16.351 14.877 13.590 12.462 11.470 0.594 22.023 19.523 17.413 15.622 14.094 12.783 11.654 10.675 4 2 Appendix D (concluded) Percent Period 2.361 2.322 2.283 2.246 2.210 2.174 2.140 2.106 1.952 1.816 1.696 1.589 1.407 2.974 2.914 2.855 2.798 2.743 2.690 2.639 2.589 2.32 2.166 1.997 1.849 1.605 3.517 3.433 3.352 3.274 3.199 3.127 3.058 2.991 2.689 2.436 2.220 2.035 1.737 3.998 3.889 3.784 3.685 3.589 3.498 3.410 3.326 2.951 2.643 2.385 2.168 1.824 4.423 4.288 4.160 4.039 3.922 3.812 3.706 3.605 3.161 2.802 2.508 2.263 1.883 4.799 4.639 4.487 4.344 4.207 4.078 3.954 3.837 3.329 2.925 2.598 2.33 1.922 5.132 4.946 4.772 4.607 4.451 4.303 4.163 4.031 3.463 3.019 2.665 2.379 1.948 5.426 5.216 5.019 4.833 4.659 4.494 4.339 4.192 3.571 3.092 2.715 2.414 1.965 5.687 5.453 5.234 5.029 4.836 4.656 4.486 4.327 3.656 3.147 2.752 2.438 1.977 5.918 5.660 5.421 5.197 4.988 4.793 4.611 4.439 3.725 3.190 2.779 2.456 1.985 6.122 5.842 5.583 5.342 5.118 4.910 4.715 4.533 3.780 3.223 2.799 2.469 1.990 6.302 6.002 5.724 5.468 5.229 5.008 4.802 4.6113.824 3.249 2.814 2.478 1.993 6.462 6.142 5.847 5.575 5.324 5.092 4.876 4.675 3.859 3.268 2.825 2.484 1.995 6.604 6.265 5.954 5.668 5.405 5.162 4.938 4.730 3.887 3.283 2.834 2.489 1.997 6.729 6.373 6.047 5.749 5.475 5.222 4.988 4.775 3.910 3.295 2.840 2.49 1.998 6.840 6.467 6.128 5.818 5.534 5.273 5.033 4.812 3.928 3.304 2.844 2.494 1.999 6.938 6.550 6.198 5.877 5.584 5.316 5.070 4.843 3.942 3.311 2.848 2.496 1.999 7.025 6.623 6.259 5.929 5.628 5.353 5.101 4.870 3.954 3.316 2.850 2.497 1.999 7.330 6.873 6.464 6.097 5.766 5.467 5.195 4.948 3.985 3.329 2.856 2.499 2.000 7.496 7.003 6.566 6.1775.829 5.517 5.235 4.979 3.995 3.332 2.857 2.500 2.000 7.634 7.105 6.642 6.233 5.871 5.548 5.258 4.997 3.999 3.333 2.857 2.500 2.000 7.675 7.133 6.661 6.246 5.880 5.554 5.262 4.999 4.000 3.333 2.857 2.500 2.000 ..2 2 2
Explanation / Answer
Let irr be x%
At irr,present value of inflows=present value of outflows.
19169=4200/1.0x+4200/1.0x^2+............+4200/1.0x^7
Hence x=IRR=12%(Approx)
Hence since IRR is greater than the cost of capital;the project should be undertaken.
