Cervantes Company is considering an investment in a new machine. Managers at the company are uncertain about the economic life of the machine, because of the speed of innovation in the technology. The machine requires an investment of $3 million. After-tax cash flows are estimated to be $545,653 each year the machine is operating (and not obsolete). The company uses a 10 percent discount rate in evaluating capital investments. Use Exhibit A.9.

Required:

What is the minimum economic life of the machine (in whole years) that would be required for it to have a positive net present value?

Exhibit A.9 Present Value of an Annuity of $1 Year 5% 6% 8% 10% 12% 14% 15% 16% 18% 20% 1 0.952 0.943 0.926 0.909 0.893 0.877 0.870 0.862 0.847 0.833 2 1.859 1.833 1.783 1.736 1.690 1.647 1.626 1.605 1.566 1.528 3 2.723 2.673 2.577 2.487 2.402 2.322 2.283 2.246 2.174 2.106 4 3.546 3.465 3.312 3.170 3.037 2.914 2.855 2.798 2.690 2.589 5 4.329 4.212 3.993 3.791 3.605 3.433 3.352 3.274 3.127 2.991 6 5.076 4.917 4.623 4.355 4.111 3.889 3.784 3.685 3.498 3.326 7 5.786 5.582 5.206 4.868 4.564 4.288 4.160 4.039 3.812 3.605 8 6.463 6.210 5.747 5.335 4.968 4.639 4.487 4.344 4.078 3.837 9 7.108 6.802 6.247 5.759 5.328 4.946 4.772 4.607 4.303 4.031 10 7.722 7.360 6.710 6.145 5.650 5.216 5.019 4.833 4.494 4.192 11 8.306 7.887 7.139 6.495 5.938 5.453 5.234 5.029 4.656 4.327 12 8.863 8.384 7.536 6.814 6.194 5.660 5.421 5.197 4.793 4.439 13 9.394 8.853 7.904 7.103 6.424 5.842 5.583 5.342 4.910 4.533 14 9.899 9.295 8.244 7.367 6.628 6.002 5.724 5.468 5.008 4.611 15 10.380 9.712 8.559 7.606 6.811 6.142 5.847 5.575 5.092 4.675 Year 22% 24% 25% 26% 28% 30% 32% 34% 35% 40% 1 0.820 0.806 0.800 0.794 0.781 0.769 0.758 0.746 0.741 0.714 2 1.492 1.457 1.440 1.424 1.392 1.361 1.331 1.303 1.289 1.224 3 2.042 1.981 1.952 1.923 1.868 1.816 1.766 1.719 1.696 1.589 4 2.494 2.404 2.362 2.320 2.241 2.166 2.096 2.029 1.997 1.849 5 2.864 2.745 2.689 2.635 2.532 2.436 2.345 2.260 2.220 2.035 6 3.167 3.020 2.951 2.885 2.759 2.643 2.534 2.433 2.385 2.168 7 3.416 3.242 3.161 3.083 2.937 2.802 2.677 2.562 2.508 2.263 8 3.619 3.421 3.329 3.241 3.076 2.925 2.786 2.658 2.598 2.331 9 3.786 3.566 3.463 3.366 3.184 3.019 2.868 2.730 2.665 2.379 10 3.923 3.682 3.571 3.465 3.269 3.092 2.930 2.784 2.715 2.414 11 4.035 3.776 3.656 3.543 3.335 3.147 2.978 2.824 2.752 2.438 12 4.127 3.851 3.725 3.606 3.387 3.190 3.013 2.853 2.779 2.456 13 4.203 3.912 3.780 3.656 3.427 3.223 3.040 2.876 2.799 2.469 14 4.265 3.962 3.824 3.695 3.459 3.249 3.061 2.892 2.814 2.478 15 4.315 4.001 3.859 3.726 3.483 3.268 3.076 2.905 2.825 2.484