Dorothy & George Company is planning to acquire a new machine at a total cost of $57,200. The machine's estimated life is 6 years and its estimated salvage value is $500. The company estimates that annual cash savings from using this machine will be $12,000. The company's after-tax cost of capital is 7% and its income tax rate is 40%. The company uses straight-line depreciation. (Use Appendix C, Table 1 and Appendix C, Table 2.) (Do not round intermediate calculations. Negative amounts should be indicated by a minus sign. Round answers to the nearest dollar amount.) Required: 1. What is this investment's net after-tax annual cash inflow? 2. Assume that the net after-tax annual cash inflow of this investment is $8,000; what is the net present value (NPV) of this investment? 3. What are the minimum net after-tax annual cost savings that make the proposed investment acceptable (i.e., the dollar cost savings that would yield an NPV of $0)? Hint: Redo the NPV analysis by setting the NPV equal to zero and making the annual after-tax cash flows equal to X; then solve for X and enter the amount as your answer. Also consider using Goal Seek in Excel. 1 $ 10.980 2. Net after-tax annual cash inflow Net present value Minimum net after-tax annual cost savings 3. TABLE 1 Present Value of $1 Periods 4% 5% 6% 7% 8% 9% 10% 11% 12% 13% 14% 15% 20% 25% 30% 1 2 3 4 5 6 7 S 9 10 11 12 13 0.962 0.952 0.943 0.935 0.926 0.917 0.909 0.901 0.893 0.885 0.877 0.870 0.833 0.500 0.769 0.925 0.907 0.390 0.373 0.357 0.542 0.526 0.812 0.797 0.783 0.769 0.756 0.694 0.640 0.592 0.889 0.864 0.840 0.816 0.794 0.772 0.751 0.731 0.712 0.693 0.675 0.658 0.579 0.512 0.455 0.855 0.823 0.792 0.763 0.735 0.708 0.683 0.659 0.636 0.613 0.592 0.572 0.452 0.410 0.350 0.822 0.784 0.747 0.713 0.681 0.650 0.621 0.593 0.567 0.543 0.519 0.497 0.402 0.328 0.269 0.790 0.746 0.705 0.666 0.630 0.596 0.564 0.535 0.507 0.430 0.456 0.432 0.335 0.262 0.207 0.760 0.711 0.665 0.623 0.583 0.547 0.513 0.482 0.452 0.425 0.400 0.376 0.279 0.210 0.159 0.731 0.677 0.627 0.582 0.540 0.502 0.467 0.434 0.404 0.376 0.351 0.327 0.233 0.168 0.123 0.703 0.645 0.592 0.544 0.500 0.460 0.424 0.391 0.361 0.333 0.308 0.284 0.194 0.134 0.094 0.676 0.614 0.558 0.508 0.463 0.422 0.386 0.352 0.322 0.295 0.270 0.247 0.162 0.107 0.073 0.650 0.585 0.527 0.475 0.429 0.388 0.350 0.317 0.287 0.261 0.237 0.215 0.135 0.086 0.056 0.625 0.557 0.497 0.444 0.397 0.356 0.319 0.286 0.257 0.231 0.205 0.157 0.112 0.069 0.043 0.601 0.530 0.469 0.415 0.368 0.326 0.290 0.25% 0.229 0.204 0.132 0.163 0.093 0.055 0.033 0.577 0.505 0.442 0.388 0.340 0.299 0.263 0.232 0.205 0.181 0.160 0.141 0.078 0.044 0.025 0.555 0.481 0.417 0.362 0.315 0.275 0.239 0.209 0.183 0.160 0.140 0.123 0.065 0.035 0.020 0.534 0.458 0.394 0.339 0.292 0.252 0.218 0.185 0.163 0.141 0.123 0.107 0.054 0.028 0.015 0.513 0.436 0.371 0.317 0.270 0.231 0.19 0.170 0.146 0.125 0.108 0.093 0.045 0.023 0.012 0.494 0.416 0.350 0.296 0.250 0.212 0.150 0.153 0.130 0.111 0.095 0.081 0.035 0.018 0.009 0.475 0.396 0.331 0.277 0.232 0.194 0.164 0.138 0.116 0.098 0.033 0.070 0.031 0.014 0.007 0.456 0.377 0.312 0.25% 0.215 0.178 0.149 0.124 0.104 0.087 0.073 0.061 0.026 0.012 0.005 0.422 0.342 0.278 0.226 0.154 0.150 0.123 0.101 0.083 0.068 0.056 0.046 0.018 0.007 0.003 0.390 0.310 0.247 0.197 0.158 0.126 0.102 0.032 0.066 0.053 0.043 0.035 0.013 0.005 0.002 0.375 0.295 0.233 0.184 0.146 0.116 0.092 0.074 0.059 0.047 0.035 0.030 0.010 0.004 0.001 0.308 0.231 0.174 0.131 0.099 0.075 0.057 0.044 0.033 0.026 0.020 0,015 0.004 0.001 0.000 0.253 0.181 0.130 0.094 0.068 0.049 0.036 0.026 0.019 0.014 0.010 0.008 0.002 0.000 0.000 0.208 0.142 0.097 0.067 0.046 0.032 0.022 0.015 0.011 0.005 0.005 0.004 0.001 0.000 0.000 14 15 16 17 18 19 20 22 24 25 30 35 40 TABLE 2 Present Value of Annuity of $1 N 5 S Periods 4% 5% 6% 7% S% 9% 10% 11% 12% 13% 14% 15% 20% 25% 30% 1 0.962 0.952 0.943 0.935 0.926 0.917 0.909 0.901 0.393 0.335 0.877 0.870 0.333 0.500 0.769 1.886 1.859 1.833 1.SOS 1.783 1.759 1.736 1.713 1.690 1.668 1.647 1.626 1.528 1.440 1.361 3 2.775 2.723 2.673 2.624 2.577 2.531 2.487 2.444 2.402 2.361 2.322 2.283 2.106 1.952 1.516 4 3.630 3.546 3.465 3.387 3.312 3.240 3.170 3.102 3.037 2.974 2.914 2.355 2.589 2.362 2.166 4.452 4.329 4.212 4.100 3.993 3.890 3.791 3.696 3.605 3.517 3.433 3.352 2.991 2.689 2.436 6 5.242 5.076 4.917 4.767 4.623 4.486 4.355 4.231 4.111 3.999 3.889 3.784 3.326 2.951 2.643 7 6.002 5.786 5.582 5.389 5.206 5.033 4.363 4.712 4.564 4.423 4.288 4.160 3.605 3.161 2.802 6.733 6.463 6.210 5.971 5.747 5.535 5.335 5.146 4.968 4.799 4.639 4.487 3.837 3.329 2.925 9 7.435 7.105 6.802 6.515 6.247 5.995 5.759 5.537 5.328 5.132 4.946 4.772 4.031 3.463 3.019 10 8.111 7.722 7.360 7.024 6.710 6.418 6.145 5.889 5.650 5.426 5.216 5.019 4.192 3.571 3.092 11 8.760 8.306 7.887 7.499 7.139 6.805 6.495 6.207 5.938 5.687 5.453 5.234 4.327 3.656 3.147 12 9.385 S. 863 8.384 7.943 7.536 7.161 6.814 6.492 6.194 5.915 5.660 5.421 4.439 3.725 3.190 13 9.986 9.394 8.353 8.358 7.904 7.487 7.103 6.750 6.424 6.122 5.342 5.583 4.533 3.780 3.223 14 10.563 9.899 9.295 8.745 8.244 7.786 7.367 6.982 6.628 6.302 6.002 5.724 4.611 3.824 3.249 15 11.118 10.380 9.712 9.108 3.559 8.061 7.606 7.191 6.811 6.462 6.142 5.847 4.675 3.559 3.268 16 11.652 10.838 10.106 9.447 8.851 8.313 7.824 7.379 6.974 6.604 6.265 5.954 4.730 3.887 3.283 12.166 11.274 10.477 9.763 9.122 8.544 3.022 7.549 7.120 6.729 6.373 6.047 4.775 3.910 3.295 1S 12.659 11.690 10.328 10.059 9.372 8.756 3.201 7.702 7.250 6.840 6.467 6.128 4.812 3.928 3.304 19 13.134 12.085 11.158 10.336 9.604 8.950 8.365 7.339 7.366 6.938 6.550 6.198 4.543 3.942 3.311 20 13.590 12.462 11.470 10.594 9.818 9.129 8.514 7.963 7.469 7.025 6.623 6.259 4.870 3.954 3.316 22 14.451 13.163 12.042 11.061 10.201 9.442 3.772 3.176 7.645 7.170 6.743 6.359 4.909 3.970 3.323 24 15.247 13.799 12.550 11.469 10.529 9.707 8.955 5.348 7.784 7.283 6.835 6.434 4.937 3.981 3.327 15.622 14.094 12.783 11.654 10.675 9.823 9.077 8.422 7.543 7.330 6.373 6.464 4.945 3.985 3.329 30 17.292 15.372 13.765 12.409 11.258 10.274 9.427 8.694 8.055 7.496 7.003 6.566 4.979 3.995 3.332 18.665 16.374 14.498 12.948 11.655 10.567 9.644 8.855 8.176 7.586 7.070 6.617 4.992 3.999 3.333 40 19.793 17.159 15.046 13.332 11.925 10.757 9.779 5.951 8.244 7.634 7.105 6.642 4.997 3.999 3.333 17 25 35