Replacement Decision, Computing After-Tax Cash Flows, Basic NPV Analysis

Okmulgee Hospital (a large metropolitan for-profit hospital) is considering replacing its MRI equipment with a new model manufactured by a different company. The old MRI equipment was acquired three years ago, has a remaining life of five years, and will have a salvage value of $100,000. The book value is $2,000,000. Straight-line depreciation with a half-year convention is being used for tax purposes. The cash operating costs of the existing MRI equipment total $1,000,000 per year.

The new MRI equipment has an initial cost of $5,000,000 and will have cash operating costs of $500,000 per year. The new MRI will have a life of five years and a salvage value of $1,000,000 at the end of the fifth year. MACRS depreciation will be used for tax purposes. If the new MRI equipment is purchased, the old one will be sold for $500,000. The company needs to decide whether to keep the old MRI equipment or buy the new one. The cost of capital is 12 percent. The combined federal and state tax rate is 40 percent.

You must use the Exhibit 19B.1 and Exhibit 19B.2 present value tables and Exhibit 19.5 to solve the following problem.

Required:

Compute the NPV of each alternative. When required, round your computations and final answers to the nearest dollar. If the NPV is negative, enter your answer as a negative value.

Old MRI equipment	$
New MRI equipment	$

EXHIBIT 19B.1 Present Value of $1* Periods 24% 40% 2% 4% 6% 8% 10% 12% 14% 16% 18% 20% 22% 26% 28% 30% 32% 1 0.980 0.962 0.943 0.926 0.909 0.893 0.877 0.862 0.847 0.833 0.820 0.806 0.650 0.794 0.781 0.769 0.758 0.714 0.961 0.925 0.890 0.857 0.826 0.797 0.769 0.743 0.718 0.694 0.672 0.630 0.610 0.592 0.574 0.510 0.942 0.889 0.840 0.794 0.751 0.712 0.675 0.641 0.609 0.579 0.551 0.524 0.500 0.477 0.455 0.435 0.364 0.924 0.855 0.792 0.735 0.683 0.636 0.592 0.552 0.516 0.482 0.451 0.423 0.397 0.373 0.350 0.329 0.260 0.906 0.822 0.747 0.681 0.621 0.567 0.519 0.476 0.437 0.402 0.370 0.341 0.315 0.291 0.269 0.250 0.186 0.705 0.227 0.178 0.888 0.790 0.636 0.564 0.507 0.456 0.410 0.370 0.335 0.303 0.275 0.250 0.207 0.189 0.133 0.095 7 0.871 0.760 0.665 0.583 0.513 0.452 0.400 0.354 0.314 0.279 0.249 0.222 0.198 0.159 0.143 0.139 0.068 0.853 0.731 0.627 0.540 0.467 0.404 0.351 0.305 0.266 0.233 0.204 0.179 0.157 0.123 0.108 0.592 0.308 0.108 0.048 0.837 0.703 0.500 0.424 0.361 0.263 0.225 0.194 0.167 0.144 0.125 0.094 0.082 10 0.820 0.676 0.558 0.463 0.386 0.322 0.270 0.227 0.191 0.162 0.137 0.116 0.099 0.085 0.073 0.062 0.035 11 0.804 0.650 0.527 0.429 0.350 0.287 0.237 0.195 0.162 0.135 0.112 0.094 0.079 0.066 0.056 0.046 0.025 12 0.788 0.625 0.497 0.397 0.319 0.257 0.208 0.168 0.137 0.112 0.092 0.076 0.062 0.052 0.043 0.036 0.018 13 0.773 0.601 0.469 0.368 0.290 0.229 0.182 0.145 0.116 0.093 0.075 0.061 0.050 0.040 0.033 0.027 0.013 0.758 0.442 0.263 0 239 0.039 0.009 14 0.577 0.340 0.205 0.160 .125 0.099 0.078 0.062 0.049 0.032 0.025 0.021 0,084 15 0.743 0.555 0.417 0.315 0.183 0.140 0.108 0.065 0.051 0.040 0.031 0.025 0.020 0.016 0.006 16 0.728 0.534 0.394 0.292 0.218 0.163 0.146 0.123 0.093 0.080 0.071 0.054 0.045 0.042 0.032 0.026 0.025 0.020 0.019 0.015 0.012 0.009 0.005 0.003 17 0.714 0.513 0.371 0.270 0.198 0.108 0.060 0.034 0.015 0.012 18 0.700 0.494 0.350 0.250 0.180 0.130 0.095 0.069 0.051 0.038 0.028 0.021 0.016 0.012 0.009 0.007 0.002 0.002 19 0.686 0.475 0.331 0.232 0.164 0.116 0.083 0.060 0.043 0.031 0.023 0.017 0.012 0.009 0.007 0.005 20 0.673 0.456 0.312 0.215 0.149 0.104 0.073 0.051 0.037 0.026 0.019 0.014 0.010 0.007 0.005 0.004 0.001 21 0.660 0.439 0.294 0.199 0.135 0.093 0.064 0.044 0.031 0.022 0.015 0.011 0.008 0.006 0.004 0.003 0.001 22 0.647 0.422 0.278 0.184 0.123 0.083 0.056 0.038 0.026 0.018 0.013 0.009 0,006 0,004 0.003 0.002 0.001 0.022 23 0.634 0.406 0.262 0.170 0.112 0.074 0.049 0.033 0.015 0.010 0.007 0.005 0.003 0.002 0.002 0.000 24 0.622 0.390 0.247 0.158 0.102 0.066 0.043 0.028 0.019 0.013 0.008 0.006 0.004 0.003 0.002 0.001 0.000 25 0.610 0.375 0.233 0.146 0.092 0.059 0.038 0.024 0.016 0.010 0.007 0.005 0.003 0.002 0.001 0.001 0.000 0.002 26 0.598 0.361 0.220 0.135 0.084 0.053 0.033 0.021 0.014 0.009 0.007 0.006 0.004 0.002 0.001 0.001 0.000 27 0.586 0.347 0.207 0.125 0.076 0.047 0.029 0.018 0.011 0.005 0.003 0.002 0.001 0.001 0.001 0.000 28 0.574 0.333 0.196 0.116 0.069 0.042 0.026 0.016 0.010 0.006 0.004 0.002 0.002 0.001 0.001 0.000 0.000 29 0.563 0.321 0 308 0.185 0.107 0.063 0.037 0.022 0.014 0.008 0.005 0.003 0.002 0.001 0.001 0.000 0.000 0.000 30 0.552 0.174 0.099 0.057 0,033 0.020 0012 0.007 0,004 0.003 0.002 0,001 0.001 0.000 0.000 0.000 *PA/(1i)" EXHIBIT 19B.2 Present Value of an Annuity of $1 in Arrears* Periods 22% 26% 40% 2% 4% 6% 8% 10% 12% 14% 16% 18% 20% 24% 28% 30% 32% 0.806 0.980 0.962 0.943 0.926 0.909 0.893 0.877 0.862 0.847 0.833 0.820 0.794 0.781 0.769 0.758 0.714 1.224 2 1.942 1.866 1.833 1.783 1.736 1.690 1.647 1.605 1.566 1.528 1.492 1.457 1.424 1.392 1.361 1.331 3 2.884 2.775 2.673 2.577 2.487 2.402 2.322 2.246 2.174 2.106 2.042 1.981 1.923 1.868 1.816 1.766 1.589 4 3.808 3.630 3.465 3.312 3.170 3.037 2.914 2.798 2.690 2.589 2.494 2.404 2.745 2.320 2.635 2.241 2.166 2.436 2.096 2.345 1.849 4.713 4.452 4.212 3.993 3.791 3.605 3.433 3.274 3.127 2.991 2.864 2.532 2.035 2.168 5.601 5.242 4.917 4.623 4.355 4.111 3.889 3.685 3.498 3.326 3.167 3.020 2.885 2.759 2.643 2.534 2.263 7 6.472 6.002 5.582 5.206 4.868 4.564 4.288 4.039 3.812 3.605 3.416 3.242 3.083 2.937 2.802 2.677 7.325 4.639 4.344 2.331 8 6.733 6.210 5.747 5.335 4.968 3.078 3.837 3.619 3.421 3.241 3.076 2.925 2.786 4.946 4.607 5.216 4,833 2.379 8.162 7.435 6.802 6.247 5.759 5.328 4.303 4.031 3.786 3.566 3.366 3.184 3.019 2.868 10 4.494 8.983 8.111 7.360 6.710 6.145 5.650 4.192 3.923 3.682 3.465 3.269 3.092 2.930 2.414 11 3.335 2.438 9.787 8.760 7.887 7.139 6.495 5.938 5.453 5.029 4.656 4.327 4.035 3.776 3.543 3.147 2.978 5.660 5.197 5.842 5.342 12 4.439 10.575 9.385 8.384 7.536 6.814 6.194 4.793 4.127 3.851 3.606 3.387 3.190 3.013 2.456 13 4.533 4.203 11.348 9.986 8.853 7.904 7.103 6.424 4.910 3.912 3.656 3.427 3.223 3.040 2.469 14 6.002 5.468 3.962 12.106 10.563 9.295 8.244 7.367 6.628 5.008 4.611 4.265 3.695 3.459 3.249 3.061 2.478 15 6.142 5.575 6.265 5.668 6.373 5.749 6.467 5818 6.550 5.877 4.315 12.849 11.118 9.712 8.559 7.606 6.811 5.092 4.675 4.001 3.726 3.483 3.268 3.076 2.484 16 13.578 11.652 10.106 14.292 12.166 10.477 4.357 2.489 8.851 7.824 6.974 5.162 4.730 4.033 3.751 3.503 3.283 3.088 17 9.122 8.022 9.372 8.201 7.120 5.222 4.775 4.391 4.059 3.771 3.518 3.295 3.097 2.492 3.304 5.273 2,494 4.419 18 14.992 12.659 0.828 7.250 4.812 4.080 3.786 3.529 3.104 9.604 8.365 9.818 8.514 10.017 8.649 19 15.678 13.134 11.158 7.366 5.316 4.843 4.442 4.097 3.799 3.539 3.311 3.109 2.496 13.590 11.470 14.029 11.764 20 16.351 7.469 6.623 5.929 5.353 5.384 4.870 4.460 4.110 3.808 3.816 3.546 3.551 3.316 3.320 3.113 3.116 2.497 6.687 5.973 21 17.011 7.562 4.891 4.476 4.121 2.498 22 2.498 2.499 2.499 17.658 14.451 12.042 10.201 8.772 7.645 6.743 6.011 5.410 4.909 4.488 4.130 3.822 3.556 3.323 3.118 23 18.292 14.857 12.303 10.371 8.883 7.718 6.792 6.044 5.432 4.925 4.499 4.137 3.827 3.559 3.325 3.120 24 3.562 18.914 15.247 12.550 10.529 8.985 7.784 6.835 6.073 5.451 4.937 4.507 4.143 3.831 3.327 3.121 25 15.622 12.783 10.675 9.077 7.843 4.147 2.499 2.500 19.523 6.873 6.097 5.467 4.948 4.514 3.834 3.564 3.329 3.122 26 20.121 15.983 13.003 10.810 9.161 7.896 6.906 6.118 5.480 4.956 4.520 4.151 3.837 3.566 3.330 3.123 27 6.935 6.136 6.961 6.152 20.707 16.330 13.211 10.935 9.237 7.943 5.492 4.964 4.524 4.154 3.839 3.567 3.331 3.123 2.500 28 21.281 16.663 13406 11.051 9.307 7.984 5.502 4.970 4.528 4.157 3.840 3.568 3.331 3.124 2.500 29 16.984 13.591 21.844 11.158 9.370 11.258 9.427 8.022 6.983 6.166 5.510 4.975 4.531 4.159 3.841 3.569 3.332 3.124 2.500 30 7.003 6.177 22.396 17.292 13.765 8.055 5.517 4.979 4.534 4.160 3.842 3.569 3.332 3.124 2.500 *P(1/ x [1 1/(1 . EXHIBIT 19.5 MACRS Depreciation Rates Three-Year Assets Year Five-Year Assets Seven-Year Assets 1 33.33% 20.00% 14.29% 44.45 14.81 2 32.00 24.49 3 19.20 17.49 7.41 4 11.52 12.49 11.52 5 8.93 6 5.76 8.92 7 8.93 4.46 EXHIBIT 19B.1 Present Value of $1* Periods 24% 40% 2% 4% 6% 8% 10% 12% 14% 16% 18% 20% 22% 26% 28% 30% 32% 1 0.980 0.962 0.943 0.926 0.909 0.893 0.877 0.862 0.847 0.833 0.820 0.806 0.650 0.794 0.781 0.769 0.758 0.714 0.961 0.925 0.890 0.857 0.826 0.797 0.769 0.743 0.718 0.694 0.672 0.630 0.610 0.592 0.574 0.510 0.942 0.889 0.840 0.794 0.751 0.712 0.675 0.641 0.609 0.579 0.551 0.524 0.500 0.477 0.455 0.435 0.364 0.924 0.855 0.792 0.735 0.683 0.636 0.592 0.552 0.516 0.482 0.451 0.423 0.397 0.373 0.350 0.329 0.260 0.906 0.822 0.747 0.681 0.621 0.567 0.519 0.476 0.437 0.402 0.370 0.341 0.315 0.291 0.269 0.250 0.186 0.705 0.227 0.178 0.888 0.790 0.636 0.564 0.507 0.456 0.410 0.370 0.335 0.303 0.275 0.250 0.207 0.189 0.133 0.095 7 0.871 0.760 0.665 0.583 0.513 0.452 0.400 0.354 0.314 0.279 0.249 0.222 0.198 0.159 0.143 0.139 0.068 0.853 0.731 0.627 0.540 0.467 0.404 0.351 0.305 0.266 0.233 0.204 0.179 0.157 0.123 0.108 0.592 0.308 0.108 0.048 0.837 0.703 0.500 0.424 0.361 0.263 0.225 0.194 0.167 0.144 0.125 0.094 0.082 10 0.820 0.676 0.558 0.463 0.386 0.322 0.270 0.227 0.191 0.162 0.137 0.116 0.099 0.085 0.073 0.062 0.035 11 0.804 0.650 0.527 0.429 0.350 0.287 0.237 0.195 0.162 0.135 0.112 0.094 0.079 0.066 0.056 0.046 0.025 12 0.788 0.625 0.497 0.397 0.319 0.257 0.208 0.168 0.137 0.112 0.092 0.076 0.062 0.052 0.043 0.036 0.018 13 0.773 0.601 0.469 0.368 0.290 0.229 0.182 0.145 0.116 0.093 0.075 0.061 0.050 0.040 0.033 0.027 0.013 0.758 0.442 0.263 0 239 0.039 0.009 14 0.577 0.340 0.205 0.160 .125 0.099 0.078 0.062 0.049 0.032 0.025 0.021 0,084 15 0.743 0.555 0.417 0.315 0.183 0.140 0.108 0.065 0.051 0.040 0.031 0.025 0.020 0.016 0.006 16 0.728 0.534 0.394 0.292 0.218 0.163 0.146 0.123 0.093 0.080 0.071 0.054 0.045 0.042 0.032 0.026 0.025 0.020 0.019 0.015 0.012 0.009 0.005 0.003 17 0.714 0.513 0.371 0.270 0.198 0.108 0.060 0.034 0.015 0.012 18 0.700 0.494 0.350 0.250 0.180 0.130 0.095 0.069 0.051 0.038 0.028 0.021 0.016 0.012 0.009 0.007 0.002 0.002 19 0.686 0.475 0.331 0.232 0.164 0.116 0.083 0.060 0.043 0.031 0.023 0.017 0.012 0.009 0.007 0.005 20 0.673 0.456 0.312 0.215 0.149 0.104 0.073 0.051 0.037 0.026 0.019 0.014 0.010 0.007 0.005 0.004 0.001 21 0.660 0.439 0.294 0.199 0.135 0.093 0.064 0.044 0.031 0.022 0.015 0.011 0.008 0.006 0.004 0.003 0.001 22 0.647 0.422 0.278 0.184 0.123 0.083 0.056 0.038 0.026 0.018 0.013 0.009 0,006 0,004 0.003 0.002 0.001 0.022 23 0.634 0.406 0.262 0.170 0.112 0.074 0.049 0.033 0.015 0.010 0.007 0.005 0.003 0.002 0.002 0.000 24 0.622 0.390 0.247 0.158 0.102 0.066 0.043 0.028 0.019 0.013 0.008 0.006 0.004 0.003 0.002 0.001 0.000 25 0.610 0.375 0.233 0.146 0.092 0.059 0.038 0.024 0.016 0.010 0.007 0.005 0.003 0.002 0.001 0.001 0.000 0.002 26 0.598 0.361 0.220 0.135 0.084 0.053 0.033 0.021 0.014 0.009 0.007 0.006 0.004 0.002 0.001 0.001 0.000 27 0.586 0.347 0.207 0.125 0.076 0.047 0.029 0.018 0.011 0.005 0.003 0.002 0.001 0.001 0.001 0.000 28 0.574 0.333 0.196 0.116 0.069 0.042 0.026 0.016 0.010 0.006 0.004 0.002 0.002 0.001 0.001 0.000 0.000 29 0.563 0.321 0 308 0.185 0.107 0.063 0.037 0.022 0.014 0.008 0.005 0.003 0.002 0.001 0.001 0.000 0.000 0.000 30 0.552 0.174 0.099 0.057 0,033 0.020 0012 0.007 0,004 0.003 0.002 0,001 0.001 0.000 0.000 0.000 *PA/(1i)" EXHIBIT 19B.2 Present Value of an Annuity of $1 in Arrears* Periods 22% 26% 40% 2% 4% 6% 8% 10% 12% 14% 16% 18% 20% 24% 28% 30% 32% 0.806 0.980 0.962 0.943 0.926 0.909 0.893 0.877 0.862 0.847 0.833 0.820 0.794 0.781 0.769 0.758 0.714 1.224 2 1.942 1.866 1.833 1.783 1.736 1.690 1.647 1.605 1.566 1.528 1.492 1.457 1.424 1.392 1.361 1.331 3 2.884 2.775 2.673 2.577 2.487 2.402 2.322 2.246 2.174 2.106 2.042 1.981 1.923 1.868 1.816 1.766 1.589 4 3.808 3.630 3.465 3.312 3.170 3.037 2.914 2.798 2.690 2.589 2.494 2.404 2.745 2.320 2.635 2.241 2.166 2.436 2.096 2.345 1.849 4.713 4.452 4.212 3.993 3.791 3.605 3.433 3.274 3.127 2.991 2.864 2.532 2.035 2.168 5.601 5.242 4.917 4.623 4.355 4.111 3.889 3.685 3.498 3.326 3.167 3.020 2.885 2.759 2.643 2.534 2.263 7 6.472 6.002 5.582 5.206 4.868 4.564 4.288 4.039 3.812 3.605 3.416 3.242 3.083 2.937 2.802 2.677 7.325 4.639 4.344 2.331 8 6.733 6.210 5.747 5.335 4.968 3.078 3.837 3.619 3.421 3.241 3.076 2.925 2.786 4.946 4.607 5.216 4,833 2.379 8.162 7.435 6.802 6.247 5.759 5.328 4.303 4.031 3.786 3.566 3.366 3.184 3.019 2.868 10 4.494 8.983 8.111 7.360 6.710 6.145 5.650 4.192 3.923 3.682 3.465 3.269 3.092 2.930 2.414 11 3.335 2.438 9.787 8.760 7.887 7.139 6.495 5.938 5.453 5.029 4.656 4.327 4.035 3.776 3.543 3.147 2.978 5.660 5.197 5.842 5.342 12 4.439 10.575 9.385 8.384 7.536 6.814 6.194 4.793 4.127 3.851 3.606 3.387 3.190 3.013 2.456 13 4.533 4.203 11.348 9.986 8.853 7.904 7.103 6.424 4.910 3.912 3.656 3.427 3.223 3.040 2.469 14 6.002 5.468 3.962 12.106 10.563 9.295 8.244 7.367 6.628 5.008 4.611 4.265 3.695 3.459 3.249 3.061 2.478 15 6.142 5.575 6.265 5.668 6.373 5.749 6.467 5818 6.550 5.877 4.315 12.849 11.118 9.712 8.559 7.606 6.811 5.092 4.675 4.001 3.726 3.483 3.268 3.076 2.484 16 13.578 11.652 10.106 14.292 12.166 10.477 4.357 2.489 8.851 7.824 6.974 5.162 4.730 4.033 3.751 3.503 3.283 3.088 17 9.122 8.022 9.372 8.201 7.120 5.222 4.775 4.391 4.059 3.771 3.518 3.295 3.097 2.492 3.304 5.273 2,494 4.419 18 14.992 12.659 0.828 7.250 4.812 4.080 3.786 3.529 3.104 9.604 8.365 9.818 8.514 10.017 8.649 19 15.678 13.134 11.158 7.366 5.316 4.843 4.442 4.097 3.799 3.539 3.311 3.109 2.496 13.590 11.470 14.029 11.764 20 16.351 7.469 6.623 5.929 5.353 5.384 4.870 4.460 4.110 3.808 3.816 3.546 3.551 3.316 3.320 3.113 3.116 2.497 6.687 5.973 21 17.011 7.562 4.891 4.476 4.121 2.498 22 2.498 2.499 2.499 17.658 14.451 12.042 10.201 8.772 7.645 6.743 6.011 5.410 4.909 4.488 4.130 3.822 3.556 3.323 3.118 23 18.292 14.857 12.303 10.371 8.883 7.718 6.792 6.044 5.432 4.925 4.499 4.137 3.827 3.559 3.325 3.120 24 3.562 18.914 15.247 12.550 10.529 8.985 7.784 6.835 6.073 5.451 4.937 4.507 4.143 3.831 3.327 3.121 25 15.622 12.783 10.675 9.077 7.843 4.147 2.499 2.500 19.523 6.873 6.097 5.467 4.948 4.514 3.834 3.564 3.329 3.122 26 20.121 15.983 13.003 10.810 9.161 7.896 6.906 6.118 5.480 4.956 4.520 4.151 3.837 3.566 3.330 3.123 27 6.935 6.136 6.961 6.152 20.707 16.330 13.211 10.935 9.237 7.943 5.492 4.964 4.524 4.154 3.839 3.567 3.331 3.123 2.500 28 21.281 16.663 13406 11.051 9.307 7.984 5.502 4.970 4.528 4.157 3.840 3.568 3.331 3.124 2.500 29 16.984 13.591 21.844 11.158 9.370 11.258 9.427 8.022 6.983 6.166 5.510 4.975 4.531 4.159 3.841 3.569 3.332 3.124 2.500 30 7.003 6.177 22.396 17.292 13.765 8.055 5.517 4.979 4.534 4.160 3.842 3.569 3.332 3.124 2.500 *P(1/ x [1 1/(1 . EXHIBIT 19.5 MACRS Depreciation Rates Three-Year Assets Year Five-Year Assets Seven-Year Assets 1 33.33% 20.00% 14.29% 44.45 14.81 2 32.00 24.49 3 19.20 17.49 7.41 4 11.52 12.49 11.52 5 8.93 6 5.76 8.92 7 8.93 4.46