Exercise 16-37 Payback, Accounting Rate of Return; Net Present Value; Taxes (Sections 1' 2, and 3) (L0 16-1, 16-6, 16-8) [The following information applies to the questions displayed below. J Metro Car Washes, Inc., is reviewing an investment proposal. The initial cost as well as the estimate of the book value of the investment at the end of each year, the net after-tax cash flows for each year, and the net income for each year are presented in the following schedule. The salvage value of the investment at the end of each year is equal to its book value. There would be no salvage value at the end of the investment's life. Initial Cost Annual Net AfteriTaX Annual Year and Book Value Cash Flows Net Income 0 $225,000 1 150,000 $101,000 $26,000 2 90,000 88,000 28,000 3 45,000 75,000 30,000 4 15,000 62,000 32,000 5 0 49,000 34,000 Management uses a 12 percent after-tax target rate of return for new investment proposals. Use Appendix A for your reference. (Use appropriate factoris) from the tables provided.) equal to its book value. There would be no salvage value at the end ofthe investments life. Initial Cost Annual Net AftereTax Annual Year and Book Value Ca'sh Flows Net Income 0 $225,000 l 150,000 $101,000 $26,000 2 90,000 88,000 28,000 3 45,000 75,000 30,000 4 15,000 62,000 32,000 5 0 49,000 34,000 Management uses a 12 percent after-tax target rate of return for new investment proposals. Use Appendix A for your reference. (Use appropriate factor(s) from the tables provided.) Exercise 16-37 Part 1 Required: 1. Compute the project's payback period. Assume that the cash ows in years 1 through 5 occur uniformly throughout each year. (Round your answer to 2 decimal places.) years \fvalue of the investment at the end of each year, the net after-tax cash flows for each year, and the net income for each year are presented in the following schedule. The salvage value of the investment at the end of each year is equal to its book value. There would be no salvage value at the end ofthe investment's life. Initial. Cost Annual Net AfterTax Annual Year and Book value Cash Fl'OWS' Net Income 0 $225,000 1 150,000 $101,000 $26,000 2 90,000 88,000 28,000 3 45,000 75,000 30,000 4 15,000 62,000 32,000 5 0 49,000 34,000 Management uses a 12 percent after-tax target rate of return for new investment proposals. Use Appendix A for your reference. (Use appropriate factorls) from the tables provided.) Exercise 16-37 Part 3 3. Compute the proposal's net present value. (Round intermediate calculations to the nearest whole dollar.) _: Future Value and Present Value Tables Table Future Value of $1.00(1 + r)n Period 4% 6% 8% 10% 12% 14% 20% 1.040 1.060 1.080 1.100 1.120 1.140 1.200 2 1.082 1.124 1.166 1.210 254 1.300 1.440 3 1.125 1.191 1.260 1.331 1.405 1.482 1.728 4 1.170 1.263 1.361 1.464 1.574 1.689 2.074 5 1.217 1.338 1.469 1.611 1.762 1.925 2.488 6 1.265 1.419 1.58/ 1.772 1.9/4 2.195 2.980 7 1.316 1.504 1.714 1.949 2.211 2.502 3.583 S 1.369 1.594 1.851 2.144 2.476 2.853 4.300 9 1.423 1.690 1.999 2.359 2.773 3.252 5.160 10 1.480 1.791 2.159 2.594 3.106 3.707 6.192 11 .540 1.898 2.332 2.853 3.479 1,226 7.430 12 1.601 2.012 2.518 3.139 3.896 4.818 8.916 13 1.665 2.133 2.720 3.452 1.364 5.492 10.699 14 1,732 2.261 2.937 3.798 4.887 6.261 12.839 15 1.801 2.397 3.172 4.177 5.474 7.138 15.407 20 2.191 3.207 4.661 6.728 9.646 13.743 $8.338 30 3.243 5.744 10.063 17.450 29.960 50.950 237.380 10 4.801 10.286 21.725 45.260 93.051 188.880 1,469.800 Table II Future Value of a Series of $1.00 Cash Flows (Ordinary Annuity)- (1 + r)" - 1 Period 4% 6% 8% 10% 12% 14% 20% 1.00 1.00 1.000 1.000 1.000 .00 1.000 2.04 2.060 2.080 2.100 2.120 2.140 2.220 3.12 3.18 3.246 3.310 3.374 3.440 3.640 4.24 4.375 4.506 4.641 4.779 4.921 5.36 .416 5.637 5.867 6.105 5.35 6.610 7.442 6.63. 6.975 7.336 7.716 3.11 8.536 9.930 7.898 8.394 8.923 9.487 10.089 10.730 12.916 9.214 9.098 10.637 11.436 12.300 13.233 16.499 10.583 11.491 12.488 13.580 14.776 16.085 20.799 10 12.006 13.18 14.487 15.938 17.549 19.337 25.959 11 13.486 14.972 16.64 18.531 20.65 23.04 32.150 15.026 16.870 18.977 21.385 24.133 27.271 39.580 13 16.627 18.882 21.495 24.523 28.029 32.089 48.497 14 18.292 21.015 24.215 27.976 32.393 37.581 59.196 15 20.024 23.276 27.152 31.773 37.280 43.84 72.035 20 29.778 36.778 45.762 57.276 75.052 91.025 186.690 30 6.085 79.058 113.283 164.496 241.330 356.790 1,181.900 40 5.026 154.762 259.057 442.597 767.090 1,342.000 7,343.900 Table III Present Value of $1.00 - ( 1 + 7 ) " Period 4% 6% 8% 10% 12% 14 % 16% 18% 22% 24% 26% 30% 32% 962 .943 .926 .909 .893 .877 .862 .847 .833 .820 .806 .794 781 .769 .758 925 890 857 826 797 769 .743 .718 694 672 650 630 610 592 574 889 840 .794 .751 ,712 .675 .641 .609 579 551 .524 500 477 455 .435 855 .792 .735 683 .636 .592 .552 .516 482 451 .423 .397 .373 .350 .329 822 .747 681 621 567 .519 .476 .437 402 370 .341 .315 .291 269 .250 6 790 .705 .630 .564 .507 .456 .410 .370 .335 .303 .275 .250 .227 .207 .189 760 .665 .583 .513 .452 .400 .354 .314 .279 .249 .222 . 198 .178 .159 .143 731 627 .540 .467 .404 .351 .305 .266 .233 .204 .179 .157 139 .123 .108 703 .592 .500 .424 .361 .308 .263 .225 194 .167 .144 .125 . 108 .094 .082 10 676 .558 .463 .386 .322 .270 .227 .191 .162 .137 .116 .099 085 .073 .062 11 650 .527 .429 .350 .287 .237 .195 .162 135 .112 .094 .079 .066 .056 .047 12 625 .497 .397 .319 .257 .208 .168 .137 112 .092 .076 .062 .052 .043 036 13 601 .469 .368 .290 .229 . 182 .145 .116 093 075 .061 050 040 .033 .027 14 577 .442 .340 .263 205 160 .125 .099 078 062 049 .039 032 .025 .021 15 555 417 .315 .239 . 183 .140 .108 084 065 051 040 031 .025 .020 .016 20 456 .312 .215 .149 .104 073 .051 .037 .026 .019 .014 .010 .007 .005 .004 .308 4 .099 .057 .033 020 .012 .007 .004 .003 .002 .001 .001 .208 .097 .046 .022 .011 .005 .003 .001 .001 Table IV Present Value of Series of $1.00 Cash Flows - (1 - (1 + )) Period 4% 6% 8% 10% 12% 14% 18% 20% 22% 24% 25% 2 28% 30% 0.96 0.943 0.926 0.909 0.893 0.877 0.862 0.847 0.833 0.820 0.806 0.800 0.794 0.781 0.769 1.886 1.833 1.783 1.736 1.690 1.647 1.605 1.566 1.528 1.492 1.457 1.440 1.424 1.392 1.361 2.77 2.673 2.577 2.487 2.402 2.322 2.246 2.174 2.106 2.042 1.981 1.952 1.923 1.868 1.816 3.630 3.465 3.312 3.170 3.037 2.914 2.798 2.690 2.589 2.494 2.404 2.362 2.320 2.241 2.166 4.452 4.212 3.993 3.791 3.605 3.433 3.274 3.127 2.991 2.864 2.745 2.689 2.635 2.532 2.436 5.242 4.917 4.623 4.355 3.889 3.685 3.498 3.326 3.167 3.020 2.951 2.759 2.643 6.00 5.582 5.206 4.868 4.564 4.288 4.039 3.812 3.605 3.416 3.242 3.161 3.083 2.937 2.802 Co .73 6.210 5.747 5.335 4.968 4.639 4 4.344 4.078 3.837 3.619 3.421 3.329 3.241 3.076 2.925 7.43 5.802 6.247 5.759 5.328 4.946 4.607 4.303 4.031 3.786 3.566 3.463 3.366 3.184 3.019 8.11 7.360 6.710 6.145 5.650 5.216 4.833 4.494 4.192 3.923 3.682 3.571 3.465 3.269 3.092 8.760 7.887 7.139 6.495 5.938 5.453 5.029 4.656 4.327 4.035 3.776 3.656 3.544 3.335 3.147 9.38 8.384 7.536 6.814 6.194 5.660 5.197 4.793 4.439 4.127 3.851 3.725 3.606 3.387 3.190 9.986 8.853 7.904 7.103 6.424 5.842 5.342 4.910 4.533 4.203 3.912 3.780 3.656 3.427 3.223 10.563 9.295 8.244 7.367 6.628 6.002 5.468 5.008 4.611 4.265 3.962 3.824 3.695 3.459 3.249 11.118 9.712 8.559 7.606 6.811 6.142 5.575 5.092 4.675 4.315 4.001 3.859 3.726 3.483 3.268 20 13.590 11.470 9.818 8.514 7.469 6.623 5.929 5.353 4.870 4.460 4.110 3.954 3.808 3.546 3.316 30 17.292 13.765 11.258 9.427 8.055 7.003 6.177 5 5.517 4 7 4.979 4.534 4.160 3.995 3.842 3.569 3.332 10 19.793 15.046 11.925 9.779 8.244 7.105 6.234 5.548 4.997 4.544 4.166 3.999 3.846 3.571 3.333Future Value and Present Value Tables Table Future Value of $1.00(1 + r)n Period 4% 6% 8% 10% 12% 14% 20% 1.040 1.060 1.080 1.100 1.120 1.140 1.200 2 1.082 1.124 1.166 1.210 254 1.300 1.440 3 1.125 1.191 1.260 1.331 1.405 1.482 1.728 4 1.170 1.263 1.361 1.464 1.574 1.689 2.074 5 1.217 1.338 1.469 1.611 1.762 1.925 2.488 6 1.265 1.419 1.58/ 1.772 1.9/4 2.195 2.980 7 1.316 1.504 1.714 1.949 2.211 2.502 3.583 S 1.369 1.594 1.851 2.144 2.476 2.853 4.300 9 1.423 1.690 1.999 2.359 2.773 3.252 5.160 10 1.480 1.791 2.159 2.594 3.106 3.707 6.192 11 .540 1.898 2.332 2.853 3.479 1,226 7.430 12 1.601 2.012 2.518 3.139 3.896 4.818 8.916 13 1.665 2.133 2.720 3.452 1.364 5.492 10.699 14 1,732 2.261 2.937 3.798 4.887 6.261 12.839 15 1.801 2.397 3.172 4.177 5.474 7.138 15.407 20 2.191 3.207 4.661 6.728 9.646 13.743 $8.338 30 3.243 5.744 10.063 17.450 29.960 50.950 237.380 10 4.801 10.286 21.725 45.260 93.051 188.880 1,469.800 Table II Future Value of a Series of $1.00 Cash Flows (Ordinary Annuity)- (1 + r)" - 1 Period 4% 6% 8% 10% 12% 14% 20% 1.00 1.00 1.000 1.000 1.000 .00 1.000 2.04 2.060 2.080 2.100 2.120 2.140 2.220 3.12 3.18 3.246 3.310 3.374 3.440 3.640 4.24 4.375 4.506 4.641 4.779 4.921 5.36 .416 5.637 5.867 6.105 5.35 6.610 7.442 6.63. 6.975 7.336 7.716 3.11 8.536 9.930 7.898 8.394 8.923 9.487 10.089 10.730 12.916 9.214 9.098 10.637 11.436 12.300 13.233 16.499 10.583 11.491 12.488 13.580 14.776 16.085 20.799 10 12.006 13.18 14.487 15.938 17.549 19.337 25.959 11 13.486 14.972 16.64 18.531 20.65 23.04 32.150 15.026 16.870 18.977 21.385 24.133 27.271 39.580 13 16.627 18.882 21.495 24.523 28.029 32.089 48.497 14 18.292 21.015 24.215 27.976 32.393 37.581 59.196 15 20.024 23.276 27.152 31.773 37.280 43.84 72.035 20 29.778 36.778 45.762 57.276 75.052 91.025 186.690 30 6.085 79.058 113.283 164.496 241.330 356.790 1,181.900 40 5.026 154.762 259.057 442.597 767.090 1,342.000 7,343.900 Table III Present Value of $1.00 - ( 1 + 7 ) " Period 4% 6% 8% 10% 12% 14 % 16% 18% 22% 24% 26% 30% 32% 962 .943 .926 .909 .893 .877 .862 .847 .833 .820 .806 .794 781 .769 .758 925 890 857 826 797 769 .743 .718 694 672 650 630 610 592 574 889 840 .794 .751 ,712 .675 .641 .609 579 551 .524 500 477 455 .435 855 .792 .735 683 .636 .592 .552 .516 482 451 .423 .397 .373 .350 .329 822 .747 681 621 567 .519 .476 .437 402 370 .341 .315 .291 269 .250 6 790 .705 .630 .564 .507 .456 .410 .370 .335 .303 .275 .250 .227 .207 .189 760 .665 .583 .513 .452 .400 .354 .314 .279 .249 .222 . 198 .178 .159 .143 731 627 .540 .467 .404 .351 .305 .266 .233 .204 .179 .157 139 .123 .108 703 .592 .500 .424 .361 .308 .263 .225 194 .167 .144 .125 . 108 .094 .082 10 676 .558 .463 .386 .322 .270 .227 .191 .162 .137 .116 .099 085 .073 .062 11 650 .527 .429 .350 .287 .237 .195 .162 135 .112 .094 .079 .066 .056 .047 12 625 .497 .397 .319 .257 .208 .168 .137 112 .092 .076 .062 .052 .043 036 13 601 .469 .368 .290 .229 . 182 .145 .116 093 075 .061 050 040 .033 .027 14 577 .442 .340 .263 205 160 .125 .099 078 062 049 .039 032 .025 .021 15 555 417 .315 .239 . 183 .140 .108 084 065 051 040 031 .025 .020 .016 20 456 .312 .215 .149 .104 073 .051 .037 .026 .019 .014 .010 .007 .005 .004 .308 4 .099 .057 .033 020 .012 .007 .004 .003 .002 .001 .001 .208 .097 .046 .022 .011 .005 .003 .001 .001 Table IV Present Value of Series of $1.00 Cash Flows - (1 - (1 + )) Period 4% 6% 8% 10% 12% 14% 18% 20% 22% 24% 25% 2 28% 30% 0.96 0.943 0.926 0.909 0.893 0.877 0.862 0.847 0.833 0.820 0.806 0.800 0.794 0.781 0.769 1.886 1.833 1.783 1.736 1.690 1.647 1.605 1.566 1.528 1.492 1.457 1.440 1.424 1.392 1.361 2.77 2.673 2.577 2.487 2.402 2.322 2.246 2.174 2.106 2.042 1.981 1.952 1.923 1.868 1.816 3.630 3.465 3.312 3.170 3.037 2.914 2.798 2.690 2.589 2.494 2.404 2.362 2.320 2.241 2.166 4.452 4.212 3.993 3.791 3.605 3.433 3.274 3.127 2.991 2.864 2.745 2.689 2.635 2.532 2.436 5.242 4.917 4.623 4.355 3.889 3.685 3.498 3.326 3.167 3.020 2.951 2.759 2.643 6.00 5.582 5.206 4.868 4.564 4.288 4.039 3.812 3.605 3.416 3.242 3.161 3.083 2.937 2.802 Co .73 6.210 5.747 5.335 4.968 4.639 4 4.344 4.078 3.837 3.619 3.421 3.329 3.241 3.076 2.925 7.43 5.802 6.247 5.759 5.328 4.946 4.607 4.303 4.031 3.786 3.566 3.463 3.366 3.184 3.019 8.11 7.360 6.710 6.145 5.650 5.216 4.833 4.494 4.192 3.923 3.682 3.571 3.465 3.269 3.092 8.760 7.887 7.139 6.495 5.938 5.453 5.029 4.656 4.327 4.035 3.776 3.656 3.544 3.335 3.147 9.38 8.384 7.536 6.814 6.194 5.660 5.197 4.793 4.439 4.127 3.851 3.725 3.606 3.387 3.190 9.986 8.853 7.904 7.103 6.424 5.842 5.342 4.910 4.533 4.203 3.912 3.780 3.656 3.427 3.223 10.563 9.295 8.244 7.367 6.628 6.002 5.468 5.008 4.611 4.265 3.962 3.824 3.695 3.459 3.249 11.118 9.712 8.559 7.606 6.811 6.142 5.575 5.092 4.675 4.315 4.001 3.859 3.726 3.483 3.268 20 13.590 11.470 9.818 8.514 7.469 6.623 5.929 5.353 4.870 4.460 4.110 3.954 3.808 3.546 3.316 30 17.292 13.765 11.258 9.427 8.055 7.003 6.177 5 5.517 4 7 4.979 4.534 4.160 3.995 3.842 3.569 3.332 10 19.793 15.046 11.925 9.779 8.244 7.105 6.234 5.548 4.997 4.544 4.166 3.999 3.846 3.571 3.333