Problem 14-28 (Algo) Net Present Value Analysis [LO14-2]

Bilboa Freightlines, S.A., of Panama, has a small truck that it uses for intracity deliveries. The truck is worn out and must be either overhauled or replaced with a new truck. The company has assembled the following information:

	Present Truck	New Truck
Purchase cost new	$ 24,000	$ 27,000
Remaining book value	$ 8,000	-
Overhaul needed now	$ 7,000	-
Annual cash operating costs	$ 11,000	$ 6,000
Salvage value-now	$ 3,000	-
Salvage value-five years from now	$ 2,000	$ 5,000

If the company keeps and overhauls its present delivery truck, then the truck will be usable for five more years. If a new truck is purchased, it will be used for five years, after which it will be traded in on another truck. The new truck would be diesel-operated, resulting in a substantial reduction in annual operating costs, as shown above.

The company computes depreciation on a straight-line basis. All investment projects are evaluated using a 18% discount rate.

Click here to view Exhibit 14B-1 and Exhibit 14B-2, to determine the appropriate discount factor(s) using tables.

Required:

1. What is the net present value of the keep the old truck alternative?

2. What is the net present value of the purchase the new truck alternative?

3. Should Bilboa Freightlines keep the old truck or purchase the new one?

EXHIBIT 14B-1 Present Value of $1; 1 (1+r) n 9% Periods 1 2 SL 21% 0.826 0.683 ---- 3 valcolm DUIDI 4 5 0.564 0.467 0.386 6 7 8 9 NONI 4% 0.962 0.925 0.889 0.855 0.822 0.790 0.760 0.731 0.703 0.676 0.650 0.625 0.601 0.577 0.555 0.534 0.513 0.494 0.475 0.456 0.439 0.422 0.406 0.390 0.375 0.361 0.347 0.333 0.321 0.308 0.208 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 40 5% 0.952 0.907 0.864 0.823 0.784 0.746 0.711 0.677 0.645 0.614 0.585 0.557 0.530 0.505 0.481 0.458 0.436 0.416 0.396 0.377 0.359 0.342 0.326 0.310 0.295 0.281 0.268 0.255 0.243 0.231 0.142 6% 0.943 0.890 0.840 0.792 0.747 0.705 0.665 0.627 0.592 0.558 0.527 0.497 0.469 0.442 0.417 0.394 0.371 0.350 0.331 0.312 0.294 0.278 0.262 0.247 0.233 0.220 0.207 0.196 0.185 7% 8% 0.935 0.926 0.873 0.857 0.816 0.794 0.763 0.735 0.713 0.681 0.666 0.630 0.623 0.583 0.582 0.540 0.544 0.500 0.508 0.463 0.475 0.429 0.444 0.397 0.415 0.368 0.388 0.340 0.362 0.315 0.339 0.292 0.317 0.270 0.296 0.250 0.277 0.232 0.258 0.215 0.242 0.199 0.226 0.184 0.211 0.170 0.197 0.158 0.184 0.146 0.172 0.135 0.161 0.125 0.150 0.116 0.141 0.107 0.131 0.099 0.067 0.046 0.917 0.842 0.772 0.708 0.650 0.596 0.547 0.502 0.460 0.422 0.388 0.356 0.326 0.299 0.275 0.252 0.231 0.212 0.194 0.178 0.164 0.150 0.138 0.126 0.116 0.106 0.098 0.090 0.082 0.075 0.032 10% 0.909 0.826 0.751 0.683 0.621 0.564 0.513 0.467 0.424 0.386 0.350 0.319 0.290 0.263 0.239 0.218 0.198 0.180 0.164 0.149 0.135 0.123 0.112 0.102 0.092 0.084 0.076 0.069 0.063 0.057 0.022 11 % 0.901 0.812 0.731 0.659 0.593 0.535 0.482 0.434 0.391 0.352 0.317 0.286 0.258 0.232 0.209 0.188 0.170 0.153 0.138 0.124 0.112 0.101 0.091 0.082 0.074 0.066 0.060 0.054 0.048 0.044 0.015 12% 0.893 0.797 0.712 0.636 0.567 0.507 0.452 0.404 0.361 0.322 0.287 0.257 0.229 0.205 0.183 0.163 0.146 0.130 0.116 0.104 0.093 0.083 0.074 0.066 0.059 0.053 0.047 0.042 0.037 0.033 0.011 13% 0.885 0.783 0.693 0.613 0.543 0.480 0.425 0.376 0.333 0.295 0.261 0.231 0.204 0.181 0.160 0.141 0.125 0.111 0.098 0.087 0.077 0.068 0.060 0.053 0.047 0.042 0.037 0.033 0.029 0.026 0.008 14% 0.877 0.769 0.675 0.592 0.519 0.456 0.400 0.351 0.308 0.270 0.237 0.208 0.182 0.160 0.140 0.123 0.108 0.095 0.083 0.073 0.064 0.056 0.049 15% 0.870 0.756 0.658 0.572 0.497 0.432 0.376 0.327 0.284 0.247 0.215 0.187 0.163 0.141 0.123 0.107 0.093 0.081 0.070 0.061 0.053 0.046 0.040 0.035 0.030 0.026 0.023 0.020 0.017 0.015 0.004 16% 0.862 0.743 0.641 0.552 0.476 0.410 0.354 0.305 0.263 0.227 0.195 0.168 0.145 0.125 0.108 0.093 0.080 0.069 0.060 0.051 0.044 0.038 0.033 0.028 0.024 0.021 0.018 0.016 0.014 0.012 0.003 17% 0.855 0.731 0.624 0.534 0.456 0.390 0.333 0.285 0.243 0.208 0.178 0.152 0.130 0.111 0.095 0.081 0.069 0.059 0.051 0.043 0.037 0.032 0.027 0.023 0.020 0.017 0.014 0.012 0.011 0.009 0.002 18% 0.847 0.718 0.609 0.516 0.437 0.370 0.314 0.266 0.225 0.191 0.162 0.137 0.116 0.099 0.084 0.071 0.060 0.051 0.043 0.037 0.031 0.026 0.022 0.019 0.016 0.014 0.011 0.010 0.008 0.007 0.001 19% 20% 0.840 0.833 0.706 0.694 0.593 0.579 0.499 0.482 0.419 0.402 0.352 0.335 0.296 0.279 0.249 0.233 0.209 0.194 0.176 0.162 0.148 0.135 0.124 0.112 0.104 0.093 0.088 0.078 0.074 0.065 0.062 0.054 0.052 0.045 0.044 0.038 0.037 0.031 0.031 0.026 0.026 0.022 0.022 0.018 0.018 0.015 0.015 0.013 0.013 0.010 0.011 0.009 0.009 0.007 0.008 0.006 0.006 0.005 0.005 0.004 0.001 0.001 22% 0.820 0.672 0.551 0.451 0.370 0.303 0.249 0.204 0.167 0.137 0.112 0.092 0.075 0.062 0.051 0.042 0.034 0.028 0.023 0.019 0.015 0.013 0.010 0.008 0.007 0.006 0.005 0.004 0.003 0.003 0.000 0.319 0.263 0.218 0.180 0.149 0.123 0.102 0.084 0.069 0.057 0.047 0.039 0.032 0.027 0.022 0.018 0.015 0.012 0.010 0.009 0.007 0.006 0.005 0.004 0.003 0.000 23% 0.813 0.661 0.537 0.437 0.355 0.289 0.235 0.191 0.155 0.126 0.103 0.083 0.068 0.055 0.045 0.036 0.030 0.024 0.020 0.016 0.013 0.011 0.009 0.007 0.006 0.005 0.004 0.003 0.002 0.002 0.000 24% 0.806 0.650 0.524 0.423 0.341 0.275 0.222 0.179 0.144 0.116 0.094 0.076 0.061 0.049 0.040 0.032 0.026 0.021 0.017 0.014 0.011 0.009 0.007 0.006 0.005 0.004 0.003 0.002 0.002 0.002 0.000 LI 25% 0.800 0.640 0.512 0.410 0.328 0.262 0.210 0.168 0.134 0.107 0.086 0.069 0.055 0.044 0.035 0.028 0.023 0.018 0.014 0.012 0.009 0.007 0.006 M 0.043 0.038 0.033 0.029 0.026 0.022 0.020 0.005 MIN 0.005 0.004 0.003 0.002 0.002 0.002 0.001 0.000 IT 0.174 0.097 EXHIBIT 14B-2 Present Value of an Annuity of $1 in Arrears; 1 r[1-1(1+r)n] Periods 1 2 3 OL -L 4 5 6 7 8 9 10 4% 5% 6% 7% 8% 9% 10% 11% 0.962 0.952 0.943 0.935 0.926 0.917 0.909 0.901 1.886 1.859 1.833 1.808 1.783 1.759 1.736 1.713 2.775 2.723 2.673 2.624 2.577 2.531 2.487 2.444 3.630 3.546 3.465 3.387 3.312 3.240 3.170 3.102 4.452 4.329 4.212 4.100 3.993 3.890 3.791 3.696 5.242 5.076 4.917 4.767 4.623 4.486 4.355 4.231 6.002 5.786 5.582 5.389 5.206 5.033 4.868 4.712 6.733 6.463 6.210 5.971 5.747 5.535 5.335 5.146 7.435 7.108 6.802 6.515 6.247 5.995 5.759 5.537 8.111 7.722 7.360 7.024 6.710 6.418 6.145 5.889 8.760 8.306 7.887 7.499 7.139 6.805 6.495 6.207 9.385 8.863 8.384 7.943 7.536 7.161 6.814 6.492 9.986 9.394 8.853 8.358 7.904 7.487 7.103 6.750 10.563 9.899 9.295 8.745 8.244 7.786 7.367 6.982 11.118 10.380 9.712 9.108 8.559 8.061 7.606 7.191 11.652 10.838 10.106 9.447 8.851 8.313 7.824 7.379 12.166 | 11.274 10.477 | 9.763 9.122 8.544 8.022 7.549 12.659 | 11.690 10.828 10.059 9.372 8.756 8.201 7.702 13.134 | 12.085 | 11.158 10.336 9.604 8.950 8.365 7.839 13.590 12.462 11.470 10.594 | 9.818 9.129 8.514 7.963 14.029 12.821 | 11.764 10.836 10.017] 9.292 8.649 8.075 14.451 | 13.163 | 12.042 11.061 10.201 9.442 8.772 8.176 14.857 | 13.489 | 12.303 | 11.272 10.371 9.580 8.883 8.266 15.247 13.799 | 12.550 | 11.469 10.529 9.707 8.985 8.348 15.622 14.094 | 12.783 | 11.654 10.675 9.823 9.077 8.422 15.983 14.375 13.003 | 11.826 10.810 | 9.929 9.161 8.488 16.330 | 14.643 | 13.211 | 11.987 | 10.935 | 10.027 | 9.237 8.548 16.663 | 14.898 | 13.406 | 12.137 11.051 | 10.116 | 9.307 8.602 16.984 15.141 | 13.591 | 12.278 11.158 | 10.198 | 9.370 8.650 17.292 15.372 13.765 12.409 | 11.258 10.274 9.427 8.694 19.793 17.159 | 15.046 13.332 11.925 10.757 | 9.779 8.951 12% 13% 0.893 0.885 1.690 1.668 2.402 2.361 3.037 2.974 3.605 3.517 4.111 3.998 4.564 4.423 4.968 4.799 5.328 5.132 5.650 5.426 5.938 5.687 6.194 5.918 6.424 6.122 6.628 6.302 6.811 6.462 6.974 6.604 7.120 6.729 7.250 6.840 7.366 6.938 7.025 7.562 7.102 7.645 7.170 7.7187.230 7.784 7.283 7.843 7.330 7.896 7.372 7.943 7.409 7.984 7.441 8.0227.470 8.055 7.496 8.244 7.634 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 40 14% 0.877 1.647 2.322 2.914 3.433 3.889 4.288 4.639 4.946 5.216 5.453 5.660 5.842 6.002 6.142 6.265 6.373 6.467 6.550 6.623 6.687 6.743 6.792 6.835 6.873 6.906 6.935 6.961 6.983 7.003 7.105 15% 16% 0.870 0.862 1.626 1.605 2.283 2.246 2.855 2.798 3.352 3.274 3.784 3.685 4.160 4.039 4.487 4.344 4.772 4.607 5.019 4.833 5.234 5.029 5.421 5.197 5.583 5.342 5.724 5.468 5.847 5.575 5.9545.668 6.047 5.749 6.128 5.818 6.198 5.877 6.259 5.929 6.312 5.973 6.359 6.011 6.399 6.044 6.434 6.073 6.464 6.097 6.491 6.118 6.514 6.136 6.534 6.152 6.551 6.166 6.566 6.177 6.642 6.233 T 17% 18% 0.855 0.847 1.585 1.566 2.210 2.174 2.743 2.690 3.1993.127 3.589 3.498 3.922 3.812 4.207 4.078 4.451 4.303 4.659 4.494 4.836 4.656 4.988 4.793 5.118 4.910 5.229 5.008 5.324 5.092 5.405 5.162 5.475 5.222 5.534 5.273 5.584 5.316 5.628 5.353 5.665 5.384 5.696 5.410 5.723 5.432 5.746 5.451 5.766 5.467 5.783 5.480 5.798 5.492 5.810 5.502 5.820 5.510 5.829 5.517 5.871 5.548 19% 20% 0.840 0.833 1.547 1.528 2.140 2.106 2.639 2.589 3.058 2.991 3.410 3.326 3.706 3.605 3.954 | 3.837 4.163 4.031 4.339 4.192 4.486 4.327 4.611 4.439 4.715 4.533 4.802 4.611 4.876 4.675 4.938 4.730 4.990 4.775 5.033 4.812 5.070 4.843 5.101 4.870 5.127 4.891 5.149 4.909 5.167 4.925 5.182 4.937 5.195 4.948 5.206 4.956 5.215 4.964 5.223 4.970 5.229 4.975 5.235 4.979 5.258 4.997 21% 0.826 1.509 2.074 2.540 2.926 3.245 3.508 3.726 3.905 4.054 4.177 4.278 4.362 4.432 4.489 4.536 4.576 4.608 4.635 4.657 4.675 4.690 4.703 4.713 4.721 4.728 4.734 4.739 4.743 4.746 4.760 22% 23% 0.820 0.813 1.492 1.474 2.042 2.011 2.494 2.448 2.864 2.803 3.167 3.092 3.416 3.327 3.619 3.518 3.786 3.673 3.923 3.799 4.035 3.902 4.127 3.985 4.203 4.053 4.265 4.108 4.315 4.153 4.357 4.189 4.391 4.219 4.419 4.243 4.442 4.263 4.460 4.279 4.476 4.292 4.488 4.302 4.499 4.311 4.507 4.318 4.514 4.323 4.520 4.328 4.524 4.332 4.528 4.335 4.531 4.337 4.534 4.339 4.544 | 4.347 24% 25% 0.806 0.800 1.457 1.440 1.981 1.952 2.404 2.362 2.745 2.689 3.020 2.951 3.242 3.161 3.421 3.329 3.566 3.463 3.682 3.571 3.776 | 3.656 3.851 3.725 3.912 3.780 3.962 3.824 4.001 3.859 4.033 3.887 4.059 3.910 4.080 3.928 4.097 3.942 4.110 3.954 4.121 3.963 4.130 3.970 4.137 3.976 4.143 3.981 4.147 3.985 4.151 | 3.988 4.154 3.990 4.157 | 3.992 4.159 3.994 4.160 3.995 4.166 3.999 7.469