# Question 3.17: From the undermentioned facts, compute the net present value......

From the undermentioned facts, compute the net present values (NPVs) of the two projects for each of the possible cash flows, using sensitivity analysis.

 $Project\>Y$ $(’000\>Rs)$ $Project\>X$ $(’000\>Rs)$ 40 40 Initial cash outlays (t = 0) 0 6 Cash inflow estimates (t = 1 – 15) $\,$    Worst 8 8 Most-likely 16 10 Best 0.10 0.10 Required rate of return 15 15 Economic life (years)
Step-by-Step
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The NPV of each project, assuming a 10 per cent required rate of return, can be calculated for each of the possiblE cash flows. Table A-4 indicates that the present value interest factor annuity (PVIFA) of Re 1 for 15 years at 10 per cent discount is 7.606. Multiplying each possible cash flow by PVIFA, we get, (Table 3.9):
$\,$  Table 3.9 demonstrates that sensitivity analysis can produce some very useful information about projects that appear equally desirable on the basis of the most likely estimates of their cash flows. Project X is less risky than Project Y. The actual selection of the project (assuming that the projects are mutually exclusive) will depend on the decision maker’s attitude towards risk. If the decision maker is conservative, he will select Project X as there is no possibility of suffering losses. On the other hand, if he is willing to take risks, he will choose Project Y as it has the possibility of paying a very high return as compared to project X. Sensitivity analysis, in spite of being crude, does provide the decision maker with more than one estimate of the project’s outcome and, thus, an insight into the variability of the returns.

Table 3.9   Determination of NPV

 $Project\>Y$ $Project\>X$ $\,$ $Expected\>cash\>inflows$ $NPV$ $PV$ $NPV$ $PV$ (Rs 40,000) Nil Rs 5,636 Rs 45,636 Worst 20,848 Rs 60,848 20,848 60,848 Most likely 81,696 1,21,696 36,060 76,060 Best

Table A-4 The Present Value of an Annuity of One Rupee

 10% 9% 8% 7% 6% 5% 4% 3% 2% 1% $Year$ .909 .917 .926 .953 .943 .952 .962 .971 .980 .990 1 1.736 1.759 1.783 1.808 1.833 1.859 1.886 1.913 1.942 1.970 2 2.487 2.531 2.577 2.624 2.673 2.723 2.775 2.829 2.884 2.941 3 3.170 3.240 3.312 3.387 3.465 3.546 3.630 3.717 3.808 3.902 4 3.791 3.890 3.993 4.100 4.212 4.329 4.452 4.580 4.713 4.853 5 4.355 4.486 4.623 4.767 4.917 5.076 5.242 5.417 5.601 5.795 6 4.868 5.033 5.206 5.389 5.582 5.786 6.002 6.230 6.472 6.728 7 5.335 5.535 5.747 5.971 6.210 6.463 6.733 7.020 7.326 7.652 8 5.759 5.995 6.247 6.515 6.802 7.108 7.435 7.786 8.162 8.566 9 6.145 6.418 6.710 7.024 7.360 7.722 8.111 8.530 8.983 9.471 10 6.495 6.805 7.139 7.499 7.887 8.306 8.760 9.253 9.787 10.368 11 6.814 7.161 7.536 7.943 8.384 8.863 9.385 9.954 10.575 11.255 12 7.103 7.487 7.904 8.358 8.853 9.394 9.986 10.635 11.348 12.134 13 7.367 7.786 8.244 8.746 9.295 9.899 10.563 11.296 12.106 13.004 14 7.606 8.061 8.560 9.108 9.712 10.380 11.118 11.938 12.849 13.865 15 7.824 8.313 8.851 9.447 10.106 10.838 11.652 12.561 13.578 14.718 16 8.022 8.544 9.122 9.763 10.477 11.274 12.166 13.166 14.292 15.562 17 8.201 8.756 9.372 10.059 10.828 11.690 12.659 13.754 14.992 16.398 18 8.365 8.950 9.604 10.336 11.158 12.085 13.134 14.324 15.679 17.226 19 8.514 9.129 9.818 10.594 11.470 12.462 13.590 14.878 16.352 18.046 20 8.649 9.292 10.017 10.836 11.764 12.821 14.029 15.415 17.011 18.857 21 8.772 9.442 10.201 11.061 12.042 13.163 14.451 15.937 17.658 19.661 22 8.883 9.580 10.371 11.272 12.303 13.489 14.857 16.444 18.292 20.456 23 8.985 9.707 10.529 11.469 12.550 13.799 15.247 16.936 18.914 21.244 24 9.077 9.823 10.675 11.654 12.783 14.094 15.622 17.413 19.524 22.023 25 9.427 10.274 11.258 12.409 13.765 15.373 17.292 19.601 22.397 25.808 30 9.644 10.567 11.655 12.948 14.498 16.374 18.665 21.487 24.999 29.409 35 9.779 10.757 11.925 12.332 15.046 17.159 19.793 23.115 27.356 32.835 40 9.863 10.881 12.108 13.606 15.456 17.774 20.720 24.519 29.490 36.095 45 9.915 10.962 12.234 13.801 15.762 18.256 21.482 25.730 31.424 39.197 50
$(Contd.)$
 20% 19% 18% 17% 16% 15% 14% 13% 12% 11% $Year$ .833 .850 .847 .855 .862 .870 .877 .885 .893 .901 1 1.528 1.547 1.566 1.585 1.605 1.626 1.647 1.668 1.690 1.713 2 2.106 2.140 2.174 2.210 2.246 2.283 2.322 2.361 2.402 2.444 3 2.589 2.639 2.690 2.743 2.798 2.855 2.914 2.974 3.037 3.102 4 2.991 3.058 3.127 3.199 3.274 3.352 3.433 3.517 3.605 3.696 5 3.326 3.410 3.498 3.589 3.685 3.784 3.889 3.998 4.111 4.231 6 3.605 3.706 3.812 3.922 4.039 4.160 4.288 4.423 4.564 4.712 7 3.837 3.954 4.078 4.207 4.344 4.487 4.639 4.799 4.968 5.146 8 4.031 4.163 4.303 4.451 4.607 4.772 4.946 5.132 5.328 5.537 9 4.192 4.339 4.494 4.659 4.833 5.019 5.216 5.426 5.650 5.889 10 4.327 4.487 4.656 4.836 5.029 5.234 5.453 5.687 5.938 6.207 11 4.439 4.611 4.793 4.988 5.197 5.421 5.660 5.918 6.194 6.492 12 4.533 4.715 4.910 5.118 5.342 5.583 5.842 6.122 6.424 6.750 13 4.611 4.802 5.008 5.229 5.468 5.724 6.002 5.303 6.628 6.982 14 4.675 4.876 5.092 5.324 5.575 5.847 6.142 6.462 6.811 7.191 15 4.730 4.938 5.162 5.405 5.669 5.954 6.265 6.604 6.974 7.379 16 4.775 4.990 5.222 5.475 5.749 6.047 6.373 6.729 7.120 7.549 17 4.812 5.033 5.273 5.534 5.818 6.128 6.467 6.840 7.250 7.702 18 4.843 5.070 5.316 5.585 5.877 6.198 6.550 6.938 7.366 7.839 19 4.870 5.101 5.353 5.628 5.929 6.259 6.623 7.024 7.469 7.963 20 4.891 5.127 5.384 5.665 5.973 6.312 6.687 7.102 7.562 8.075 21 4.909 5.149 5.410 5.696 6.011 6.359 6.743 7.170 7.645 8.176 22 4.925 5.167 5.432 6.723 6.044 6.399 6.792 7.230 7.718 8.266 23 4.937 5.182 5.451 5.747 6.073 6.434 6.835 7.283 7.784 8.348 24 4.948 5.195 5.467 5.766 6.097 6.464 6.873 7.330 7.843 8.422 25 4.979 5.235 5.517 5.829 6.177 6.566 7.003 7.496 8.055 8.694 30 4.992 5.251 5.539 5.858 6.215 6.617 7.070 7.586 8.176 8.855 35 4.997 5.258 5.548 5.871 6.233 6.642 7.105 7.634 8.244 8.951 40 4.999 5.261 5.552 5.877 6.242 6.654 7.123 7.661 8.283 9.008 45 4.999 5.262 5.554 5.880 6.246 6.661 7.133 7.675 8.305 9.042 50
$(Contd.)$
 30% 29% 28% 27% 26% 25% 24% 23% 22% 21% $Year$ .769 .775 .781 .787 .794 .800 .806 .813 .820 .826 1 1.361 1.376 1.392 1.407 1.424 1.440 1.457 1.474 1.492 1.509 2 1.816 1.842 1.868 1.896 1.923 1.952 1.981 2.011 2.042 2.074 3 2.166 2.203 2.241 2.280 2.320 2.362 2.404 2.448 2.494 2.540 4 2.436 2.483 2.532 2.583 2.635 2.689 2.745 2.803 2.864 2.926 5 2.643 2.700 2.759 2.821 2.885 2.951 3.020 3.092 3.167 3.245 6 2.802 2.868 2.937 3.009 3.083 3.161 3.242 3.327 3.416 3.508 7 2.925 2.999 3.076 3.156 3.241 3.329 3.421 3.518 3.619 3.726 8 3.019 3.100 3.184 3.273 3.366 3.463 3.566 3.673 3.786 3.905 9 3.092 3.178 3.269 3.364 3.465 3.570 3.682 3.799 3.923 4.054 10 3.147 3.239 3.335 3.437 3.544 3.656 3.776 4.902 4.035 4.177 11 3.190 3.286 3.387 3.493 3.606 3.752 3.851 3.985 4.127 4.278 12 3.223 3.322 3.427 3.538 3.656 3.780 3.912 4.053 4.203 4.362 13 3.249 3.351 3.459 3.573 3.695 3.824 3.962 4.108 4.265 4.432 14 3.268 3.373 3.483 3.601 3.726 3.859 4.001 4.153 4.315 4.489 15 3.283 3.390 3.503 3.623 3.751 3.887 4.033 4.189 4.357 4.536 16 3.295 3.403 3.518 3.640 3.771 3.910 4.059 4.219 4.391 4.576 17 3.304 3.413 3.529 3.654 3.786 3.928 4.080 4.243 4.419 4.608 18 3.311 3.421 3.539 3.664 3.799 3.942 4.097 4.263 4.442 4.635 19 3.316 3.427 3.546 3.673 3.808 3.954 4.110 4.279 4.460 4.657 20 3.320 3.432 3.551 3.679 3.816 3.963 4.121 4.292 4.476 4.675 21 3.323 3.436 3.556 3.684 3.822 3.970 4.130 4.302 4.488 4.690 22 3.325 3.438 3.559 3.689 3.827 3.976 4.137 4.311 4.499 4.703 23 3.327 3.441 3.562 3.692 3.831 3.981 4.143 4.318 4.507 4.713 24 3.329 3.442 3.564 3.694 3.834 3.985 4.147 4.323 4.514 4.721 25 3.332 3.447 3.569 3.701 3.842 3.995 4.160 4.339 4.534 4.746 30 3.333 3.448 3.571 3.703 3.845 3.998 4.164 4.345 4.541 4.756 35 3.333 3.448 3.571 3.703 3.846 3.999 4.166 4.347 4.544 4.760 40 3.333 3.448 3.571 3.704 3.846 4.000 4.166 4.347 4.545 4.761 45 3.333 3.448 3.571 3.704 3.846 4.000 4.167 4.348 4.545 4.762 50

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