Finansal Yönetim - II Time Value of Money - Appendices appendices appendix A COMPOUND SUM OF $1 appendix B COMPOUND SUM OF AN ANNUITY OF $1 appendix C PRESENT VALUE OF $1 appendix D PRESENT VALUE OF AN ANNUITY OF $1 appendix E TIME VALUE OF MONEY AND INVESTMENT APPLICATIONS appendix F USING CALCULATORS FOR FINANCIAL ANALYSIS hir39632_app.qxd 5/10/2002 8:16 AM Page 645646 Appendix A Compound Sum of $1 Percent Period 1% 2% 3% 4% 5% 6% 7% 8% 9% 10% 11% 1 . . . . . 1.010 1.020 1.030 1.040 1.050 1.060 1.070 1.080 1.090 1.100 1.110 2 . . . . . 1.020 1.040 1.061 1.082 1.103 1.124 1.145 1.166 1.188 1.210 1.232 3 . . . . . 1.030 1.061 1.093 1.125 1.158 1.191 1.225 1.260 1.295 1.331 1.368 4 . . . . . 1.041 1.082 1.126 1.170 1.216 1.262 1.311 1.360 1.412 1.464 1.518 5 . . . . . 1.051 1.104 1.159 1.217 1.276 1.338 1.403 1.469 1.539 1.611 1.685 6 . . . . . 1.062 1.126 1.194 1.265 1.340 1.419 1.501 1.587 1.677 1.772 1.870 7 . . . . . 1.072 1.149 1.230 1.316 1.407 1.504 1.606 1.714 1.828 1.949 2.076 8 . . . . . 1.083 1.172 1.267 1.369 1.477 1.594 1.718 1.851 1.993 2.144 2.305 9 . . . . . 1.094 1.195 1.305 1.423 1.551 1.689 1.838 1.999 2.172 2.358 2.558 10 . . . . . 1.105 1.219 1.344 1.480 1.629 1.791 1.967 2.159 2.367 2.594 2.839 11 . . . . . 1.116 1.243 1.384 1.539 1.710 1.898 2.105 2.332 2.580 2.853 3.152 12 . . . . . 1.127 1.268 1.426 1.601 1.796 2.012 2.252 2.518 2.813 3.138 3.498 13 . . . . . 1.138 1.294 1.469 1.665 1.886 2.133 2.410 2.720 3.066 3.452 3.883 14 . . . . . 1.149 1.319 1.513 1.732 1.980 2.261 2.579 2.937 3.342 3.797 4.310 15 . . . . . 1.161 1.346 1.558 1.801 2.079 2.397 2.759 3.172 3.642 4.177 4.785 16 . . . . . 1.173 1.373 1.605 1.873 2.183 2.540 2.952 3.426 3.970 4.595 5.311 17 . . . . . 1.184 1.400 1.653 1.948 2.292 2.693 3.159 3.700 4.328 5.054 5.895 18 . . . . . 1.196 1.428 1.702 2.206 2.407 2.854 3.380 3.996 4.717 5.560 6.544 19 . . . . . 1.208 1.457 1.754 2.107 2.527 3.026 3.617 4.316 5.142 6.116 7.263 20 . . . . . 1.220 1.486 1.806 2.191 2.653 3.207 3.870 4.661 5.604 6.727 8.062 25 . . . . . 1.282 1.641 2.094 2.666 3.386 4.292 5.427 6.848 8.623 10.835 13.585 30 . . . . . 1.348 1.811 2.427 3.243 4.322 5.743 7.612 10.063 13.268 17.449 22.892 40 . . . . . 1.489 2.208 3.262 4.801 7.040 10.286 14.974 21.725 31.409 42.259 65.001 50 . . . . . 1.645 2.692 4.384 7.107 11.467 18.420 29.457 46.902 74.358 117.39 184.57 APPENDIX A Compound Sum of $1 hir39632_app.qxd 5/10/2002 8:16 AM Page 646Appendix A Compound Sum of $1 647 Percent Period 12% 13% 14% 15% 16% 17% 18% 19% 20% 25% 30% 1 . . . 1.120 1.130 1.140 1.150 1.160 1.170 1.180 1.190 1.200 1.250 1.300 2 . . . 1.254 1.277 1.300 1.323 1.346 1.369 1.392 1.416 1.440 1.563 1.690 3 . . . 1.405 1.443 1.482 1.521 1.561 1.602 1.643 1.685 1.728 1.953 2.197 4 . . . 1.574 1.630 1.689 1.749 1.811 1.874 1.939 2.005 2.074 2.441 2.856 5 . . . 1.762 1.842 1.925 2.011 2.100 2.192 2.288 2.386 2.488 3.052 3.713 6 . . . 1.974 2.082 2.195 2.313 2.436 2.565 2.700 2.840 2.986 3.815 4.827 7 . . . 2.211 2.353 2.502 2.660 2.826 3.001 3.185 3.379 3.583 4.768 6.276 8 . . . 2.476 2.658 2.853 3.059 3.278 3.511 3.759 4.021 4.300 5.960 8.157 9 . . . 2.773 3.004 3.252 3.518 3.803 4.108 4.435 4.785 5.160 7.451 10.604 10 . . . 3.106 3.395 3.707 4.046 4.411 4.807 5.234 5.696 6.192 9.313 13.786 11 . . . 3.479 3.836 4.226 4.652 5.117 5.624 6.176 6.777 7.430 11.642 17.922 12 . . . 3.896 4.335 4.818 5.350 5.936 6.580 7.288 8.064 8.916 14.552 23.298 13 . . . 4.363 4.898 5.492 6.153 6.886 7.699 8.599 9.596 10.699 18.190 30.288 14 . . . 4.887 5.535 6.261 7.076 7.988 9.007 10.147 11.420 12.839 22.737 39.374 15 . . . 5.474 6.254 7.138 8.137 9.266 10.539 11.974 13.590 15.407 28.422 51.186 16 . . . 6.130 7.067 8.137 9.358 10.748 12.330 14.129 16.172 18.488 35.527 66.542 17 . . . 6.866 7.986 9.276 10.761 12.468 14.426 16.672 19.244 22.186 44.409 86.504 18 . . . 7.690 9.024 10.575 12.375 14.463 16.879 19.673 22.091 26.623 55.511 112.46 19 . . . 8.613 10.197 12.056 14.232 16.777 19.748 23.214 27.252 31.948 69.389 146.19 20 . . . 9.646 11.523 13.743 16.367 19.461 23.106 27.393 32.429 38.338 86.736 190.05 25 . . . 17.000 21.231 26.462 32.919 40.874 50.658 62.699 77.388 95.396 264.70 705.64 30 . . . 29.960 39.116 50.950 66.212 85.850 111.07 143.37 184.68 237.38 807.79 2,620.0 40 . . . 93.051 132.78 188.88 267.86 378.72 533.87 750.38 1,051.7 1,469.8 7,523.2 36,119. 50 . . . 289.00 450.74 700.23 1,083.7 1,670.7 2,566.2 3,927.4 5,988.9 9,100.4 70,065. 497,929. APPENDIX A Compound Sum of $1 (concluded) hir39632_app.qxd 5/10/2002 8:16 AM Page 647648 Appendix B Compound Sum of an Annuity of $1 Percent Period 1% 2% 3% 4% 5% 6% 7% 8% 9% 10% 11% 1 . . . 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 2 . . . 2.010 2.020 2.030 2.040 2.050 2.060 2.070 2.080 2.090 2.100 2.110 3 . . . 3.030 3.060 3.091 3.122 3.153 3.184 3.215 3.246 3.278 3.310 3.342 4 . . . 4.060 4.122 4.184 4.246 4.310 4.375 4.440 4.506 4.573 4.641 4.710 5 . . . 5.101 5.204 5.309 5.416 5.526 5.637 5.751 5.867 5.985 6.105 6.228 6 . . . 6.152 6.308 6.468 6.633 6.802 6.975 7.153 7.336 7.523 7.716 7.913 7 . . . 7.214 7.434 7.662 7.898 8.142 8.394 8.654 8.923 9.200 9.487 9.783 8 . . . 8.286 8.583 8.892 9.214 9.549 9.897 10.260 10.637 11.028 11.436 11.859 9 . . . 9.369 9.755 10.159 10.583 11.027 11.491 11.978 12.488 13.021 13.579 14.164 10 . . . 10.462 10.950 11.464 12.006 12.578 13.181 13.816 14.487 15.193 15.937 16.722 11 . . . 11.567 12.169 12.808 13.486 14.207 14.972 15.784 16.645 17.560 18.531 19.561 12 . . . 12.683 13.412 14.192 15.026 15.917 16.870 17.888 18.977 20.141 21.384 22.713 13 . . . 13.809 14.680 15.618 16.627 17.713 18.882 20.141 21.495 22.953 24.523 26.212 14 . . . 14.947 15.974 17.086 18.292 19.599 21.015 22.550 24.215 26.019 27.975 30.095 15 . . . 16.097 17.293 18.599 20.024 21.579 23.276 25.129 27.152 29.361 31.772 34.405 16 . . . 17.258 18.639 20.157 21.825 23.657 25.673 27.888 30.324 33.003 35.950 39.190 17 . . . 18.430 20.012 21.762 23.698 25.840 20.213 30.840 33.750 36.974 40.545 44.501 18 . . . 19.615 21.412 23.414 25.645 28.132 30.906 33.999 37.450 41.301 45.599 50.396 19 . . . 20.811 22.841 25.117 27.671 30.539 33.760 37.379 41.446 46.018 51.159 56.939 20 . . . 22.019 24.297 26.870 29.778 33.066 36.786 40.995 45.762 51.160 57.275 64.203 25 . . . 28.243 32.030 36.459 41.646 47.727 54.865 63.249 73.106 84.701 98.347 114.41 30 . . . 34.785 40.588 47.575 56.085 66.439 79.058 94.461 113.28 136.31 164.49 199.02 40 . . . 48.886 60.402 75.401 95.026 120.80 154.76 199.64 259.06 337.89 442.59 581.83 50 . . . 64.463 84.579 112.80 152.67 209.35 290.34 406.53 573.77 815.08 1,163.9 1,668.8 APPENDIX B Compound Sum of an Annuity of $1 hir39632_app.qxd 5/10/2002 8:16 AM Page 648Appendix B Compound Sum of an Annuity of $1 649 Percent Period 12% 13% 14% 15% 16% 17% 18% 19% 20% 25% 30% 1 . . . 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 2 . . . 2.120 2.130 2.140 2.150 2.160 2.170 2.180 2.190 2.200 2.250 2.300 3 . . . 3.374 3.407 3.440 3.473 3.506 3.539 3.572 3.606 3.640 3.813 3.990 4 . . . 4.779 4.850 4.921 4.993 5.066 5.141 5.215 5.291 5.368 5.766 6.187 5 . . . 6.353 6.480 6.610 6.742 6.877 7.014 7.154 7.297 7.442 8.207 9.043 6 . . . 8.115 8.323 8.536 9.754 8.977 9.207 9.442 0.683 9.930 11.259 12.756 7 . . . 10.089 10.405 10.730 11.067 11.414 11.772 12.142 12.523 12.916 15.073 17.583 8 . . . 12.300 12.757 13.233 13.727 14.240 14.773 15.327 15.902 16.499 19.842 23.858 9 . . . 14.776 15.416 16.085 16.786 17.519 18.285 19.086 19.923 20.799 25.802 32.015 10 . . . 17.549 18.420 19.337 20.304 21.321 22.393 23.521 24.701 25.959 33.253 42.619 11 . . . 20.655 21.814 23.045 24.349 25.733 27.200 28.755 30.404 32.150 42.566 56.405 12 . . . 24.133 25.650 27.271 29.002 30.850 32.824 34.931 37.180 39.581 54.208 74.327 13 . . . 28.029 29.985 32.089 34.352 36.786 39.404 42.219 45.244 48.497 68.760 97.625 14 . . . 32.393 34.883 37.581 40.505 43.672 47.103 50.818 54.841 59.196 86.949 127.91 15 . . . 37.280 40.417 43.842 47.580 51.660 56.110 60.965 66.261 72.035 109.69 167.29 16 . . . 42.753 46.672 50.980 55.717 60.925 66.649 72.939 79.850 87.442 138.11 218.47 17 . . . 48.884 53.739 59.118 65.075 71.673 78.979 87.068 96.022 105.93 173.64 285.01 18 . . . 55.750 61.725 68.394 75.836 84.141 93.406 103.74 115.27 128.12 218.05 371.52 19 . . . 63.440 70.749 78.969 88.212 98.603 110.29 123.41 138.17 154.74 273.56 483.97 20 . . . 72.052 80.947 91.025 102.44 115.38 130.03 146.63 165.42 186.69 342.95 630.17 25 . . . 133.33 155.62 181.87 212.79 249.21 292.11 342.60 402.04 471.98 1,054.8 2,348.80 30 . . . 241.33 293.20 356.79 434.75 530.31 647.44 790.95 966.7 1,181.9 3,227.2 8,730.0 40 . . . 767.09 1,013.7 1,342.0 1,779.1 2,360.8 3,134.5 4,163.21 5,529.8 7,343.9 30,089. 120,393. 50 . . . 2,400.0 3,459.5 4,994.5 7,217.7 10,436. 15,090. 21,813. 31,515. 45,497. 280,256. 1,659,731. APPENDIX B Compound Sum of an Annuity of $1 (concluded) hir39632_app.qxd 5/10/2002 8:16 AM Page 649650 Appendix C Present Value of $1 Percent Period 1% 2% 3% 4% 5% 6% 7% 8% 9% 10% 11% 12% 1 . . . . 0.990 0.980 0.971 0.962 0.952 0.943 0.935 0.926 0.917 0.909 0.901 0.893 2 . . . . 0.980 0.961 0.943 0.925 0.907 0.890 0.873 0.857 0.842 0.826 0.812 0.797 3 . . . . 0.971 0.942 0.915 0.889 0.864 0.840 0.816 0.794 0.772 0.751 0.731 0.712 4 . . . . 0.961 0.924 0.885 0.855 0.823 0.792 0.763 0.735 0.708 0.683 0.659 0.636 5 . . . . 0.951 0.906 0.863 0.822 0.784 0.747 0.713 0.681 0.650 0.621 0.593 0.567 6 . . . . 0.942 0.888 0.837 0.790 0.746 0.705 0.666 0.630 0.596 0.564 0.535 0.507 7 . . . . 0.933 0.871 0.813 0.760 0.711 0.665 0.623 0.583 0.547 0.513 0.482 0.452 8 . . . . 0.923 0.853 0.789 0.731 0.677 0.627 0.582 0.540 0.502 0.467 0.434 0.404 9 . . . . 0.914 0.837 0.766 0.703 0.645 0.592 0.544 0.500 0.460 0.424 0.391 0.361 10 . . . . 0.905 0.820 0.744 0.676 0.614 0.558 0.508 0.463 0.422 0.386 0.352 0.322 11 . . . . 0.896 0.804 0.722 0.650 0.585 0.527 0.475 0.429 0.388 0.350 0.317 0.287 12 . . . . 0.887 0.788 0.701 0.625 0.557 0.497 0.444 0.397 0.356 0.319 0.286 0.257 13 . . . . 0.879 0.773 0.681 0.601 0.530 0.469 0.415 0.368 0.326 0.290 0.258 0.229 14 . . . . 0.870 0.758 0.661 0.577 0.505 0.442 0.388 0.340 0.299 0.263 0.232 0.205 15 . . . . 0.861 0.743 0.642 0.555 0.481 0.417 0.362 0.315 0.275 0.239 0.209 0.183 16 . . . . 0.853 0.728 0.623 0.534 0.458 0.394 0.339 0.292 0.252 0.218 0.188 0.163 17 . . . . 0.844 0.714 0.605 0.513 0.436 0.371 0.317 0.270 0.231 0.198 0.170 0.146 18 . . . . 0.836 0.700 0.587 0.494 0.416 0.350 0.296 0.250 0.212 0.180 0.153 0.130 19 . . . . 0.828 0.686 0.570 0.475 0.396 0.331 0.277 0.232 0.194 0.164 0.138 0.116 20 . . . . 0.820 0.673 0.554 0.456 0.377 0.312 0.258 0.215 0.178 0.149 0.124 0.104 25 . . . . 0.780 0.610 0.478 0.375 0.295 0.233 0.184 0.146 0.116 0.092 0.074 0.059 30 . . . . 0.742 0.552 0.412 0.308 0.231 0.174 0.131 0.099 0.075 0.057 0.044 0.033 40 . . . . 0.672 0.453 0.307 0.208 0.142 0.097 0.067 0.046 0.032 0.022 0.015 0.011 50 . . . . 0.608 0.372 0.228 0.141 0.087 0.054 0.034 0.021 0.013 0.009 0.005 0.003 APPENDIX C Present Value of $1 hir39632_app.qxd 5/10/2002 8:16 AM Page 650Appendix C Present Value of $1 651 Percent Period 13% 14% 15% 16% 17% 18% 19% 20% 25% 30% 35% 40% 50% 1 . . . . 0.885 0.877 0.870 0.862 0.855 0.847 0.840 0.833 0.800 0.769 0.741 0.714 0.667 2 . . . . 0.783 0.769 0.756 0.743 0.731 0.718 0.706 0.694 0.640 0.592 0.549 0.510 0.444 3 . . . . 0.693 0.675 0.658 0.641 0.624 0.609 0.593 0.579 0.512 0.455 0.406 0.364 0.296 4 . . . . 0.613 0.592 0.572 0.552 0.534 0.515 0.499 0.482 0.410 0.350 0.301 0.260 0.198 5 . . . . 0.543 0.519 0.497 0.476 0.456 0.437 0.419 0.402 0.320 0.269 0.223 0.186 0.132 6 . . . . 0.480 0.456 0.432 0.410 0.390 0.370 0.352 0.335 0.262 0.207 0.165 0.133 0.088 7 . . . . 0.425 0.400 0.376 0.354 0.333 0.314 0.296 0.279 0.210 0.159 0.122 0.095 0.059 8 . . . . 0.376 0.351 0.327 0.305 0.285 0.266 0.249 0.233 0.168 0.123 0.091 0.068 0.039 9 . . . . 0.333 0.300 0.284 0.263 0.243 0.225 0.209 0.194 0.134 0.094 0.067 0.048 0.026 10 . . . . 0.295 0.270 0.247 0.227 0.208 0.191 0.176 0.162 0.107 0.073 0.050 0.035 0.017 11 . . . . 0.261 0.237 0.215 0.195 0.178 0.162 0.148 0.135 0.086 0.056 0.037 0.025 0.012 12 . . . . 0.231 0.208 0.187 0.168 0.152 0.137 0.124 0.112 0.069 0.043 0.027 0.018 0.008 13 . . . . 0.204 0.182 0.163 0.145 0.130 0.116 0.104 0.093 0.055 0.033 0.020 0.013 0.005 14 . . . . 0.181 0.160 0.141 0.125 0.111 0.099 0.088 0.078 0.044 0.025 0.015 0.009 0.003 15 . . . . 0.160 0.140 0.123 0.108 0.095 0.084 0.074 0.065 0.035 0.020 0.011 0.006 0.002 16 . . . . 0.141 0.123 0.107 0.093 0.081 0.071 0.062 0.054 0.028 0.015 0.008 0.005 0.002 17 . . . . 0.125 0.108 0.093 0.080 0.069 0.060 0.052 0.045 0.023 0.012 0.006 0.003 0.001 18 . . . . 0.111 0.095 0.081 0.069 0.059 0.051 0.044 0.038 0.018 0.009 0.005 0.002 0.001 19 . . . . 0.098 0.083 0.070 0.060 0.051 0.043 0.037 0.031 0.014 0.007 0.003 0.002 0 20 . . . . 0.087 0.073 0.061 0.051 0.043 0.037 0.031 0.026 0.012 0.005 0.002 0.001 0 25 . . . . 0.047 0.038 0.030 0.024 0.020 0.016 0.013 0.010 0.004 0.001 0.001 0 0 30 . . . . 0.026 0.020 0.015 0.012 0.009 0.007 0.005 0.004 0.001 0 0 0 0 40 . . . . 0.008 0.005 0.004 0.003 0.002 0.001 0.001 0.001 0 0 0 0 0 50 . . . . 0.002 0.001 0.001 0.001 0 0 0 0 0 0 0 0 0 APPENDIX C Present Value of $1 (concluded) hir39632_app.qxd 5/10/2002 8:16 AM Page 651652 Appendix D Present Value of an Annuity of $1 Percent Period 1% 2% 3% 4% 5% 6% 7% 8% 9% 10% 11% 12% 1 . . . . 0.990 0.980 0.971 0.962 0.952 0.943 0.935 0.926 0.917 0.909 0.901 0.893 2 . . . . 1.970 1.942 1.913 1.886 1.859 1.833 1.808 1.783 1.759 1.736 1.713 1.690 3 . . . . 2.941 2.884 2.829 2.775 2.723 2.673 2.624 2.577 2.531 2.487 2.444 2.402 4 . . . . 3.902 3.808 3.717 3.630 3.546 3.465 3.387 3.312 3.240 3.170 3.102 3.037 5 . . . . 4.853 4.715 4.580 4.452 4.329 4.212 4.100 3.993 3.890 3.791 3.696 3.605 6 . . . . 5.795 5.601 5.417 5.242 5.076 4.917 4.767 4.623 4.486 4.355 4.231 4.111 7 . . . . 6.728 6.472 6.230 6.002 5.786 5.582 5.389 5.206 5.033 4.868 4.712 4.564 8 . . . . 7.652 7.325 7.020 6.733 6.463 6.210 5.971 5.747 5.535 5.335 5.146 4.968 9 . . . . 8.566 8.162 7.786 7.435 7.108 6.802 6.515 6.247 5.995 5.759 5.537 5.328 10 . . . . 9.471 8.983 8.530 8.111 7.722 7.360 7.024 6.710 6.418 6.145 5.889 5.650 11 . . . . 10.368 9.787 9.253 8.760 8.306 7.887 7.499 7.139 6.805 6.495 6.207 5.938 12 . . . . 11.255 10.575 9.954 9.385 8.863 8.384 7.943 7.536 7.161 6.814 6.492 6.194 13 . . . . 12.134 11.348 10.635 9.986 9.394 8.853 8.358 7.904 7.487 7.103 6.750 6.424 14 . . . . 13.004 12.106 11.296 10.563 9.899 9.295 8.745 8.244 7.786 7.367 6.982 6.628 15 . . . . 13.865 12.849 11.939 11.118 10.380 9.712 9.108 8.559 8.061 7.606 7.191 6.811 16 . . . . 14.718 13.578 12.561 11.652 10.838 10.106 9.447 8.851 8.313 7.824 7.379 6.974 17 . . . . 15.562 14.292 13.166 12.166 11.274 10.477 9.763 9.122 8.544 8.022 7.549 7.102 18 . . . . 16.398 14.992 13.754 12.659 11.690 10.828 10.059 9.372 8.756 8.201 7.702 7.250 19 . . . . 17.226 15.678 14.324 13.134 12.085 11.158 10.336 9.604 8.950 8.365 7.839 7.366 20 . . . . 18.046 16.351 14.877 13.590 12.462 11.470 10.594 9.818 9.129 8.514 7.963 7.469 25 . . . . 22.023 19.523 17.413 15.622 14.094 12.783 11.654 10.675 9.823 9.077 8.422 7.843 30 . . . . 25.808 22.396 19.600 17.292 15.372 13.765 12.409 11.258 10.274 9.427 8.694 8.055 40 . . . . 32.835 27.355 23.115 19.793 17.160 15.046 13.332 11.925 10.757 9.779 8.951 8.244 50 . . . . 39.196 31.424 25.730 21.482 18.256 15.762 13.801 12.233 10.962 9.915 9.042 8.304 APPENDIX D Present Value of an Annuity of $1 hir39632_app.qxd 5/10/2002 8:16 AM Page 652Appendix D Present Value of an Annuity of $1 653 Percent Period 13% 14% 15% 16% 17% 18% 19% 20% 25% 30% 35% 40% 50% 1 . . . . 0.885 0.877 0.870 0.862 0.855 0.847 0.840 0.833 0.800 0.769 0.741 0.714 0.667 2 . . . . 1.668 1.647 1.626 1.605 1.585 1.566 1.547 1.528 1.440 1.361 1.289 1.224 1.111 3 . . . . 2.361 2.322 2.283 2.246 2.210 2.174 2.140 2.106 1.952 1.816 1.696 1.589 1.407 4 . . . . 2.974 2.914 2.855 2.798 2.743 2.690 2.639 2.589 2.362 2.166 1.997 1.849 1.605 5 . . . . 3.517 3.433 3.352 3.274 3.199 3.127 3.058 2.991 2.689 2.436 2.220 2.035 1.737 6 . . . . 3.998 3.889 3.784 3.685 3.589 3.498 3.410 3.326 2.951 2.643 2.385 2.168 1.824 7 . . . . 4.423 4.288 4.160 4.039 3.922 3.812 3.706 3.605 3.161 2.802 2.508 2.263 1.883 8 . . . . 4.799 4.639 4.487 4.344 4.207 4.078 3.954 3.837 3.329 2.925 2.598 2.331 1.922 9 . . . . 5.132 4.946 4.772 4.607 4.451 4.303 4.163 4.031 3.463 3.019 2.665 2.379 1.948 10 . . . . 5.426 5.216 5.019 4.833 4.659 4.494 4.339 4.192 3.571 3.092 2.715 2.414 1.965 11 . . . . 5.687 5.453 5.234 5.029 4.836 4.656 4.486 4.327 3.656 3.147 2.752 2.438 1.977 12 . . . . 5.918 5.660 5.421 5.197 4.988 4.793 4.611 4.439 3.725 3.190 2.779 2.456 1.985 13 . . . . 6.122 5.842 5.583 5.342 5.118 4.910 4.715 4.533 3.780 3.223 2.799 2.469 1.990 14 . . . . 6.302 6.002 5.724 5.468 5.229 5.008 4.802 4.611 3.824 3.249 2.814 2.478 1.993 15 . . . . 6.462 6.142 5.847 5.575 5.324 5.092 4.876 4.675 3.859 3.268 2.825 2.484 1.995 16 . . . . 6.604 6.265 5.954 5.668 5.405 5.162 4.938 4.730 3.887 3.283 2.834 2.489 1.997 17 . . . . 6.729 6.373 6.047 5.749 5.475 5.222 4.988 4.775 3.910 3.295 2.840 2.492 1.998 18 . . . . 6.840 6.467 6.128 5.818 5.534 5.273 5.003 4.812 3.928 3.304 2.844 2.494 1.999 19 . . . . 6.938 6.550 6.198 5.877 5.584 5.316 5.070 4.843 3.942 3.311 2.848 2.496 1.999 20 . . . . 7.025 6.623 6.259 5.929 5.628 5.353 5.101 4.870 3.954 3.316 2.850 2.497 1.999 25 . . . . 7.330 6.873 6.464 6.097 5.766 5.467 5.195 4.948 3.985 3.329 2.856 2.499 2.000 30 . . . . 7.496 7.003 6.566 6.177 5.829 5.517 5.235 4.979 3.995 3.332 2.857 2.500 2.000 40 . . . . 7.634 7.105 6.642 6.233 5.871 5.548 5.258 4.997 3.999 3.333 2.857 2.500 2.000 50 . . . . 7.675 7.133 6.661 6.246 5.880 5.554 5.262 4.999 4.000 3.333 2.857 2.500 2.000 APPENDIX D Present Value of an Annuity of $1 (concluded) hir39632_app.qxd 5/10/2002 8:16 AM Page 653Time Value of Money and Investment Applications Many applications for the time value of money exist. Applications use either the compound sum (sometimes referred to as future value) or the present value. Additionally some cash flows are annuities. An annuity represents cash flows that are equally spaced in time and are constant dollar amounts. Car payments, mortgage payments, and bond interest payments are examples of annuities. An- nuities can either be present value annuities or compound sum annuities. In the next section, we present the concept of compound sum and develop common applications related to investments. Compound Sum: Single Amount In determining the compound sum, we measure the future value of an amount that is allowed to grow at a given rate over a period of time. Assume an investor buys an asset worth $1,000. This asset (gold, diamonds, art, real estate, etc.) is expected to increase in value by 10 percent per year, and the investor wants to know what it will be worth after the fourth year. At the end of the first year, the investor will have $1,000 (1 0.10),or $1,100.By the end of year two,the $1,100 will have grown by another 10 percent to $1,210 ($1,100 1.10).The four-year pattern is indicated below: 1st year: $1,000 1.10 $1,100 2nd year: $1,100 1.10 $1,210 3rd year: $1,210 1.10 $1,331 4th year: $1,331 1.10 $1,464 E appendix OVERVIEW COMPOUND SUM hir39632_app.qxd 5/10/2002 8:16 AM Page 654After the fourth year, the investor has accumulated $1,464. Because com- pounding problems often cover a long time,a generalized formula is necessary to describe the compounding process.We shall let: S Compound sum P Principal or present value i Interest rate, growth rate, or rate of return n Number of periods compounded The simple formula is: S P(1 i ) n (E–1) In the preceding example, the beginning amount, P, was equal to $1,000; the growth rate, i, equaled 10 percent; and the number of periods, n, equaled 4, so we get: S $1,000 (1.10) 4 , or $1,000 1.464 $1,464 The term (1.10) 4 is found to equal 1.464 by multiplying 1.10 four times itself. This mathematical calculation is called an exponential, where you take (1.10) to the fourth power. On your calculator, you would have an exponential key y x where y represents (1.10) and x represents 4. For students with calculators, we have prepared Appendix F for both Hewlett-Packard and Texas Instruments calculators. For those not proficient with calculators or who have calculators without financial functions,Table E–1 is a shortened version of the compound sum table found in Appendix A.The table tells us the amount $1 would grow to if it were invested for any number of periods at a given rate of return. Using this table for our previous example, we find an interest factor for the compound sum in the row where n 4 and the column where i 10 percent.The factor is 1.464, the same as previously calculated. We multiply this factor times any beginning amount to determine the compound sum. When using compound sum tables to calculate the compound sum, we shorten our formula from S P(1 i) n to: S P S IF (E–2) Appendix E Time Value of Money and Investment Applications 655 Periods 1% 2% 3% 4% 6% 8% 10% 1 1.010 1.020 1.030 1.040 1.060 1.080 1.100 2 1.020 1.040 1.061 1.082 1.124 1.166 1.210 3 1.030 1.061 1.093 1.125 1.191 1.260 1.331 4 1.041 1.082 1.126 1.170 1.262 1.360 1.464 5 1.051 1.104 1.159 1.217 1.338 1.469 1.611 10 1.105 1.219 1.344 1.480 1.791 2.159 2.594 20 1.220 1.486 1.806 2.191 3.207 4.661 6.727 30 1.348 1.811 2.427 3.243 5.743 10.063 13.268 TABLE E–1 Compound Sum of $1 (S IF ) hir39632_app.qxd 5/10/2002 8:16 AM Page 655where S IF equals the interest factor for the compound sum found in Table E–1 or Appendix A. Using a new example, assume $5,000 is invested for 20 years at 6 percent. Using Table E–1, the interest factor for the compound sum would be 3.207, and the total value would be: S P S IF (n 20, i 6%) $5,000 3.207 $16,035 Example—Compound Sum, Single Amount Problem: Mike Donegan receives a bonus from his employer of $3,200. He will invest the money at a 12 percent rate of return for the next eight years. How much will he have after eight years? Solution: Compound sum, single amount: S P S IF (n 8, i 12%) Appendix A $3,200 2.476 $7,923.20 Compound Sum: Annuity Our previous example was a one-time single investment. Let us examine a com- pound sum of an annuity where constant payments are made at equally spaced periods and grow to a future value. The normal assumption for a com- pound sum of an annuity is that the payments are made at the end of each period, so the last payment does not compound or earn a rate of return. Figure E–1 demonstrates the timing and compounding process when $1,000 per year is contributed to a fund for four consecutive years.The $1,000 for each period is multiplied by the compound sum factors for the appropriate periods of compounding.The first $1,000 comes in at the end of the first period and has three periods to compound; the second $1,000 at the end of the second period, with two periods to compound; the third payment has one period to compound; and the last payment is multiplied by a factor of 1.00 showing no compounding at all. Because compounding the individual values is tedious, compound sum of an- nuity tables can be used.These tables simply add up the interest factors from the compound sum tables for a single amount.Table E–2 is a shortened version of Ap- pendix B, the compound sum of an annuity table showing the compound sum factors for a specified period and rate of return.Notice that all the way across the table, the factor in period one is 1.00.This reflects the fact that the last payment does not compound. One example of the compound sum of an annuity applies to the individual retirement account (IRA) and Keogh retirement plans.The IRA allows workers to invest $2,000 per year in a tax-free account and the Keogh allows a maximum of $30,000 per year to be invested in a retirement account for self-employed in- dividuals. 1 Assume Dr. Piotrowski shelters $30,000 per year from age 35 to 65. If she makes 30 payments of $30,000 and earns a rate of return of 8 percent, her Keogh account at retirement would be more than $3 million. 656 Appendix E Time Value of Money and Investment Applications 1 The annual allowable deductibles are scheduled to increase between 2001 and 2011. hir39632_app.qxd 5/10/2002 8:16 AM Page 656S R SA IF (n 30, i 8% return) (E–3) $30,000 113.280 $3,398,400 While this seems like a lot of money in today’s world,we need to measure what it will buy 30 years from now after inflation is considered.One way to examine this is to calculate what the $30,000 payments would have to be if they only kept up with inflation. Let’s assume inflation of 3 percent over the next 30 years and recalculate the sum of the annuity: S R SA IF (n 30, i 3% inflation) $30,000 47.575 $1,427,250 Appendix E Time Value of Money and Investment Applications 657 Period 0 Period 1 Period 2 Period 3 Period 4 $1,000 for three periods—10% $1,000 for two periods—10% $1,000 for one period—10% $1,000 1.000 = $1,000 $1,000 1.100 = $1,100 $1,000 1.210 = $1,210 $1,000 1.331 = $1,331 $4,641 [Table E–1] Periods 1% 2% 3% 4% 6% 8% 10% 1 1.000 1.000 1.000 1.000 1.000 1.000 1.000 2 2.010 2.020 2.030 2.040 2.060 2.080 2.100 3 3.030 3.060 3.091 3.122 3.184 3.246 3.310 4 4.060 4.122 4.184 4.246 4.375 4.506 4.641 5 5.101 5.204 5.309 5.416 5.637 5.867 6.105 10 10.462 10.950 11.464 12.006 13.181 14.487 15.937 20 22.019 24.297 26.870 29.778 36.786 45.762 57.275 30 34.785 40.588 47.575 56.085 79.058 113.280 164.490 FIGURE E–1 Compounding Process for Annuity TABLE E–2 Compound Sum of an Annuity of $1 (SA IF ) hir39632_app.qxd 5/10/2002 8:16 AM Page 657To maintain the purchasing power of each $30,000 contribution, Dr. Piotrowski needs to accumulate $1,427,250 at the estimated 3 percent rate of inflation. Since her rate of return of 8 percent is 5 percentage points higher than the infla- tion rate, she is adding additional purchasing power to her portfolio. Example—Compound Sum, Annuity Problem: Sonny Outlook invests $2,000 in an IRA at the end of each year for the next 40 years.With an anticipated rate of return of 11 percent, how much will the funds grow to after 40 years? Solution: Compound sum, annuity: S R SA IF (n 40, i 11%) Appendix B $2,000 581.83 $1,163.660 Present Value: Single Amount The present value is the exact opposite of the compound sum. A future value is discounted to the present. For example, earlier we determined the compound sum of $1,000 for four periods at 10 percent was $1,464.We could reverse the process to state that $1,464 received four years from today is worth only $1,000 today if one can earn a 10 percent return on money during the four years.This $1,000 value is called its present value.The relationship is depicted in Figure E–2. The formula for present value is derived from the original formula for the compound sum. As the following two formulas demonstrate, the present value is simply the inverse of the compound sum. 658 Appendix E Time Value of Money and Investment Applications PRESENT VALUE CONCEPT $ $1,000 present value 10% interest $1,464 compound sum 01234 Number of periods FIGURE E–2 Relationship of Present Value and Compound Sum hir39632_app.qxd 5/10/2002 8:16 AM Page 658S P(1 i ) n Compound sum P S 1/(1 i ) n Present value (E–4) The present value can be determined by solving for a mathematical solution to the above formula, or by using Table E–3, the Present Value of $1.When we use Table E–3, the present value interest factor 1/(1 i ) n is found in the table and represented by PV IF .We substitute it into the formula above: P S PV IF (E–5) Let’s demonstrate that the present value of $1,464, based on our assump- tions, is worth $1,000 today: P S PV IF (n 4, i 10%) Table E–3 or Appendix C $1,464 0.683 $1,000 Present value becomes very important in determining the value of invest- ments. Assume you think a certain piece of land will be worth $500,000 10 years from now. If you can earn a 10 percent rate of return on investments of similar risk, what would you be willing to pay for this land? P S PV IF (n 10, i 10%) $500,000 0.386 $193,000 This land’s present value to you today would be $193,000.What would you have 10 years from today if you invested $193,000 at a 10 percent return? For this answer, we go to the compound sum factor from Table E–1: S P S IF (n 10, i 10%) $193,000 2.594 $500,642 The compound sum would be $500,642.The two answers do not equal $500,000 because of the mathematical rounding used to construct tables with three deci- mal points. If we carry out the interest factors to four places, 0.386 becomes 0.3855 and 2.594 becomes 2.5937 and the two answers will be quite similar. Near the end of the compound sum of an annuity section, we showed that Dr. Piotrowski could accumulate $3,398,400 by the time she retired in 30 years. Appendix E Time Value of Money and Investment Applications 659 Periods 1% 2% 3% 4% 6% 8% 10% 1 0.990 0.980 0.971 0.962 0.943 0.926 0.909 2 0.980 0.961 0.943 0.925 0.890 0.857 0.826 3 0.971 0.942 0.915 0.889 0.840 0.794 0.751 4 0.961 0.924 0.888 0.855 0.792 0.735 0.683 5 0.951 0.906 0.863 0.822 0.747 0.681 0.621 10 0.905 0.820 0.744 0.676 0.558 0.463 0.386 20 0.820 0.673 0.554 0.456 0.312 0.215 0.149 30 0.742 0.552 0.412 0.308 0.174 0.099 0.057 TABLE E–3 Present Value of $1 (PV IF ) hir39632_app.qxd 5/10/2002 8:16 AM Page 659What would be the present value of this future sum if we brought it back to the present at the rate of inflation of 3 percent? P S PV IF (n 30, i 3%) $3,398,400 0.412 $1,400,141 The amount she will have accumulated will be worth $1,400,141 in today’s dol- lars. If the rate of inflation averaged 6 percent over this time, the amount would fall to $591,322 ($3,398,400 0.174). Notice how sensitive the present value is to a 3 percentage point change in the inflation rate. Another concern is being able to forecast inflation correctly.These examples are simply meant to heighten your awareness that money has a time value and financial decisions require this to be considered. Example—Present Value, Single Amount Problem: Barbara Samuels received a trust fund at birth that will be paid out to her at age 18. If the fund will accumulate to $400,000 by then and the discount rate is 9 percent, what is the present value of her future accumulation? Solution: Present value, single amount: P S PV IF (n 18, i 9%) Appendix C $400,000 0.212 $84,800 Present Value: Annuity To find the present value of an annuity, we are simply finding the present value of an equal cash flow for several periods instead of one single cash pay- ment.The analysis is the same as taking the present value of several cash flows and adding them. Since we are dealing with an annuity (equal dollar amounts), we can save time by creating tables that add up the interest factors for the pres- ent value of single amounts and make present value annuity factors.We do this in Table E–4, a shortened version of Appendix D. Before using Table E–4, let’s com- pute the present value of $1,000 to be received each year for five years at 6 per- cent. We could use the present value of five single amounts and Table E–3. Period Receipt IF @ 6% 1 $1,000 0.943 $ 943 2 $1,000 0.890 $ 890 3 $1,000 0.840 $ 840 4 $1,000 0.792 $ 792 5 $1,000 0.747 $ 747 4.212 $4,212 Present value Another way to get the same value is to use Table E–4.The present value annuity factor under 6 percent and 5 periods is equal to 4.212, or the same value we got from adding the individual present value factors for a single amount.We can sim- ply calculate the answer as follows: where: A the present value of an annuity R the annuity amount PVA IF the interest factor from Table E–4 660 Appendix E Time Value of Money and Investment Applications hir39632_app.qxd 5/10/2002 8:16 AM Page 660A R PVA IF (n 5, i 6%) (E–6) $1,000 4.212 $4,212 Present value of annuities applies to many financial products such as mortgages, car payments,and retirement benefits.Some financial products such as bonds are a combination of an annuity and a single payment. Interest payments from bonds are annuities, and the principal repayment at maturity is a single payment. Both cash flows determine the present value of a bond. Example—Present Value, Annuity Problem: Ross “The Hoss” Sullivan has just renewed his contract with the Chicago Bears for an annual payment of $3 million per year for the next eight years.The newspapers report the deal is worth $24 million. If the discount rate is 14 percent, what is the true present value of the contract? Solution: Present value, annuity: A R PVA IF (n 8, i 14%) Appendix D $3,000,000 4.639 $13,917,000 Present Value: Uneven Cash Flow Many investments are a series of uneven cash flows. For example, buying com- mon stock generally implies an uneven cash flow from future dividends and the sale price. We hope to buy common stock in companies that are growing and have increasing dividends. Assume you want to purchase Caravan Motors com- mon stock on January 1, 2001.You expect to hold the stock for five years and then sell it at $60 in December 2005. You also expect to receive dividends of $1.60, $2.00, $2.00, $2.50, and $3.00 during those five years. What would you be willing to pay for the common stock if your required re- turn on a stock of this risk is 14 percent. Let’s set up a present value analysis for an uneven cash flow using Appendix C, the present value of a single amount. Since this is not an annuity, each cash flow must be evaluated separately. For sim- plicity, we assume all cash flows come at the end of the year. Also, the cash flow in year 2005 combines the $3.00 dividend and expected $60 sale price. Appendix E Time Value of Money and Investment Applications 661 Periods 1% 2% 3% 4% 6% 8% 10% 1 0.990 0.980 0.971 0.962 0.943 0.926 0.909 2 1.970 1.942 1.913 1.886 1.833 1.783 1.736 3 2.941 2.884 2.829 2.775 2.673 2.577 2.487 4 3.902 3.808 3.717 3.630 3.465 3.312 3.170 5 4.853 4.713 4.580 4.452 4.212 3.993 3.791 8 7.652 7.325 7.020 6.773 6.210 5.747 5.335 10 9.471 8.983 8.530 8.111 7.360 6.710 6.145 20 18.046 16.351 14.877 13.590 11.470 9.818 8.514 30 25.808 22.396 19.600 17.292 13.765 11.258 9.427 TABLE E–4 Present Value of an Annuity of $1 (PVA IF ) hir39632_app.qxd 5/10/2002 8:16 AM Page 661YearCash Flow PV IF 14% Present Value 2001 $ 1.60 0.877 $ 1.40 2002 2.00 0.769 1.54 2003 2.00 0.675 1.35 2004 2.50 0.592 1.48 2005 63.00 0.519 32.70 Present value of Caravan Motors under these assumptions: $38.47 If you were satisfied that your assumptions were reasonably accurate, you would be willing to buy Caravan at any price equal to or less than $38.47.This price will provide you with a 14 percent return if all your forecasts come true. Example—Present Value, Uneven Cash Flow Problem: Joann Zinke buys stock in Collins Publishing Company. She will re- ceive dividends of $2.00, $2.40, $2.88, and $3.12 for the next four years. She as- sumes she can sell the stock for $50 after the last dividend payment (at the end of four years). If the discount rate is 12 percent, what is the present value of the future cash flows? (Round all values to two places to the right of the decimal point.) The present value of future cash flows is assumed to equal the value of the stock. Solution: Present value, uneven cash flow: YearCash Flow PV IF 12% Present Value 1 $ 2.00 0.893 $ 1.79 2 2.40 0.797 1.91 3 2.88 0.712 2.05 4 53.12 0.636 33.78 $39.53 The present value of the cash flows is $39.53. Example—Present Value, Uneven Cash Flow Problem: Sherman Lollar wins a malpractice suit against his accounting profes- sor, and the judgment provides him with $3,000 a year for the next 40 years, plus a single lump-sum payment of $10,000 after 50 years.With a discount rate of 10 percent, what is the present value of his future benefits? Solution: Present value, annuity plus a single amount: Annuity A R PVA IF (n 40, i 10%) Appendix D $3,000 9.779 $29,337 Single amount P S PV IF (n 50, i 10%) Appendix C $10,000 0.009 $90 Total present value $29,337 $90 $29,427 662 Appendix E Time Value of Money and Investment Applications hir39632_app.qxd 5/10/2002 8:16 AM Page 662Using Calculators for Financial Analysis This appendix is designed to help you use either an algebraic calculator (Texas Instruments BA-35 Student Business Analyst) or the Hewlett-Packard 12C Finan- cial Calculator. We realize that most calculators come with comprehensive in- structions, and this appendix is only meant to provide basic instructions for commonly used financial calculations. There are always two things to do before starting your calculations as indi- cated in the first table: clear the calculator, and set the decimal point. If you do not want to lose data stored in memory, do not perform steps 2 and 3 in the first box below. Each step is listed vertically as a number followed by a decimal point. After each step you will find either a number or a calculator function denoted by a box . Entering the number on your calculator is one step and entering the function is another. Notice that the HP 12C is color coded.When two boxes are found one after another, you may have an or a in the first box. An is orange coded and refers to the orange functions above the keys. After typing the function, you will automatically look for an orange-coded key to punch. For example, after in the first Hewlett-Packard box (right-hand panel), you will punch in the orange-color-coded . If the function is not followed by another box, you merely type in and the value indicated. f f REG f f f g f F appendix Texas Instruments BA-35 Hewlett-Packard 12C First clear the calculator. 1. 1. Clears Screen 2. 0 2. 3. Clears memory 3. Clears Memory 1. 1. 2. 2. 4 (# of decimals) STO f 2nd REG STO f CLX ON/C ON/C Set the decimal point. The TI BA-35 has two choices: 2 decimal points or variable decimal points. The screen will indicate Dec 2 or the decimal will be variable. The HP 12C allows you to choose the number of decimal points. If you are uncertain, just provide the indicated input exactly as shown on the right. hir39632_app.qxd 5/10/2002 8:16 AM Page 663The is coded blue and refers to the functions on the bottom of the function keys. After the function key, you will automatically look for blue- coded keys.This first occurs on page 668 of this appendix. Familiarize yourself with the keyboard before you start. In the more compli- cated calculations, keystrokes will be combined into one step. In the first four calculations on this page and on page 665 we simply instruct you on how to get the interest factors for Appendices A, B, C, and D. We have chosen to use examples as our method of instruction. g g 664 Appendix F Using Calculators for Financial Analysis Texas Instruments BA-35 Hewlett-Packard 12C A. Appendix A To Find Interest Factor To Find Interest Factor Compound Sum of $1 1. 1 1. 1 i 9% or 0.09; n 5 years 2. 2. S IF (1 i ) n 3. 0.09 (interest rate) 3. 0.09 (interest rate) Sum Present Value S IF 4. 4. S P S IF 5. 5. 5 (# of periods) 6. 5 (# of periods) 6. answer 1.5386 7. answer 1.538624 B. Appendix B To Find Interest Factor To Find Interest Factor Compound Sum of an Annuity of $1 Repeat steps 1 through 7 in part A of Repeat steps 1 through 6 in part A this section. Continue with step 8. of this section. Continue with step 7. i 9% or 0.09; n 5 years SA IF 8. 7. 1 Sum Receipt SA IF 9. 1 8. S R SA IF 10. 9. 0.09 11. 10. answer 5.9847 12. 0.09 13. answer 5.9847106 (1 i ) n 1 1 y x Check the answer against the number in Appendix A. Numbers in the appendix are rounded. Try different rates and years. y x enter Check your answer with Appendix B. Repeat example using different numbers and check your results with the number in Appendix B. Numbers in appendix are rounded. hir39632_app.qxd 5/10/2002 8:16 AM Page 664On the following pages, you can determine bond valuation, yield to maturity, net present value of an annuity,net present value of an uneven cash flow,internal rate of return for an annuity, and internal rate of return for an uneven cash flow. Appendix F Using Calculators for Financial Analysis 665 Texas Instruments BA-35 Hewlett-Packard 12C C. Appendix C Present Value of $1 To Find Interest Factor To Find Interest Factor Repeat steps 1 through 7 in part A of Repeat steps 1 through 6 in part A i 9% or 0.09; n 5 years this section. Continue with step 8. of this section. Continue with step 7. PV IF (1 i ) n 8. answer 0.6499314 7. answer 0.6499 Present Value Sum PV IF P S PV IF Check the answer against the number in Appendix C. Numbers in the appendix are rounded. D. Appendix D To Find Interest Factor To Find Interest Factor Present Value of an Annuity of $1 Repeat steps 1 through 8 in parts A Repeat steps 1 through 7 in parts A i 9% or 0.09; n 5 years and C. Continue with step 9. and C. Continue with step 8. PV IF 9. 8. 1 Present Value Annuity PVA IF 10. 1 9. 11. 10. A R PVA IF 12. 11. 0.09 13. 12. answer 3.8897 14. 0.09 15. answer 3.8896513 / CH5 1 [(1/(1 i ) n ] i 1/ x 1/ x Check your answer with Appendix D. Repeat example using different numbers and check your results with the number in Appendix D. Numbers in appendix are rounded. hir39632_app.qxd 5/10/2002 8:16 AM Page 665Solve for V Price of the bond, given: C t $80 annual coupon payments or 8 percent coupon ($40 semiannually) P n $1,000 principal (par value) n 10 years to maturity (20 periods semiannually) i 9.0 percent rate in the market (4.5 percent semiannually) You may choose to refer to Chapter 12 for a complete discussion of bond valuation. 666 Appendix F Using Calculators for Financial Analysis BOND VALUATION USING BOTH THE TI BA-35 AND THE HP 12C Texas Instruments BA-35 Hewlett-Packard 12C Bond Valuation Set Finance Mode Clear Memory Set decimal to 2 places Set decimal to 3 places Decimal 3 1. 9.0 (yield to maturity) 1. 40 (semiannual coupon) 2. 2. 3. 8.0 (coupon in percent) 3. 4.5 (yield to maturity) 4. semiannual basis 4. 5. 1.092002 (today’s date month-day-year)* 5. 1000 principal 6. 6. 7. 1.092012 (maturity date month-day-year)* 7. 20 (semiannual periods to maturity) 8. 8. 9. Answer 93.496 9. 10. answer 934.96 Answer is given in dollars, rather than % of par value. PV CPT Price N f FV enter %i PMT PMT i STO 2nd f REG f FIN 2nd All steps begin with number 1. Numbers following each step are keystrokes followed by a box . Each box represents a keystroke and indicates which calculator function is performed. The Texas Instruments calculator requires that data be adjusted for semiannual compounding; otherwise it assumes annual compounding. The Hewlett-Packard 12C internally assumes that semiannual compounding is used and requires annual data to be entered. The HP 12C is more detailed in that it requires the actual day, month, and year. If you want an answer for a problem that requires a given number of years (e.g., 10 years), simply start on a date of your choice and end on the same date 10 years later, as in the example. Answer is given as % of par value and equals $934.96. If Error message occurs, clear memory and start over. *See instructions in the third paragraph of the first column. hir39632_app.qxd 5/10/2002 8:16 AM Page 666Solve for Y Yield to maturity, given: V $895.50 price of bond C t $80 annual coupon payments or 8 percent coupon ($40 semiannually) P n $1,000 principal (par value) n 10 years to maturity (20 periods semiannually) You may choose to refer to Chapter 12 for a complete discussion of yield to maturity. Appendix F Using Calculators for Financial Analysis 667 Texas Instruments BA-35 Hewlett-Packard 12C Yield to Maturity Set Finance Mode Clear Memory Set decimal to 2 places Set decimal 2 Decimal 1. 89.55 (bond price as a percentof par) 2. 1. 20 (semiannual periods) 3. 8.0 (coupon in %) 2. 4. 3. 1000 (par value) 5. 1.092002 (today’s date)* 4. 6. 5. 40 (semiannual coupon) 7. 1.092012 (maturity date)* 6. 8. 7. 895.50 (bond price) 9. answer 9.65% 8. 9. 10. answer 4.83% 11. and start over. 12. 2 13. answer 9.65% (annual rate) REG f %i CPT PV YTM f PMT enter FV PMT N PV STO 2nd f REG f FIN 2nd YIELD TO MATURITY ON BOTH THE TI BA-35 AND HP 12C In case you receive an Error message, you have probably made a keystroke error. Clear the memory *See instructions in the third paragraph of the first column. All steps are numbered. All numbers following each step are keystrokes followed by a box . Each box represents a keystroke and indicates which calculator function is performed. The Texas Instruments BA-35 does not internally compute to a semiannual rate, so that data must be adjusted to reflect semiannual payments and periods. The answer received in step 10 is a semiannual rate, which must be multiplied by 2 to reflect an annual yield. The Hewlett-Packard 12C internally assumes that semiannual payments are made and, therefore, the answer in step 9 is the annual yield to maturity based on semiannual coupons. If you want an answer on the HP for a given number of years (e.g., 10 years), simply start on a date of your choice and end on the same date 10 years later, as in the example. hir39632_app.qxd 5/10/2002 8:16 AM Page 667Solve for A Present value of annuity, given: n 10 years (number of years cash flow will continue) PMT $5,000 per year (amount of the annuity) i 12 percent (cost of capital K a ) Cost $20,000 668 Appendix F Using Calculators for Financial Analysis Texas Instruments BA-35 Hewlett-Packard 12C Net Present Value of an Annuity Set Finance Mode Set decimal to 2 places Set decimal to 2 places 2 Decimal clears memory 1. 20000 (cash outflow) 1. 10 (years of cash flow) 2. changes sign 2. 3. 3. 5000 (annual payments) 4. 4. 5. 5000 (annual payments) 5. 12 (cost of capital) 6. 6. 7. 10 (years) 7. 8. 12 (cost of capital) 8. 9. 9. answer $8,251.12 10. 20,000 If an Error message appears, start over by clearing the memory with 11. answer $8,251.12 REG f NPV f PV i CPT N j g %i Cfj g PMT CFo g N CHS STO 2nd REG f f FIN 2nd NET PRESENT VALUE OF AN ANNUITY ON BOTH THE TI BA-35 AND THE HP 12C All steps are numbered and some steps include keystrokes. All numbers following each step are keystrokes followed by a box . Each box represents a keystroke and indicates which calculator function is performed on that number. The calculation for the present value of an annuity on the TI BA-35 requires that the project cost be subtracted from the present value of the cash inflows. The HP 12C could solve the problem exactly with the same keystrokes as the TI. However, since the HP uses a similar method to solve uneven cash flows, we elected to use the method that requires more keystrokes but which includes a negative cash outflow for the cost of the capital budgeting project. To conserve space, several keystrokes have been put into one step. hir39632_app.qxd 5/10/2002 8:16 AM Page 668Solve for NPV Net present value, given: n 5 years (number of years cash flow will continue) PMT $5,000 (yr. 1); 6,000 (yr. 2); 7,000 (yr. 3); 8,000 (yr. 4); 9,000 (yr. 5) i 12 percent (cost of capital K a ) Cost $25,000 Appendix F Using Calculators for Financial Analysis 669 NET PRESENT VALUE OF AN UNEVEN CASH FLOW ON BOTH THE TI BA-35 AND HP 12C Texas Instruments BA-35 Hewlett-Packard 12C Net Present Value of an Uneven Clear memory 0 Set decimal to 2 places Cash Flow Set decimal to 2 places 2 Decimal clears memory 1. 25000 (cash outflow) Set finance mode 2. changes sign 3. 1. 12 4. 5000 2. 5000 5. 6000 3. 1 6. 7000 4. 6000 7. 8000 5. 2 8. 9000 6. 7000 9. 12 7. 3 10. 8. 8000 answer $579.10 Negative Net Present Value 9. 4 10. 9000 11. 5 12. (answer 24420.90 and start over with step 1. 13. 14. 25000 (cash outflow) 15. answer $579.10 Negative Net Present Value RCL REG f SUM PV CPT N FV SUM PV CPT N FV NPV f SUM PV CPT N i FV CFj g SUM PV CPT N CFj g FV CFj g SUM PV CPT N CFj g FV CFj g %i CFo g FIN 2nd CHS STO 2nd REG f f STO ON/C If you receive an Error message, you have probably made a keystroke error. Clear memory with All steps are numbered and some steps include several keystrokes. All numbers following each step are keystrokes followed by a box . Each box represents a keystroke and indicates which calculator function is performed on that number. Because we are dealing with uneven cash flows, each number must be entered. The TI BA-35 requires that you make use of the memory. In step 2, you enter the future cash inflow in year 1, and in step 3, you determine its present value, which is stored in memory. After the first 1-year calculation, following year present values are calculated in the same way and added to the stored value using the key. Finally, the recall key is used to recall the present value of the total cash inflows. The HP 12C requires each cash flow to be entered in order. The key represents the cash flow in time period 0. The key automatically counts the year of the cash flow in the order entered and so no years need to be entered. Finally, the cost of capital of 12% is entered and the key and key are used to complete the problem. NPV f CFj CFo RCL SUM hir39632_app.qxd 5/10/2002 8:16 AM Page 669Solve for IRR Internal rate of return, given: n 10 years (number of years cash flow will continue) PMT $10,000 per year (amount of the annuity) Cost $50,000 (this is the present value of the annuity) 670 Appendix F Using Calculators for Financial Analysis Texas Instruments BA-35 Hewlett-Packard 12C Internal Rate of Return of Clear memory 0 Set decimal to 2 places an Annuity Set Finance Mode 2 Decimal clears memory 1. 5000 (cash outflow) 1. 10 (years of cash flow) 2. changes sign 2. 3. 3. 10000 (annual payments) 4. 4. 5. 10000 (annual payments) 5. 50000 (present value) 6. 6. 7. 10 (years) 7. 8. 8. answer is 15.10% answer is 15.10% If an Error message appears, start over by clearing the memory with REG f %i IRR f CPT Nj g PV Cfj g PMT CFo g N CHS STO 2nd REG f f FIN 2nd STO ON/C INTERNAL RATE OF RETURN FOR AN ANNUITY ON BOTH THE TI BA-35 AND HP 12C At an internal rate of return of 15.10%, the present value of the $50,000 outflow is equal to the present value of $10,000 cash inflows over the next10years. All steps are numbered and some steps include several keystrokes. All numbers following each step are keystrokes followed by a box . Each box represents a keystroke and indicates which calculator function is performed on that number. The calculation for the internal rate of return on an annuity using the TI BA-35 requires relatively few keystrokes. The HP 12C requires more keystrokes than the TI BA-35, because it needs to use the function keys and to enter data into the internal programs. The HP method requires that the cash outflow be expressed as a negative, while the TI BA-35 uses a positive number for the cash outflow. To conserve space, several keystrokes have been put into one step. g f hir39632_app.qxd 5/10/2002 8:16 AM Page 670Solve for IRR Internal rate of return (return which causes present value of outflows to equal present value of the inflows), given: n 5 years (number of years cash flow will continue) PMT $5,000 (yr. 1); 6,000 (yr. 2); 7,000 (yr. 3); 8,000 (yr. 4); 9,000 (yr. 5) Cost $25,000 Appendix F Using Calculators for Financial Analysis 671 INTERNAL RATE OF RETURN WITH AN UNEVEN CASH FLOW ON BOTH THE TI BA-35 AND HP 12C Texas Instruments BA-35 Hewlett-Packard 12C Internal Rate of an Uneven Clear memory 0 Set decimal to 2 places Cash Flow Set decimal to 2 places 2 Decimal clears memory 1. 25000 (cash outflow) Set finance mode 2. changes sign 3. 1. 12 (your IRR est.) 4. 5000 2. 5000 5. 6000 3. 1 6. 7000 4. 6000 7. 8000 5. 2 8. 9000 6. 7000 9. 7. 3 answer 11.15% 8. 8000 9. 4 10. 9000 11. 5 and start over with step 1. 12. (answer 24,420.90) 13. 14. 25000 (cash outflow) 15. answer $579.10 Negative NPV Start over with a lower discount rate (try 11.15). Answer is 24999.75. With a cash outflow of $25,000, the IRR would be 11.15% RCL SUM PV CPT N REG f FV SUM PV CPT N FV SUM PV CPT N IRR f FV CFj g SUM PV CPT N CFj g FV CFj g STO PV CPT N CFj g FV CFj g %i CFo g FIN 2nd CHS STO 2nd REG f f STO ON/C If you receive an Error message, you have probably made a keystroke error. Clear memory with All steps are numbered and some steps include several keystrokes. All numbers following each step are keystrokes followed by a box . Each box represents a keystroke and indicates which calculator function is performed on that number. Because we are dealing with uneven cash flows, the mathematics of solving this problem with the TI BA-35 is notpossible. Amore advanced algebraic calculator would be required. However, for the student willing to use trial and error, the student can use the NPV method and try different discount rates until the NPV equals zero. Check Chapter 12 on methods for approximating the IRR. This will provide a start. The HP 12C requires each cash flow to be entered in order. The key represents the cash flow in time period 0. The key automatically counts the year of the cash flow in the order entered and so no years need to be entered. To find the internal rate of return, use the keys and complete the problem. IRR f CFj CFo hir39632_app.qxd 5/10/2002 8:16 AM Page 671