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Present Value Tables

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Brealey−Myers−Allen: Principles of Corporate Finance, Eighth Edition

Back Matter

Appendix A: Present Value Tables

© The McGraw−Hill Companies, 2005

APPENDIX A

PRESENT VALUE TABLES
A P P E N D I X TA B L E 1
Discount factors: Present value of $1 to be received after t years 1/(1 r)t.
Interest Rate per Year Number of Years 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 1% .990 .980 .971 .961 .951 .942 .933 .923 .914 .905 .896 .887 .879 .870 .861 .853 .844 .836 .828 .820 2% .980 .961 .942 .924 .906 .888 .871 .853 .837 .820 .804 .788 .773 .758 .743 .728 .714 .700 .686 .673 3% .971 .943 .915 .888 .863 .837 .813 .789 .766 .744 .722 .701 .681 .661 .642 .623 .605 .587 .570 .554 4% .962 .925 .889 .855 .822 .790 .760 .731 .703 .676 .650 .625 .601 .577 .555 .534 .513 .494 .475 .456 5% .952 .907 .864 .823 .784 .746 .711 .677 .645 .614 .585 .557 .530 .505 .481 .458 .436 .416 .396 .377 6% .943 .890 .840 .792 .747 .705 .665 .627 .592 .558 .527 .497 .469 .442 .417 .394 .371 .350 .331 .312 7% .935 .873 .816 .763 .713 .666 .623 .582 .544 .508 .475 .444 .415 .388 .362 .339 .317 .296 .277 .258 8% .926 .857 .794 .735 .681 .630 .583 .540 .500 .463 .429 .397 .368 .340 .315 .292 .270 .250 .232 .215 9% .917 .842 .772 .708 .650 .596 .547 .502 .460 .422 .388 .356 .326 .299 .275 .252 .231 .212 .194 .178 10% .909 .826 .751 .683 .621 .564 .513 .467 .424 .386 .350 .319 .290 .263 .239 .218 .198 .180 .164 .149 11% .901 .812 .731 .659 .593 .535 .482 .434 .391 .352 .317 .286 .258 .232 .209 .188 .170 .153 .138 .124 12% .893 .797 .712 .636 .567 .507 .452 .404 .361 .322 .287 .257 .229 .205 .183 .163 .146 .130 .116 .104 13% .885 .783 .693 .613 .543 .480 .425 .376 .333 .295 .261 .231 .204 .181 .160 .141 .125 .111 .098 .087 14% .877 .769 .675 .592 .519 .456 .400 .351 .308 .270 .237 .208 .182 .160 .140 .123 .108 .095 .083 .073 15% .870 .756 .658 .572 .497 .432 .376 .327 .284 .247 .215 .187 .163 .141 .123 .107 .093 .081 .070 .061

Interest Rate per Year Number of Years 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 16% .862 .743 .641 .552 .476 .410 .354 .305 .263 .227 .195 .168 .145 .125 .108 .093 .080 .069 .060 .051 17% .855 .731 .624 .534 .456 .390 .333 .285 .243 .208 .178 .152 .130 .111 .095 .081 .069 .059 .051 .043 18% .847 .718 .609 .516 .437 .370 .314 .266 .225 .191 .162 .137 .116 .099 .084 .071 .060 .051 .043 .037 19% .840 .706 .593 .499 .419 .352 .296 .249 .209 .176 .148 .124 .104 .088 .074 .062 .052 .044 .037 .031 20% .833 .694 .579 .482 .402 .335 .279 .233 .194 .162 .135 .112 .093 .078 .065 .054 .045 .038 .031 .026 21% .826 .683 .564 .467 .386 .319 .263 .218 .180 .149 .123 .102 .084 .069 .057 .047 .039 .032 .027 .022 22% .820 .672 .551 .451 .370 .303 .249 .204 .167 .137 .112 .092 .075 .062 .051 .042 .034 .028 .023 .019 23% .813 .661 .537 .437 .355 .289 .235 .191 .155 .126 .103 .083 .068 .055 .045 .036 .030 .024 .020 .016 24% .806 .650 .524 .423 .341 .275 .222 .179 .144 .116 .094 .076 .061 .049 .040 .032 .026 .021 .017 .014 25% .800 .640 .512 .410 .328 .262 .210 .168 .134 .107 .086 .069 .055 .044 .035 .028 .023 .018 .014 .012 26% .794 .630 .500 .397 .315 .250 .198 .157 .125 .099 .079 .062 .050 .039 .031 .025 .020 .016 .012 .010 27% .787 .620 .488 .384 .303 .238 .188 .148 .116 .092 .072 .057 .045 .035 .028 .022 .017 .014 .011 .008 28% .781 .610 .477 .373 .291 .227 .178 .139 .108 .085 .066 .052 .040 .032 .025 .019 .015 .012 .009 .007 29% .775 .601 .466 .361 .280 .217 .168 .130 .101 .078 .061 .047 .037 .028 .022 .017 .013 .010 .008 .006 30% .769 .592 .455 .350 .269 .207 .159 .123 .094 .073 .056 .043 .033 .025 .020 .015 .012 .009 .007 .005

Note: For example, if the interest rate is 10 percent per year, the present value of $1 received at year 5 is $.621.

Brealey−Myers−Allen: Principles of Corporate Finance, Eighth Edition

Back Matter

Appendix A: Present Value Tables

© The McGraw−Hill Companies, 2005

APPENDIX A Present Value Tables A P P E N D I X TA B L E 2
Future value of $1 after t years (1 r)t.
Interest Rate per Year Number of Years 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 1% 1.010 1.020 1.030 1.041 1.051 1.062 1.072 1.083 1.094 1.105 1.116 1.127 1.138 1.149 1.161 1.173 1.184 1.196 1.208 1.220 2% 1.020 1.040 1.061 1.082 1.104 1.126 1.149 1.172 1.195 1.219 1.243 1.268 1.294 1.319 1.346 1.373 1.400 1.428 1.457 1.486 3% 1.030 1.061 1.093 1.126 1.159 1.194 1.230 1.267 1.305 1.344 1.384 1.426 1.469 1.513 1.558 1.605 1.653 1.702 1.754 1.806 4% 1.040 1.082 1.125 1.170 1.217 1.265 1.316 1.369 1.423 1.480 1.539 1.601 1.665 1.732 1.801 1.873 1.948 2.026 2.107 2.191 5% 1.050 1.102 1.158 1.216 1.276 1.340 1.407 1.477 1.551 1.629 1.710 1.796 1.886 1.980 2.079 2.183 2.292 2.407 2.527 2.653 6% 1.060 1.124 1.191 1.262 1.338 1.419 1.504 1.594 1.689 1.791 1.898 2.012 2.133 2.261 2.397 2.540 2.693 2.854 3.026 3.207 7% 1.070 1.145 1.225 1.311 1.403 1.501 1.606 1.718 1.838 1.967 2.105 2.252 2.410 2.579 2.759 2.952 3.159 3.380 3.617 3.870 8% 1.080 1.166 1.260 1.360 1.469 1.587 1.714 1.851 1.999 2.159 2.332 2.518 2.720 2.937 3.172 3.426 3.700 3.996 4.316 4.661 9% 1.090 1.188 1.295 1.412 1.539 1.677 1.828 1.993 2.172 2.367 2.580 2.813 3.066 3.342 3.642 3.970 4.328 4.717 5.142 5.604 10% 1.100 1.210 1.331 1.464 1.611 1.772 1.949 2.144 2.358 2.594 2.853 3.138 3.452 3.797 4.177 4.595 5.054 5.560 6.116 6.727 11% 1.110 1.232 1.368 1.518 1.685 1.870 2.076 2.305 2.558 2.839 3.152 3.498 3.883 4.310 4.785 5.311 5.895 6.544 7.263 8.062 12% 1.120 1.254 1.405 1.574 1.762 1.974 2.211 2.476 2.773 3.106 3.479 3.896 4.363 4.887 5.474 6.130 6.866 7.690 8.613 9.646 13% 1.130 1.277 1.443 1.630 1.842 2.082 2.353 2.658 3.004 3.395 3.836 4.335 4.898 5.535 6.254 7.067 7.986 9.024 10.20 11.52 14% 1.140 1.300 1.482 1.689 1.925 2.195 2.502 2.853 3.252 3.707 4.226 4.818 5.492 6.261 7.138 8.137 9.276 10.58 12.06 13.74

969

15% 1.150 1.323 1.521 1.749 2.011 2.313 2.660 3.059 3.518 4.046 4.652 5.350 6.153 7.076 8.137 9.358 10.76 12.38 14.23 16.37

Interest Rate per Year Number of Years 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 16% 1.160 1.346 1.561 1.811 2.100 2.436 2.826 3.278 3.803 4.411 17% 1.170 1.369 1.602 1.874 2.192 2.565 3.001 3.511 4.108 4.807 18% 1.180 1.392 1.643 1.939 2.288 2.700 3.185 3.759 4.435 5.234 19% 1.190 1.416 1.685 2.005 2.386 2.840 3.379 4.021 4.785 5.695 20% 1.200 1.440 1.728 2.074 2.488 2.986 3.583 4.300 5.160 6.192 21% 1.210 1.464 1.772 2.144 2.594 3.138 3.797 4.595 5.560 6.728 22% 1.220 1.488 1.816 2.215 2.703 3.297 4.023 4.908 5.987 7.305 8.912 10.87 13.26 16.18 19.74 24.09 29.38 35.85 43.74 53.36 23% 1.230 1.513 1.861 2.289 2.815 3.463 4.259 5.239 6.444 7.926 9.749 11.99 14.75 18.14 22.31 27.45 33.76 41.52 51.07 62.82 24% 1.240 1.538 1.907 2.364 2.932 3.635 4.508 5.590 6.931 8.594 10.66 13.21 16.39 20.32 25.20 31.24 38.74 48.04 59.57 73.86 25% 1.250 1.563 1.953 2.441 3.052 3.815 4.768 5.960 7.451 9.313 11.64 14.55 18.19 22.74 28.42 35.53 44.41 55.51 69.39 86.74 26% 1.260 1.588 2.000 2.520 3.176 4.002 5.042 6.353 8.005 10.09 12.71 16.01 20.18 25.42 32.03 40.36 50.85 64.07 80.73 101.7 27% 1.270 1.613 2.048 2.601 3.304 4.196 5.329 6.768 8.595 10.92 13.86 17.61 22.36 28.40 36.06 45.80 58.17 73.87 93.81 119.1 28% 1.280 1.638 2.097 2.684 3.436 4.398 5.629 7.206 9.223 11.81 15.11 19.34 24.76 31.69 40.56 51.92 66.46 85.07 108.9 139.4 29% 1.290 1.664 2.147 2.769 3.572 4.608 5.945 7.669 9.893 12.76 16.46 21.24 27.39 35.34 45.59 58.81 75.86 97.86 126.2 162.9 30% 1.300 1.690 2.197 2.856 3.713 4.827 6.275 8.157 10.60 13.79 17.92 23.30 30.29 39.37 51.19 66.54 86.50 112.5 146.2 190.0

5.117 5.624 6.176 6.777 7.430 8.140 5.936 6.580 7.288 8.064 8.916 9.850 6.886 7.699 8.599 9.596 10.70 11.92 7.988 9.007 10.15 11.42 12.84 14.42 9.266 10.54 11.97 13.59 15.41 17.45 10.75 12.47 14.46 16.78 19.46 12.33 14.43 16.88 19.75 23.11 14.13 16.67 19.67 23.21 27.39 16.17 19.24 22.90 27.25 32.43 18.49 22.19 26.62 31.95 38.34 21.11 25.55 30.91 37.40 45.26

Note: For example, if the interest rate is 10 percent per year, the investment of $1 today will be worth $1.611 at year 5.

Brealey−Myers−Allen: Principles of Corporate Finance, Eighth Edition

Back Matter

Appendix A: Present Value Tables

© The McGraw−Hill Companies, 2005

970

APPENDIX A Present Value Tables

A P P E N D I X TA B L E 3
Annuity table: Present value of $1 per year for each of t years 1/r 1/[r (1 r)t].

Interest Rate per Year Number of Years 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 1% .990 1.970 2.941 3.902 4.853 5.795 6.728 7.652 8.566 9.471 10.37 11.26 12.13 13.00 13.87 14.72 15.56 16.40 17.23 18.05 2% .980 1.942 2.884 3.808 4.713 5.601 6.472 7.325 8.162 8.983 3% .971 1.913 2.829 3.717 4.580 5.417 6.230 7.020 7.786 8.530 4% .962 1.886 2.775 3.630 4.452 5.242 6.002 6.733 7.435 8.111 5% .952 1.859 2.723 3.546 4.329 5.076 5.786 6.463 7.108 7.722 6% .943 1.833 2.673 3.465 4.212 4.917 5.582 6.210 6.802 7.360 7.887 8.384 8.853 9.295 9.712 10.11 10.48 10.83 11.16 11.47 7% .935 1.808 2.624 3.387 4.100 4.767 5.389 5.971 6.515 7.024 7.499 7.943 8.358 8.745 9.108 9.447 9.763 10.06 10.34 10.59 8% .926 1.783 2.577 3.312 3.993 4.623 5.206 5.747 6.247 6.710 7.139 7.536 7.904 8.244 8.559 8.851 9.122 9.372 9.604 9.818 9% .917 1.759 2.531 3.240 3.890 4.486 5.033 5.535 5.995 6.418 6.805 7.161 7.487 7.786 8.061 8.313 8.544 8.756 8.950 9.129 10% .909 1.736 2.487 3.170 3.791 4.355 4.868 5.335 5.759 6.145 6.495 6.814 7.103 7.367 7.606 7.824 8.022 8.201 8.365 8.514 11% .901 1.713 2.444 3.102 3.696 4.231 4.712 5.146 5.537 5.889 6.207 6.492 6.750 6.982 7.191 7.379 7.549 7.702 7.839 7.963 12% .893 1.690 2.402 3.037 3.605 4.111 4.564 4.968 5.328 5.650 5.938 6.194 6.424 6.628 6.811 6.974 7.120 7.250 7.366 7.469 13% .885 1.668 2.361 2.974 3.517 3.998 4.423 4.799 5.132 5.426 5.687 5.918 6.122 6.302 6.462 6.604 6.729 6.840 6.938 7.025 14% .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 15% .870 1.626 2.283 2.855 3.352 3.784 4.160 4.487 4.772 5.019 5.234 5.421 5.583 5.724 5.847 5.954 6.047 6.128 6.198 6.259

9.787 9.253 8.760 8.306 10.58 9.954 9.385 8.863 11.35 10.63 9.986 9.394 12.11 11.30 10.56 9.899 12.85 11.94 11.12 10.38 13.58 14.29 14.99 15.68 16.35 12.56 13.17 13.75 14.32 14.88 11.65 12.17 12.66 13.13 13.59 10.84 11.27 11.69 12.09 12.46

Interest Rate per Year Number of Years 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 16% .862 1.605 2.246 2.798 3.274 3.685 4.039 4.344 4.607 4.833 5.029 5.197 5.342 5.468 5.575 5.668 5.749 5.818 5.877 5.929 17% .855 1.585 2.210 2.743 3.199 3.589 3.922 4.207 4.451 4.659 4.836 4.988 5.118 5.229 5.324 5.405 5.475 5.534 5.584 5.628 18% .847 1.566 2.174 2.690 3.127 3.498 3.812 4.078 4.303 4.494 4.656 4.793 4.910 5.008 5.092 5.162 5.222 5.273 5.316 5.353 19% .840 1.547 2.140 2.639 3.058 3.410 3.706 3.954 4.163 4.339 4.486 4.611 4.715 4.802 4.876 4.938 4.990 5.033 5.070 5.101 20% .833 1.528 2.106 2.589 2.991 3.326 3.605 3.837 4.031 4.192 4.327 4.439 4.533 4.611 4.675 4.730 4.775 4.812 4.843 4.870 21% .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 22% .820 1.492 2.042 2.494 2.864 3.167 3.416 3.619 3.786 3.923 4.035 4.127 4.203 4.265 4.315 4.357 4.391 4.419 4.442 4.460 23% .813 1.474 2.011 2.448 2.803 3.092 3.327 3.518 3.673 3.799 3.902 3.985 4.053 4.108 4.153 4.189 4.219 4.243 4.263 4.279 24% .806 1.457 1.981 2.404 2.745 3.020 3.242 3.421 3.566 3.682 3.776 3.851 3.912 3.962 4.001 4.033 4.059 4.080 4.097 4.110 25% .800 1.440 1.952 2.362 2.689 2.951 3.161 3.329 3.463 3.571 3.656 3.725 3.780 3.824 3.859 3.887 3.910 3.928 3.942 3.954 26% .794 1.424 1.923 2.320 2.635 2.885 3.083 3.241 3.366 3.465 3.543 3.606 3.656 3.695 3.726 3.751 3.771 3.786 3.799 3.808 27% .787 1.407 1.896 2.280 2.583 2.821 3.009 3.156 3.273 3.364 3.437 3.493 3.538 3.573 3.601 3.623 3.640 3.654 3.664 3.673 28% .781 1.392 1.868 2.241 2.532 2.759 2.937 3.076 3.184 3.269 3.335 3.387 3.427 3.459 3.483 3.503 3.518 3.529 3.539 3.546 29% .775 1.376 1.842 2.203 2.483 2.700 2.868 2.999 3.100 3.178 3.239 3.286 3.322 3.351 3.373 3.390 3.403 3.413 3.421 3.427 30% .769 1.361 1.816 2.166 2.436 2.643 2.802 2.925 3.019 3.092 3.147 3.190 3.223 3.249 3.268 3.283 3.295 3.304 3.311 3.316

Note: For example, if the interest rate is 10 percent per year, the investment of $1 received in each of the next 5 years is $3.791.

Brealey−Myers−Allen: Principles of Corporate Finance, Eighth Edition

Back Matter

Appendix A: Present Value Tables

© The McGraw−Hill Companies, 2005

APPENDIX A Present Value Tables A P P E N D I X TA B L E 4
Values of ert. Future value of $1 invested at a continuously compounded rate r for t years. rt .00 .10 .20 .30 .40 .50 .60 .70 .80 .90 1.00 1.10 1.20 1.30 1.40 1.50 1.60 1.70 1.80 1.90 2.00 2.10 2.20 2.30 2.40 2.50 2.60 2.70 2.80 2.90 3.00 3.10 3.20 3.30 3.40 3.50 3.60 3.70 3.80 3.90 .00 1.000 1.105 1.221 1.350 1.492 1.649 1.822 2.014 2.226 2.460 2.718 3.004 3.320 3.669 4.055 4.482 4.953 5.474 6.050 6.686 7.389 8.166 9.025 9.974 11.02 12.18 13.46 14.88 16.44 18.17 20.09 22.20 24.53 27.11 29.96 33.12 36.60 40.45 44.70 49.40 .01 1.010 1.116 1.234 1.363 1.507 1.665 1.840 2.034 2.248 2.484 2.746 3.034 3.353 3.706 4.096 4.527 5.003 5.529 6.110 6.753 7.463 8.248 9.116 10.07 11.13 12.30 13.60 15.03 16.61 18.36 20.29 22.42 24.78 27.39 30.27 33.45 36.97 40.85 45.15 49.90 .02 1.020 1.127 1.246 1.377 1.522 1.682 1.859 2.054 2.271 2.509 2.773 3.065 3.387 3.743 4.137 4.572 5.053 5.585 6.172 6.821 7.538 8.331 9.207 10.18 11.25 12.43 13.74 15.18 16.78 18.54 20.49 22.65 25.03 27.66 30.57 33.78 37.34 41.26 45.60 50.40 .03 1.030 1.139 1.259 1.391 1.537 1.699 1.878 2.075 2.293 2.535 2.801 3.096 3.421 3.781 4.179 4.618 5.104 5.641 6.234 6.890 7.614 8.415 9.300 10.28 11.36 12.55 13.87 15.33 16.95 18.73 20.70 22.87 25.28 27.94 30.88 34.12 37.71 41.68 46.06 50.91 .04 1.041 1.150 1.271 1.405 1.553 1.716 1.896 2.096 2.316 2.560 2.829 3.127 3.456 3.819 4.221 4.665 5.155 5.697 6.297 6.959 7.691 8.499 9.393 10.38 11.47 12.68 14.01 15.49 17.12 18.92 20.91 23.10 25.53 28.22 31.19 34.47 38.09 42.10 46.53 51.42 .05 1.051 1.162 1.284 1.419 1.568 1.733 1.916 2.117 2.340 2.586 2.858 3.158 3.490 3.857 4.263 4.711 5.207 5.755 6.360 7.029 7.768 8.585 9.488 10.49 11.59 12.81 14.15 15.64 17.29 19.11 21.12 23.34 25.79 28.50 31.50 34.81 38.47 42.52 46.99 51.94 .06 1.062 1.174 1.297 1.433 1.584 1.751 1.935 2.138 2.363 2.612 2.886 3.190 3.525 3.896 4.306 4.759 5.259 5.812 6.424 7.099 7.846 8.671 9.583 10.59 11.70 12.94 14.30 15.80 17.46 19.30 21.33 23.57 26.05 28.79 31.82 35.16 38.86 42.95 47.47 52.46 .07 1.073 1.185 1.310 1.448 1.600 1.768 1.954 2.160 2.387 2.638 2.915 3.222 3.561 3.935 4.349 4.807 5.312 5.871 6.488 7.171 7.925 8.758 9.679 10.70 11.82 13.07 14.44 15.96 17.64 19.49 21.54 23.81 26.31 29.08 32.14 35.52 39.25 43.38 47.94 52.98 .08 1.083 1.197 1.323 1.462 1.616 1.786 1.974 2.181 2.411 2.664 2.945 3.254 3.597 3.975 4.393 4.855 5.366 5.930 6.553 7.243 8.004 8.846 9.777 10.80 11.94 13.20 14.59 16.12 17.81 19.69 21.76 24.05 26.58 29.37 32.46 35.87 39.65 43.82 48.42 53.52

971

.09 1.094 1.209 1.336 1.477 1.632 1.804 1.994 2.203 2.435 2.691 2.974 3.287 3.633 4.015 4.437 4.904 5.419 5.989 6.619 7.316 8.085 8.935 9.875 10.91 12.06 13.33 14.73 16.28 17.99 19.89 21.98 24.29 26.84 29.67 32.79 36.23 40.04 44.26 48.91 54.05

Note: For example, if the continuously compounded interest rate is 10 percent per year, the investment of $1 today will be worth $1.105 at year 1 and $1.221 at year 2.

Brealey−Myers−Allen: Principles of Corporate Finance, Eighth Edition

Back Matter

Appendix A: Present Value Tables

© The McGraw−Hill Companies, 2005

972

APPENDIX A Present Value Tables

A P P E N D I X TA B L E 5
Present value of $1 per year received in a continuous stream for each of t years (discounted at an annually compounded rate r) {1 1/(1 r)t}/{ln(1 r)}.
Interest Rate per Year Number of Years 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 1% .995 1.980 2.956 3.922 4.878 5.825 6.762 7.690 8.609 9.519 10.42 11.31 12.19 13.07 13.93 14.79 15.64 16.48 17.31 18.14 2% .990 1.961 2.913 3.846 4.760 5.657 6.536 7.398 8.243 9.072 9.884 10.68 11.46 12.23 12.98 13.71 14.43 15.14 15.83 16.51 3% .985 1.942 2.871 3.773 4.648 5.498 6.323 7.124 7.902 8.657 4% .981 1.924 2.830 3.702 4.540 5.346 6.121 6.867 7.583 8.272 5% .976 1.906 2.791 3.634 4.437 5.202 5.930 6.623 7.284 7.913 6% .971 1.888 2.752 3.568 4.337 5.063 5.748 6.394 7.004 7.579 7% .967 1.871 2.715 3.504 4.242 4.931 5.576 6.178 6.741 7.267 7.758 8.218 8.647 9.048 9.423 8% .962 1.854 2.679 3.443 4.150 4.805 5.412 5.974 6.494 6.975 7.421 7.834 8.216 8.570 8.897 9% .958 1.837 2.644 3.383 4.062 4.685 5.256 5.780 6.261 6.702 7.107 7.478 7.819 8.131 8.418 8.681 8.923 9.144 9.347 9.533 10% .954 1.821 2.609 3.326 3.977 4.570 5.108 5.597 6.042 6.447 6.815 7.149 7.453 7.729 7.980 8.209 8.416 8.605 8.777 8.932 11% .950 1.805 2.576 3.270 3.896 4.459 4.967 5.424 5.836 6.208 6.542 6.843 7.115 7.359 7.579 7.778 7.957 8.118 8.263 8.394 12% .945 1.790 2.543 3.216 3.817 4.353 4.832 5.260 5.642 5.983 6.287 6.559 6.802 7.018 7.212 7.385 7.539 7.676 7.799 7.909 13% .941 1.774 2.512 3.164 3.741 4.252 4.704 5.104 5.458 5.772 6.049 6.294 6.512 6.704 6.874 7.024 7.158 7.275 7.380 7.472 14% .937 1.759 2.481 3.113 3.668 4.155 4.582 4.956 5.285 5.573 5.826 6.048 6.242 6.413 6.563 6.694 6.809 6.910 6.999 7.077 15% .933 1.745 2.450 3.064 3.598 4.062 4.465 4.816 5.121 5.386 5.617 5.818 5.992 6.144 6.276 6.390 6.490 6.577 6.652 6.718

9.391 8.935 8.512 8.121 10.10 9.572 9.083 8.633 10.79 10.18 9.627 9.116 11.46 10.77 10.14 9.571 12.12 11.34 10.64 10.00 12.75 13.36 13.96 14.54 15.10 11.88 12.41 12.91 13.39 13.86 11.11 11.55 11.98 12.39 12.77 10.41 10.79 11.15 11.49 11.81

9.774 9.201 10.10 9.482 10.41 9.742 10.69 9.983 10.96 10.21

Interest Rate per Year Number of Years 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 16% .929 1.730 2.421 3.016 3.530 3.972 4.354 4.682 4.966 5.210 5.421 5.603 5.759 5.894 6.010 6.111 6.197 6.272 6.336 6.391 17% .925 1.716 2.392 2.970 3.464 3.886 4.247 4.555 4.819 5.044 5.237 5.401 5.542 5.662 5.765 5.853 5.928 5.992 6.047 6.094 18% .922 1.703 2.365 2.925 3.401 3.804 4.145 4.434 4.680 4.887 5.063 5.213 5.339 5.446 5.537 5.614 5.679 5.735 5.781 5.821 19% .918 1.689 2.337 2.882 3.340 3.724 4.048 4.319 4.547 4.739 4.900 5.036 5.150 5.245 5.326 5.393 5.450 5.498 5.538 5.571 20% .914 1.676 2.311 2.840 3.281 3.648 3.954 4.209 4.422 4.599 4.747 4.870 4.972 5.058 5.129 5.188 5.238 5.279 5.313 5.342 21% .910 1.663 2.285 2.799 3.223 3.574 3.865 4.104 4.302 4.466 4.602 4.713 4.806 4.882 4.945 4.998 5.041 5.076 5.106 5.130 22% .907 1.650 2.259 2.759 3.168 3.504 3.779 4.004 4.189 4.340 4.465 4.566 4.650 4.718 4.774 4.820 4.858 4.889 4.914 4.935 23% .903 1.638 2.235 2.720 3.115 3.436 3.696 3.909 4.081 4.221 4.335 4.428 4.503 4.564 4.614 4.655 4.687 4.714 4.736 4.754 24% .900 1.625 2.211 2.682 3.063 3.370 3.617 3.817 3.978 4.108 4.213 4.297 4.365 4.420 4.464 4.500 4.529 4.552 4.571 4.586 25% .896 1.613 2.187 2.646 3.013 3.307 3.542 3.730 3.880 4.000 4.096 4.173 4.235 4.284 4.324 4.355 4.381 4.401 4.417 4.430 26% .893 1.601 2.164 2.610 2.964 3.246 3.469 3.646 3.786 3.898 3.986 4.057 4.112 4.157 4.192 4.220 4.242 4.259 4.273 4.284 27% .889 1.590 2.141 2.576 2.917 3.187 3.399 3.566 3.697 3.801 3.882 3.946 3.997 4.036 4.068 4.092 4.112 4.127 4.139 4.149 28% .886 1.578 2.119 2.542 2.872 3.130 3.331 3.489 3.612 3.708 3.783 3.841 3.887 3.923 3.951 3.973 3.990 4.003 4.014 4.022 29% .883 1.567 2.098 2.509 2.828 3.075 3.266 3.415 3.530 3.619 3.689 3.742 3.784 3.816 3.841 3.860 3.875 3.887 3.896 3.903 30% .880 1.556 2.077 2.477 2.785 3.022 3.204 3.344 3.452 3.535 3.599 3.648 3.686 3.715 3.737 3.754 3.767 3.778 3.785 3.791

Note: For example, if the interest rate is 10 percent per year, a continuous cash flow of $1 a year for each of 5 years is worth $3.977. A continuous flow of $1 in year 5 only is worth $3.977 $3.326 $.651.

Brealey−Myers−Allen: Principles of Corporate Finance, Eighth Edition

Back Matter

Appendix A: Present Value Tables

© The McGraw−Hill Companies, 2005

APPENDIX A Present Value Tables A P P E N D I X TA B L E 6
Cumulative probability [N(d)] that a normally distributed variable will be less than d standard deviations above the mean. d 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2 2.1 2.2 2.3 2.4 2.5 0 .5000 .5398 .5793 .6179 .6554 .6915 .7257 .7580 .7881 .8159 .8413 .8643 .8849 .9032 .9192 .9332 .9452 .9554 .9641 .9713 .9772 .9821 .9861 .9893 .9918 .9938 0.01 .5040 .5438 .5832 .6217 .6591 .6950 .7291 .7611 .7910 .8186 .8438 .8665 .8869 .9049 .9207 .9345 .9463 .9564 .9649 .9719 .9778 .9826 .9864 .9896 .9920 .9940
.22, N(d)

973

0.02 .5080 .5478 .5871 .6255 .6628 .6985 .7324 .7642 .7939 .8212 .8461 .8686 .8888 .9066 .9222 .9357 .9474 .9573 .9656 .9726 .9783 .9830 .9868 .9898 .9922 .9941

0.03 .5120 .5517 .5910 .6293 .6664 .7019 .7357 .7673 .7967 .8238 .8485 .8708 .8907 .9082 .9236 .9370 .9484 .9582 .9664 .9732 .9788 .9834 .9871 .9901 .9925 .9943

0.04 .5160 .5557 .5948 .6331 .6700 .7054 .7389 .7704 .7995 .8264 .8508 .8729 .8925 .9099 .9251 .9382 .9495 .9591 .9671 .9738 .9793 .9838 .9875 .9904 .9927 .9945

0.05 .5199 .5596 .5987 .6368 .6736 .7088 .7422 .7734 .8023 .8289 .8531 .8749 .8944 .9115 .9265 .9394 .9505 .9599 .9678 .9744 .9798 .9842 .9878 .9906 .9929 .9946

0.06 .5239 .5636 .6026 .6406 .6772 .7123 .7454 .7764 .8051 .8315 .8554 .8770 .8962 .9131 .9279 .9406 .9515 .9608 .9686 .9750 .9803 .9846 .9881 .9909 .9931 .9948

0.07 .5279 .5675 .6064 .6443 .6808 .7157 .7486 .7794 .8078 .8340 .8577 .8790 .8980 .9147 .9292 .9418 .9525 .9616 .9693 .9756 .9808 .9850 .9884 .9911 .9932 .9949

0.08 .5319 .5714 .6103 .6480 .6844 .7190 .7517 .7823 .8106 .8365 .8599 .8810 .8997 .9162 .9306 .9429 .9535 .9625 .9699 .9761 .9812 .9854 .9887 .9913 .9934 .9951

0.09 .5359 .5753 .6141 .6517 .6879 .7224 .7549 .7852 .8133 .8389 .8621 .8830 .9015 .9177 .9319 .9441 .9545 .9633 .9706 .9767 .9817 .9857 .9890 .9916 .9936 .9952

Note: For example, if d

.5871 (i.e., there is a .5871 probability that a normally distributed variable will be less than .22 standard deviations above the mean).

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