Brealey−Myers−Allen: Principles of Corporate Finance, Eighth EditionBack Matter Appendix A: Present Value Tables© The McGraw−Hill Companies, 2005PRESENT VALUE TABLESAPPENDIX AAPPENDIX TABLE 1Discount factors: Present value of $1 to be received after t years ⫽ 1/(1 ⫹ r)t.NumberInterest Rate per Yearof Years 1% 2% 3% 4% 5% 6% 7% 8% 9% 10% 11% 12% 13% 14% 15%1 .990 .980 .971 .962 .952 .943 .935 .926 .917 .909 .901 .893 .885 .877 .8702 .980 .961 .943 .925 .907 .890 .873 .857 .842 .826 .812 .797 .783 .769 .7563 .971 .942 .915 .889 .864 .840 .816 .794 .772 .751 .731 .712 .693 .675 .6584 .961 .924 .888 .855 .823 .792 .763 .735 .708 .683 .659 .636 .613 .592 .5725 .951 .906 .863 .822 .784 .747 .713 .681 .650 .621 .593 .567 .543 .519 .4976 .942 .888 .837 .790 .746 .705 .666 .630 .596 .564 .535 .507 .480 .456 .4327 .933 .871 .813 .760 .711 .665 .623 .583 .547 .513 .482 .452 .425 .400 .3768 .923 .853 .789 .731 .677 .627 .582 .540 .502 .467 .434 .404 .376 .351 .3279 .914 .837 .766 .703 .645 .592 .544 .500 .460 .424 .391 .361 .333 .308 .28410 .905 .820 .744 .676 .614 .558 .508 .463 .422 .386 .352 .322 .295 .270 .24711 .896 .804 .722 .650 .585 .527 .475 .429 .388 .350 .317 .287 .261 .237 .21512 .887 .788 .701 .625 .557 .497 .444 .397 .356 .319 .286 .257 .231 .208 .18713 .879 .773 .681 .601 .530 .469 .415 .368 .326 .290 .258 .229 .204 .182 .16314 .870 .758 .661 .577 .505 .442 .388 .340 .299 .263 .232 .205 .181 .160 .14115 .861 .743 .642 .555 .481 .417 .362 .315 .275 .239 .209 .183 .160 .140 .12316 .853 .728 .623 .534 .458 .394 .339 .292 .252 .218 .188 .163 .141 .123 .10717 .844 .714 .605 .513 .436 .371 .317 .270 .231 .198 .170 .146 .125 .108 .09318 .836 .700 .587 .494 .416 .350 .296 .250 .212 .180 .153 .130 .111 .095 .08119 .828 .686 .570 .475 .396 .331 .277 .232 .194 .164 .138 .116 .098 .083 .07020 .820 .673 .554 .456 .377 .312 .258 .215 .178 .149 .124 .104 .087 .073 .061Note: For example, if the interest rate is 10 percent per year, the present value of $1 received at year 5 is $.621.NumberInterest Rate per Yearof Years 16% 17% 18% 19% 20% 21% 22% 23% 24% 25% 26% 27% 28% 29% 30%1 .862 .855 .847 .840 .833 .826 .820 .813 .806 .800 .794 .787 .781 .775 .7692 .743 .731 .718 .706 .694 .683 .672 .661 .650 .640 .630 .620 .610 .601 .5923 .641 .624 .609 .593 .579 .564 .551 .537 .524 .512 .500 .488 .477 .466 .4554 .552 .534 .516 .499 .482 .467 .451 .437 .423 .410 .397 .384 .373 .361 .3505 .476 .456 .437 .419 .402 .386 .370 .355 .341 .328 .315 .303 .291 .280 .2696 .410 .390 .370 .352 .335 .319 .303 .289 .275 .262 .250 .238 .227 .217 .2077 .354 .333 .314 .296 .279 .263 .249 .235 .222 .210 .198 .188 .178 .168 .1598 .305 .285 .266 .249 .233 .218 .204 .191 .179 .168 .157 .148 .139 .130 .1239 .263 .243 .225 .209 .194 .180 .167 .155 .144 .134 .125 .116 .108 .101 .09410 .227 .208 .191 .176 .162 .149 .137 .126 .116 .107 .099 .092 .085 .078 .07311 .195 .178 .162 .148 .135 .123 .112 .103 .094 .086 .079 .072 .066 .061 .05612 .168 .152 .137 .124 .112 .102 .092 .083 .076 .069 .062 .057 .052 .047 .04313 .145 .130 .116 .104 .093 .084 .075 .068 .061 .055 .050 .045 .040 .037 .03314 .125 .111 .099 .088 .078 .069 .062 .055 .049 .044 .039 .035 .032 .028 .02515 .108 .095 .084 .074 .065 .057 .051 .045 .040 .035 .031 .028 .025 .022 .02016 .093 .081 .071 .062 .054 .047 .042 .036 .032 .028 .025 .022 .019 .017 .01517 .080 .069 .060 .052 .045 .039 .034 .030 .026 .023 .020 .017 .015 .013 .01218 .069 .059 .051 .044 .038 .032 .028 .024 .021 .018 .016 .014 .012 .010 .00919 .060 .051 .043 .037 .031 .027 .023 .020 .017 .014 .012 .011 .009 .008 .00720 .051 .043 .037 .031 .026 .022 .019 .016 .014 .012 .010 .008 .007 .006 .005Brealey−Myers−Allen: Principles of Corporate Finance, Eighth EditionBack Matter Appendix A: Present Value Tables© The McGraw−Hill Companies, 2005APPENDIX A Present Value Tables 969APPENDIX TABLE 2Future value of $1 after t years ⫽ (1 ⫹ r)t.NumberInterest Rate per Yearof Years 1% 2% 3% 4% 5% 6% 7% 8% 9% 10% 11% 12% 13% 14% 15%1 1.010 1.020 1.030 1.040 1.050 1.060 1.070 1.080 1.090 1.100 1.110 1.120 1.130 1.140 1.1502 1.020 1.040 1.061 1.082 1.102 1.124 1.145 1.166 1.188 1.210 1.232 1.254 1.277 1.300 1.3233 1.030 1.061 1.093 1.125 1.158 1.191 1.225 1.260 1.295 1.331 1.368 1.405 1.443 1.482 1.5214 1.041 1.082 1.126 1.170 1.216 1.262 1.311 1.360 1.412 1.464 1.518 1.574 1.630 1.689 1.7495 1.051 1.104 1.159 1.217 1.276 1.338 1.403 1.469 1.539 1.611 1.685 1.762 1.842 1.925 2.0116 1.062 1.126 1.194 1.265 1.340 1.419 1.501 1.587 1.677 1.772 1.870 1.974 2.082 2.195 2.3137 1.072 1.149 1.230 1.316 1.407 1.504 1.606 1.714 1.828 1.949 2.076 2.211 2.353 2.502 2.6608 1.083 1.172 1.267 1.369 1.477 1.594 1.718 1.851 1.993 2.144 2.305 2.476 2.658 2.853 3.0599 1.094 1.195 1.305 1.423 1.551 1.689 1.838 1.999 2.172 2.358 2.558 2.773 3.004 3.252 3.51810 1.105 1.219 1.344 1.480 1.629 1.791 1.967 2.159 2.367 2.594 2.839 3.106 3.395 3.707 4.04611 1.116 1.243 1.384 1.539 1.710 1.898 2.105 2.332 2.580 2.853 3.152 3.479 3.836 4.226 4.65212 1.127 1.268 1.426 1.601 1.796 2.012 2.252 2.518 2.813 3.138 3.498 3.896 4.335 4.818 5.35013 1.138 1.294 1.469 1.665 1.886 2.133 2.410 2.720 3.066 3.452 3.883 4.363 4.898 5.492 6.15314 1.149 1.319 1.513 1.732 1.980 2.261 2.579 2.937 3.342 3.797 4.310 4.887 5.535 6.261 7.07615 1.161 1.346 1.558 1.801 2.079 2.397 2.759 3.172 3.642 4.177 4.785 5.474 6.254 7.138 8.13716 1.173 1.373 1.605 1.873 2.183 2.540 2.952 3.426 3.970 4.595 5.311 6.130 7.067 8.137 9.35817 1.184 1.400 1.653 1.948 2.292 2.693 3.159 3.700 4.328 5.054 5.895 6.866 7.986 9.276 10.7618 1.196 1.428 1.702 2.026 2.407 2.854 3.380 3.996 4.717 5.560 6.544 7.690 9.024 10.58 12.3819 1.208 1.457 1.754 2.107 2.527 3.026 3.617 4.316 5.142 6.116 7.263 8.613 10.20 12.06 14.2320 1.220 1.486 1.806 2.191 2.653 3.207 3.870 4.661 5.604 6.727 8.062 9.646 11.52 13.74 16.37NumberInterest Rate per Yearof Years 16% 17% 18% 19% 20% 21% 22% 23% 24% 25% 26% 27% 28% 29% 30%1 1.160 1.170 1.180 1.190 1.200 1.210 1.220 1.230 1.240 1.250 1.260 1.270 1.280 1.290 1.3002 1.346 1.369 1.392 1.416 1.440 1.464 1.488 1.513 1.538 1.563 1.588 1.613 1.638 1.664 1.6903 1.561 1.602 1.643 1.685 1.728 1.772 1.816 1.861 1.907 1.953 2.000 2.048 2.097 2.147 2.1974 1.811 1.874 1.939 2.005 2.074 2.144 2.215 2.289 2.364 2.441 2.520 2.601 2.684 2.769 2.8565 2.100 2.192 2.288 2.386 2.488 2.594 2.703 2.815 2.932 3.052 3.176 3.304 3.436 3.572 3.7136 2.436 2.565 2.700 2.840 2.986 3.138 3.297 3.463 3.635 3.815 4.002 4.196 4.398 4.608 4.8277 2.826 3.001 3.185 3.379 3.583 3.797 4.023