Problem 13-02 a. A $1,000 bond has a 5.5 percent coupon and matures after eleven years. If current interest rates are 8 percent, what should be the price of the bond? Assume that the bond pays interest annually. Use Appendix B and Appendix D to answer the question. Round your answer to the nearest dollar. $ b. If after six years interest rates are still 8 percent, what should be the price of the bond? Use Appendix B and Appendix D to answer the question. Assume that the bond pays interest annually. Round your answer to the nearest dollar. $ C. Even though interest rates did not change in a and b, why did the price of the bond change? The price of the bond with the longer term is -Select-than the price of the bond with the shorter term as the investors will collect the -Select- v interest payments and receive the principal within a longer period of time. d. Change the interest rate in a and b to 3 percent and rework your answers. Assume that the bond pays interest annually. Round your answers to the nearest dollar. Price of the bond (eleven years to maturity): $ Price of the bond (five years to maturity): $ Even though the interest rate is 3 percent in both calculations, why are the bond prices different? The price of the bond with the longer term is -Select-than the price of the bond with the shorter term as the investors will collect the -Select- vinterest payments for a longer period of time. Interest Factors for the Present Value of an Annuity of One Dollar 1% 7% 8% 36% Time Period (e.g. year) 1 2 3 4 5 2% 3% 4% 5% 6% 9% 10% 12% 14% 16% 18% 20% 24% 28% 32% 0.990 0.980 0.971 0.962 0.952 0.943 0.935 0.926 0.917 0.909 0.893 0.877 0.862 0.847 0.833 0.806 0.781 0.758 0.735 1.970 1.942 1.913 1.886 1.859 1.833 1.808 1.783 1.759 1.736 1.690 1.647 1.605 1.566 1.528 1.457 1.392 1.332 1.276 2.941 2.884 2.829 2.775 2.723 2.673 2.624 2.577 2.531 2.487 2.402 2.322 2.246 2.174 2.106 1.981 1.868 1.766 1.674 3.902 3.808 3.717 3.630 3.546 3.465 3.387 3.312 3.240 3.170 3.037 2.914 2.798 2.690 2.589 2.404 2.241 2.096 1.966 4.853 4.713 4.580 4.452 4.329 4.212 4.100 3.993 3.890 3.791 3.605 3.433 3.274 3.127 2.991 2.745 2.532 2.345 2.181 000 6 7 8 9 10 5.795 5.601 5.417 5.242 5.076 4.917 4.766 4.623 4.486 4.355 4.111 3.889 3.685 3.498 3.326 3.020 2.759 2.534 2.399 6.728 6.472 6.230 6.002 5.786 5.582 5.389 5.206 5.033 4.868 4.564 4.288 4.039 3.812 3.605 3.242 2.937 2.678 2.455 7.652 7.325 7.020 6.733 6.463 6.210 5.971 5.747 5.535 5.335 4.968 4.639 4.344 4.078 3.837 3.421 3.076 2.786 2.540 8.566 8.162 7.786 7.435 7.108 6.802 6.515 6.247 5.985 5.759 5.328 4.946 4.607 4.303 4.031 3.566 3.184 2.868 2.603 9.471 8.983 8.530 8.111 7.722 7.360 7.024 6.710 6.418 6.145 5.650 5.216 4.833 4.494 4.193 3.682 3.269 2.930 2.650 11 10.368 9.787 9.253 8.760 8.306 7.887 7.499 7.139 6.805 6.495 5.988 5.453 5.029 4.656 4.327 3.776 3.335 2.978 2.683 12 11.255 10.575 9.954 9.385 8.863 8.384 7.943 7.536 7.161 6.814 6.194 5.660 5.197 4.793 4.439 3.851 3.387 3.013 2.708 13 12.134 11.348 10.635 9.986 9.394 8.534 8.358 7.904 7.487 7.103 6.424 5.842 5.342 4.910 4.533 3.912 3.427 3.040 2.727 14 13.004 12.106 11.296 10.563 9.899 9.295 8.745 8.244 7.786 7.367 6.628 6.002 5.468 5.008 4.611 3.962 3.459 3.061 2.740 15 13.865 12.849 11.938 11.118 10.380 9.712 9.108 8.559 8.060 7.606 6.811 6.142 5.575 5.092 4.675 4.001 3.483 3.076 2.750 16 17 18 19 20 14.718 13.578 12.561 11.652 10.838 10.106 9.447 8.851 8.312 7.824 6.974 6.265 5.669 5.162 4.730 4.003 3.503 3.088 2.758 15.562 14.292 13.166 12.166 11.274 10.477 9.763 9.122 8.544 8.002 7.120 6.373 5.749 5.222 4.775 4.059 3.518 3.097 2.763 16.398 14.992 13.754 12.659 11.690 10.828 10.059 9.372 8.756 8.201 7.250 6.467 5.818 5.273 4.812 4.080 3.529 3.104 2.767 17.226 15.678 14.324 13.134 12.085 11.158 10.336 9.604 8.950 8.365 7.366 6.550 5.877 5.316 4.844 4.097 3.539 3.109 2.770 18.046 16.351 14.877 13.590 12.462 11.470 10.594 9.818 9.128 8.514 7.469 6.623 5.929 5.353 4.870 4.110 3.546 3.113 2.772 25 22.023 19.523 17.413 15.622 14.094 12.783 11.654 10.675 9.823 9.077 7.843 6.873 6.097 5.467 4.948 4.147 3.564 3.122 2.776 30 25.808 22.937 19.600 17.292 15.373 13.765 12.409 11.258 10.274 9.427 8.055 7.003 6.177 5.517 4.979 4.160 3.569 3.124 2.778 Interest Factors for the Present Value of One Dollar Time Period (e.g., year) 1 1% 4% NM .990 980 971 961 951 2% 980 961 .942 924 .906 3% .971 962 .943 .925 915 .889 .889 855 .863 .822 5% 952 907 .864 .823 .784 6% .943 .890 .840 .792 .747 7% 8% 9% 10% 12% .935 .926 917 909 .893 .873 .857 .842 .826 .797 .816 .794 .772 .751 .712 .763 .735 .708 .683 636 .713 .681.650 .621 .567 14% .877 .769 .675 .592 .519 15% .870 .756 .658 .572 497 16% .862 .743 .641 .552 .476 18% .847 .718 .609 .516 437 20% .833 .694 .579 482 402 24% .806 .650 .524 .423 .341 28% .781 .610 .477 373 -291 4 5 6 7 8 9 10 942 .888 933 .871 .923 853 1914 .837 905 820 .838 .813 .789 .766 .744 .790 .760 .731 .703 .676 .746 711 .677 .645 .614 .705.666 630 596 564 507 .665.623 583 547 513 452 .627 582 .540 502 467 404 .592 .544 .500 460 .424 361 .558 .508 463 .422 386 .322 456 432 400 376 351 .327 .308 .284 .270 .247 410 .370 .335 .354 .314 .279 .305 .266 233 .263 .226 .194 .227 191 .162 .275 .222 .179 .144 .116 .227 .178 .139 .108 .085 11 12 13 14 15 .896 804 .887 .788 .879 .773 .870 .758 .861 .743 .722 .701 .681 .661 .642 .650 .625 .601 577 .555 .585 .557 .530 .505 .481 .527 .497 469 .442 417 475 444 415 388 .362 429 .397 .368 .340 .315 .388 .356 .326 .299 .275 .350 .319 .290 .263 .239 .287 .257 .229 .205 .237 215 .208 .187 .182 .163 .160 .141 .140 .123 .195 162 .168 .137 .145 .116 .125 .099 .108 .084 .135 .112 .093 .078 .065 .094 .076 .061 .049 .040 .066 ,052 .040 .032 .025 .183 16 17 18 19 20 .853 .844 .836 .828 .820 .728 .714 .700 .686 .673 .623 .605 .587 .570 .554 .534 .513 494 475 456 .458 .436 416 396 377 .394 .371 .350 .331 .312 .339 .317 .296 .276 .258 .292 .270 .250 .232 .215 .252 .231 .212 .194 .178 .218 .198 .180 .164 .149 .163.123.107 .146 . 108.093 .130 .095 .081 .116 .083.070 .104 .073 .061 .093 071 .054 .032.019 .080 .060 .045.026.015 .069 .051.038 021 .012 ,060 .043 .031 .017 .009 .051 .037 .026 2014 .007 25 .780 .610 478 375 .295 .233 .184 -146 .116 .092 .059 .038 .030 .024 .016 .010 .005 .002 30 .742 .552 .412 308 .231 .174 .131 .099 .075 .057.033 .020 015 .012 .007 .004 .002 .001 Problem 13-02 a. A $1,000 bond has a 5.5 percent coupon and matures after eleven years. If current interest rates are 8 percent, what should be the price of the bond? Assume that the bond pays interest annually. Use Appendix B and Appendix D to answer the question. Round your answer to the nearest dollar. $ b. If after six years interest rates are still 8 percent, what should be the price of the bond? Use Appendix B and Appendix D to answer the question. Assume that the bond pays interest annually. Round your answer to the nearest dollar. $ C. Even though interest rates did not change in a and b, why did the price of the bond change? The price of the bond with the longer term is -Select-than the price of the bond with the shorter term as the investors will collect the -Select- v interest payments and receive the principal within a longer period of time. d. Change the interest rate in a and b to 3 percent and rework your answers. Assume that the bond pays interest annually. Round your answers to the nearest dollar. Price of the bond (eleven years to maturity): $ Price of the bond (five years to maturity): $ Even though the interest rate is 3 percent in both calculations, why are the bond prices different? The price of the bond with the longer term is -Select-than the price of the bond with the shorter term as the investors will collect the -Select- vinterest payments for a longer period of time. Interest Factors for the Present Value of an Annuity of One Dollar 1% 7% 8% 36% Time Period (e.g. year) 1 2 3 4 5 2% 3% 4% 5% 6% 9% 10% 12% 14% 16% 18% 20% 24% 28% 32% 0.990 0.980 0.971 0.962 0.952 0.943 0.935 0.926 0.917 0.909 0.893 0.877 0.862 0.847 0.833 0.806 0.781 0.758 0.735 1.970 1.942 1.913 1.886 1.859 1.833 1.808 1.783 1.759 1.736 1.690 1.647 1.605 1.566 1.528 1.457 1.392 1.332 1.276 2.941 2.884 2.829 2.775 2.723 2.673 2.624 2.577 2.531 2.487 2.402 2.322 2.246 2.174 2.106 1.981 1.868 1.766 1.674 3.902 3.808 3.717 3.630 3.546 3.465 3.387 3.312 3.240 3.170 3.037 2.914 2.798 2.690 2.589 2.404 2.241 2.096 1.966 4.853 4.713 4.580 4.452 4.329 4.212 4.100 3.993 3.890 3.791 3.605 3.433 3.274 3.127 2.991 2.745 2.532 2.345 2.181 000 6 7 8 9 10 5.795 5.601 5.417 5.242 5.076 4.917 4.766 4.623 4.486 4.355 4.111 3.889 3.685 3.498 3.326 3.020 2.759 2.534 2.399 6.728 6.472 6.230 6.002 5.786 5.582 5.389 5.206 5.033 4.868 4.564 4.288 4.039 3.812 3.605 3.242 2.937 2.678 2.455 7.652 7.325 7.020 6.733 6.463 6.210 5.971 5.747 5.535 5.335 4.968 4.639 4.344 4.078 3.837 3.421 3.076 2.786 2.540 8.566 8.162 7.786 7.435 7.108 6.802 6.515 6.247 5.985 5.759 5.328 4.946 4.607 4.303 4.031 3.566 3.184 2.868 2.603 9.471 8.983 8.530 8.111 7.722 7.360 7.024 6.710 6.418 6.145 5.650 5.216 4.833 4.494 4.193 3.682 3.269 2.930 2.650 11 10.368 9.787 9.253 8.760 8.306 7.887 7.499 7.139 6.805 6.495 5.988 5.453 5.029 4.656 4.327 3.776 3.335 2.978 2.683 12 11.255 10.575 9.954 9.385 8.863 8.384 7.943 7.536 7.161 6.814 6.194 5.660 5.197 4.793 4.439 3.851 3.387 3.013 2.708 13 12.134 11.348 10.635 9.986 9.394 8.534 8.358 7.904 7.487 7.103 6.424 5.842 5.342 4.910 4.533 3.912 3.427 3.040 2.727 14 13.004 12.106 11.296 10.563 9.899 9.295 8.745 8.244 7.786 7.367 6.628 6.002 5.468 5.008 4.611 3.962 3.459 3.061 2.740 15 13.865 12.849 11.938 11.118 10.380 9.712 9.108 8.559 8.060 7.606 6.811 6.142 5.575 5.092 4.675 4.001 3.483 3.076 2.750 16 17 18 19 20 14.718 13.578 12.561 11.652 10.838 10.106 9.447 8.851 8.312 7.824 6.974 6.265 5.669 5.162 4.730 4.003 3.503 3.088 2.758 15.562 14.292 13.166 12.166 11.274 10.477 9.763 9.122 8.544 8.002 7.120 6.373 5.749 5.222 4.775 4.059 3.518 3.097 2.763 16.398 14.992 13.754 12.659 11.690 10.828 10.059 9.372 8.756 8.201 7.250 6.467 5.818 5.273 4.812 4.080 3.529 3.104 2.767 17.226 15.678 14.324 13.134 12.085 11.158 10.336 9.604 8.950 8.365 7.366 6.550 5.877 5.316 4.844 4.097 3.539 3.109 2.770 18.046 16.351 14.877 13.590 12.462 11.470 10.594 9.818 9.128 8.514 7.469 6.623 5.929 5.353 4.870 4.110 3.546 3.113 2.772 25 22.023 19.523 17.413 15.622 14.094 12.783 11.654 10.675 9.823 9.077 7.843 6.873 6.097 5.467 4.948 4.147 3.564 3.122 2.776 30 25.808 22.937 19.600 17.292 15.373 13.765 12.409 11.258 10.274 9.427 8.055 7.003 6.177 5.517 4.979 4.160 3.569 3.124 2.778 Interest Factors for the Present Value of One Dollar Time Period (e.g., year) 1 1% 4% NM .990 980 971 961 951 2% 980 961 .942 924 .906 3% .971 962 .943 .925 915 .889 .889 855 .863 .822 5% 952 907 .864 .823 .784 6% .943 .890 .840 .792 .747 7% 8% 9% 10% 12% .935 .926 917 909 .893 .873 .857 .842 .826 .797 .816 .794 .772 .751 .712 .763 .735 .708 .683 636 .713 .681.650 .621 .567 14% .877 .769 .675 .592 .519 15% .870 .756 .658 .572 497 16% .862 .743 .641 .552 .476 18% .847 .718 .609 .516 437 20% .833 .694 .579 482 402 24% .806 .650 .524 .423 .341 28% .781 .610 .477 373 -291 4 5 6 7 8 9 10 942 .888 933 .871 .923 853 1914 .837 905 820 .838 .813 .789 .766 .744 .790 .760 .731 .703 .676 .746 711 .677 .645 .614 .705.666 630 596 564 507 .665.623 583 547 513 452 .627 582 .540 502 467 404 .592 .544 .500 460 .424 361 .558 .508 463 .422 386 .322 456 432 400 376 351 .327 .308 .284 .270 .247 410 .370 .335 .354 .314 .279 .305 .266 233 .263 .226 .194 .227 191 .162 .275 .222 .179 .144 .116 .227 .178 .139 .108 .085 11 12 13 14 15 .896 804 .887 .788 .879 .773 .870 .758 .861 .743 .722 .701 .681 .661 .642 .650 .625 .601 577 .555 .585 .557 .530 .505 .481 .527 .497 469 .442 417 475 444 415 388 .362 429 .397 .368 .340 .315 .388 .356 .326 .299 .275 .350 .319 .290 .263 .239 .287 .257 .229 .205 .237 215 .208 .187 .182 .163 .160 .141 .140 .123 .195 162 .168 .137 .145 .116 .125 .099 .108 .084 .135 .112 .093 .078 .065 .094 .076 .061 .049 .040 .066 ,052 .040 .032 .025 .183 16 17 18 19 20 .853 .844 .836 .828 .820 .728 .714 .700 .686 .673 .623 .605 .587 .570 .554 .534 .513 494 475 456 .458 .436 416 396 377 .394 .371 .350 .331 .312 .339 .317 .296 .276 .258 .292 .270 .250 .232 .215 .252 .231 .212 .194 .178 .218 .198 .180 .164 .149 .163.123.107 .146 . 108.093 .130 .095 .081 .116 .083.070 .104 .073 .061 .093 071 .054 .032.019 .080 .060 .045.026.015 .069 .051.038 021 .012 ,060 .043 .031 .017 .009 .051 .037 .026 2014 .007 25 .780 .610 478 375 .295 .233 .184 -146 .116 .092 .059 .038 .030 .024 .016 .010 .005 .002 30 .742 .552 .412 308 .231 .174 .131 .099 .075 .057.033 .020 015 .012 .007 .004 .002 .001