Do the Math 14-6 Yield, Price, and YTM
A corporate bond maturing in 15 years with a coupon rate of 7.9 percent was purchased for $970 and it now selling for $1,000.
-
What is its current yield? Round your answer to one decimal place.
%
-
What will be its selling price in two years if comparable market interest rates drop 1.9 percentage points? (Hint: Use Appendix A-2 and Appendix A-4 or the Garman/Forgue companion website.) Round Present Value of a Single Amount and Present Value of Series of Equal Amounts in intermediate calculations to four decimal places. Round your answer to the nearest cent.
$
- Calculate the bond's YTM using Equation 14.5 or the Garman/Forgue companion website. Round your answer to two decimal places.
Appendix A-2 Present Value of a Single Amount (S1) (Used to Compute the Discounted Present Value of Some Known Future Single Lump Sum) n 1% 2% 3% 4% 5% 6% 7% 10% 11% 12% 13% 14% 15% 16% 17% 18% 19% 20% 1 0.9901 0.9804 0.9709 0.9615 0.9524 0.9434 0.9346 8% 0.9259 0.8573 9% 0.9174 0.8417 0.9091 0.9009 0.8929 0.8850 0.8772 0.8696 0.8621 0.8547 0.8475 0.8403 0.8333 2 0.9803 0.9612 0.94 26 0.9246 0.9070 0.8900 0.8734 0.8264 0.8116 0.7972 0.7831 0.7695 0.7561 0.7432 0.7305 0.7182 0.7062 0.6944 3 0.9706 0.9151 0.8890 0.8638 0.8396 0.8163 0.7938 0.7722 0.7312 0.7118 0.6931 0.6750 0.6575 0.6407 0.6244 0.6086 0.9423 0.9238 0.7513 0.6830 0.5934 0.4987 0.5787 0.4823 4 0.9610 0.8885 0.8548 0.8227 0.7921 0.7629 0.7350 0.7084 0.6587 0.6355 0.6133 0.5921 0.5718 0.5523 0.5337 0.5158 5 0.9515 0.9057 0.8626 0.8219 0.7835 0.7473 0.7130 0.6806 0.6499 0.6209 0.5935 0.5674 0.5428 0.5194 0.4972 0.4761 0.4561 0.4371 0.4190 0.4019 6 0.9420 0.8880 0.8375 0.7903 0.7462 0.7050 0.6663 0.6302 0.5963 0.5645 0.5346 0.5066 0.4803 0.4556 0.4323 0.4104 0.3898 0.3704 0.3521 0.3349 7 0.9327 0.8706 0.8131 0.7599 0.7107 0.6651 0.6227 0.5835 0.5470 0.5132 0.4817 0.4523 0.4251 0.3996 0.3759 0.3538 0.3332 0.3139 0.2959 0.2791 8 0.9235 0.8535 0.7894 0.7307 0.6768 0.6274 0.5820 0.5403 0.5019 0.4665 0.4339 0.4039 0.3762 0.3506 0.3269 0.3050 0.2848 0.2660 0.2487 0.2326 9 0.9143 0.8368 0.7664 0.7026 0.6446 0.5919 0.5439 0.5002 0.4604 0.4241 0.3909 0.3606 0.3329 0.3075 0.2843 0.2630 0.2434 0.2255 0.2090 0.1938 10 0.9053 0.8203 0.7441 0.6756 0.6139 0.5584 0.5083 0.4632 0.4224 0.3855 0.3522 0.3220 0.2946 0.2697 0.2472 0.2267 0.2080 0.1911 0.1756 0.1615 11 0.8963 0.8043 0.7224 0.6496 0.5847 0.5268 0.4751 0.4289 0.3875 0.3505 0.3173 0.2875 0.2607 0.2366 0.2149 0.1954 0.1778 0.1619 0.1476 0.1346 12 0.8874 0.7885 0.7014 0.5568 0.4970 0.4440 0.3971 0.3555 0.3186 0.2858 0.2567 0.2307 0.2076 0.1685 0.1520 0.1372 0.1240 0.1122 0.6246 0.6006 0.1869 0.1625 13 0.8787 0.7730 0.6810 0.5303 0.4688 0.4150 0.3677 0.3262 0.2897 0.2575 0.2292 0.2042 0.1821 0.1452 0.1299 0.1163 0.1042 0.0935 14 0.8700 0.7579 0.6611 0.5775 0.5051 0.4423 0.3878 0.3405 0.2992 0.2633 0.2320 0.2046 0.1807 0.1597 0.1413 0.1252 0.1110 0.0985 0.0876 0.0779 15 0.8613 0.7430 0.6419 0.5553 0.4810 0.4173 0.3624 0.3152 0.2745 0.2394 0.2090 0.1827 0.1599 0.1401 0.1229 0.1079 0.0949 0.0835 0.0736 0.0649 16 0.8528 0.7284 0.6232 0.5339 0.4581 0.3936 0.3387 0.2919 0.2519 0.2176 0.1883 0.1631 0.1415 0.1229 0.1069 0.0811 0.0708 0.0618 0.0541 0.0930 0.0802 17 0.8444 0.7142 0.6050 0.5134 0.4363 0.3714 0.3166 0.2311 0.1978 0.1696 0.1456 0.1252 0.1078 0.0929 0.0693 0.0600 0.0520 0.0451 0.2703 0.2502 18 0.8360 0.700Z 0.5874 0.4936 0.4155 0.3503 0.2959 0.2120 0.1799 0.1528 0.1300 0.1108 0.0946 0.0808 0.0691 0.0592 0.0508 0.0437 0.0376 19 0.8277 0.6864 0.5703 0.4746 0.3957 0.2765 0.2317 0.1945 0.1635 0.1377 0.1161 0.0981 0.0829 0.0703 0.0506 0.0431 0.0367 0.0313 0.3305 0.3118 0.0596 0.0514 20 0.8195 0.6730 0.5537 0.4564 0.3769 0.2584 0.2145 0.1784 0.1486 0.1240 0.1037 0.0868 0.0728 0.0611 0,0433 0.0365 0.0308 0.0261 21 0.8114 0.6598 0.5375 0.4388 0.3589 0.2942 0.2415 0.1987 0.1637 0.1351 0.1117 0.0926 0.0768 0.0638 0.0531 0.0443 0.0370 0.0309 0.0259 0.0217 22 0.8034 0.6468 0.52 19 0.4220 0.3418 0.2775 0.2257 0.1839 0.1502 0.1228 0.1007 0.0826 0.0680 0.0560 0.0462 0.0382 0.03 16 0.0262 0.0218 0.0181 23 0.7954 0.6342 0.5067 0.4057 0.3256 0.2618 0.2 109 0.1703 0.1378 0.1117 0.0907 0.0738 0.0601 0.0491 0.0402 0.0329 0.0270 0.0222 0.0183 0.0151 24 0.7876 0.6217 0.4919 0.3901 0.3101 0.2470 0.1577 0.1264 0.1015 0.0817 0.0659 0.0532 0.0431 0.0349 0.0284 0.0231 0.0188 0.0154 0.0126 0.1971 0.1842 25 0.7798 0.6095 0.4776 0.3751 0.2953 0.2330 0.1460 0.1160 0.0923 0.0736 0.0588 0.0471 0.0378 0.0304 0.0245 0.0197 0.0160 0.0129 0.0105 0.5976 0.4637 0.3607 0.2812 0.2198 0.1722 0.1352 0.1064 0.0839 0.0663 0.0525 0.0417 0.0331 0.0264 0.0211 0.0169 0.0135 0.0109 0.0087 26 0.7720 27 0.7644 0.5859 0.4502 0.3468 0.2678 0.2074 0.1609 0.1252 0.0976 0.0763 0.0597 0.0469 0.0369 0.0291 0.0230 0.0182 0.0144 0.0115 0.0091 0.0073 28 0.7568 0.5744 0.4371 0.3335 0.2551 0.1956 0.1504 0.1159 0.0895 0.0693 0.0538 0.0419 0.0326 0.0255 0.0200 0.0157 0.0123 0.0097 0.0077 0.0061 29 0.7493 0.5631 0.4243 0.3207 0.2429 0.1846 0.1406 0.1073 0.0822 0.0630 0.0485 0.0374 0.0289 0.0224 0.0174 0.0135 0.0105 0.0082 0.0064 0.0051 30 0.7419 0.5521 0.4120 0.3083 0.2314 0.1741 0.1314 0.0994 0.0754 0.0573 0.0437 0.0334 0.0256 0.0196 0.0151 0.0116 0.0090 0.0070 0.0054 0.0042 40 0.6717 0.4529 0.3066 0.2003 0.1420 0.0972 0.0668 0.0460 0.0318 0.0221 0.0154 0.0107 0.0075 0.0053 0.0037 0.0019 0.0013 0.0010 0.0007 0.0026 0.0006 50 0.6080 0.3715 0.2281 0.1407 0.0872 0.0543 0.0339 0.0213 0.0134 0.0085 0.0054 0.0035 0.0022 0.0014 0.0009 0.0004 0.0003 0.0002 0.0001 Appendix A-4 Present Value of a Series of Equal Amounts (an Annuity of $1 Received at the End of Each Period) (Used to compute the Discounted Present Value of a Stream of Income Payments) n 1% 3% 4% 5% 9% 11% 12% 13% 14% 15% 18% 19% 20% 2% 09804 6% 6 0.9434 7% 0.9346 8% 0.9259 10% 0.9091 16% 17% 0.8621 0.8547 1 0.9901 0.9709 0.9615 0.9524 0.9174 0.9009 08929 0.8850 0.8772 0.8696 0.8475 0.8403 0.8333 2 1.9704 1.9416 1.9135 1.8861 1.8594 1.8334 1.8080 1.7833 1.7591 1.7355 1.7125 1.6901 1,6681 1,6467 1.6257 1.6052 1.5852 1.5656 1.5465 1.5278 3 2.9410 2.8839 2.8286 2.7751 2.7232 2.6730 2.6243 2.5771 25313 2.4869 2.4437 2.4018 2.3612 2.3216 2.2832 2.2459 2.2096 2.1743 2.1399 2.1065 4 3.9020 3.8077 3.7171 3.6299 3.5460 3.4651 3.3872 3.3121 3.2397 3.1699 3.1024 3.0373 2.9745 2.9137 2.8550 2.7982 2.7432 2.6901 2.6386 2.5887 2.9906 5 4.8534 4.7135 4.5797 4.4518 4 3295 4.2124 4.1002 3.9927 3.8897 3.7908 3.6959 3.6048 3.5172 3,4331 3.3522 3.2743 3.1993 3.1272 3,0576 6 5.7955 5.6014 54172 5.2421 5.0757 4.9173 4.7665 4.6229 4.4859 4.3553 4.2305 4.1114 3.8887 3.7845 3.6847 3.5892 3.4976 3.4098 3.3255 3.9975 4.4226 7 6.7282 6.4720 6.2303 6.0021 5.7864 55824 53893 5.2064 5.0330 4.8684 4.7122 4.5638 4.2883 4.1604 4.0386 3.9224 3.8115 3.7057 3.6046 8 7.6517 7.3255 7.0197 6.7327 6.4632 6.2098 5.9713 5.5348 5.3349 5.1461 4.9676 4.7988 4.6389 4.4873 4.2072 4.0776 3.9544 3.8372 5.7466 6.2469 4.3436 4.6065 9 85660 8.1622 7.7861 7.4353 7.1078 6.8017 6.5152 5.9952 5.7590 5.5370 5.3282 5.1317 4.9464 4.7716 4.4506 43030 41633 4.0310 10 9.4713 8.9826 8.5302 8.1109 7.7217 7.3601 6.7101 6.4177 6.1446 5.8892 5.6502 5.4262 5.2161 5.0188 4.8332 4.6586 4.4941 4.3389 4.1925 7.0236 7.4987 11 10.3676 9.7868 9.2526 8.7605 8.3064 7.8869 7.1390 6.8052 6.4951 6.2065 5.9377 5.6869 5.2337 5.0286 4.8364 4.6560 4.4865 4.3271 5.4527 5.6603 12 11.2551 10.5753 9.9540 9.3851 8.8633 8.3838 7.9427 7.5361 7.1607 6.8137 6.4924 6.1944 59176 5.4206 5.1971 49884 4.7932 4.6105 4.4392 13 12.1337 11.3484 9.9856 9.3936 8.3577 7.9038 7.4869 7.1034 6.7499 6.4235 6.12 18 5.8424 5.5831 5.3423 5.1183 4.9095 4.7147 4.5327 10.6350 11.2961 8.8527 9.2950 14 13.0037 12.1062 10.5631 9.8986 8.7455 8.2442 7.7862 7.3667 6.9819 6.6282 6.3025 6.0021 5.7245 5.4675 5.2293 5.0081 4.8023 4.6106 15 13.8651 12.8493 11.9379 11.1184 103797 9.7122 9.1079 B.5595 80607 7.6061 7.1909 6.8109 6.4624 6.1422 5.8474 5.5755 5.3242 5.0916 4.8759 4.6755 4.7296 16 14.7179 13.5777 12.5611 11.6523 10.8378 10.1059 9.4466 B.8514 8.3126 7.8237 7.3792 6.9740 6.6039 6.2651 5.9542 5.6685 5.4053 5.1624 4.9377 17 15.5623 14.2919 13.1661 12.1657 11.2741 10.4773 9.7632 9.1216 8.5436 80216 7.5488 7.1196 6.3729 6.0472 5.7487 5.4746 5.2223 4.9897 4.7746 6.7291 6.8399 18 16.3983 14.9920 13.7535 12.6593 11.6896 10.0591 9.3719 8.7556 8.2014 7.7016 7.2497 6.4674 6.1280 5.8178 5.5339 5.2732 5.0333 10.8276 11.1581 4.8122 4.8435 19 17.2260 15.6785 14.3238 13.1339 12.0853 10.3356 9.6036 8.9501 8.3649 7.8393 7.3658 6.9381 6.5504 6.1982 5.8775 5.5845 5.3162 5.0 700 5.1009 20 18.0456 163514 14.8775 13.5903 12.4622 11.4699 10.5940 9.8181 9.1285 8.5136 79633 7.4694 7.0248 6.6231 6.2593 5.9288 5.6278 5.3527 4.8696 21 18.8570 17.0112 15.4150 14.0292 12.8212 11.7641 10.8355 10.0168 9.2922 8.6487 8.0751 7.5620 7.1016 6.6870 6.3125 5.9731 5.6648 5.3837 5.1268 4.8913 22 19.6604 17.6580 15.9369 14.4511 13.1630 10.2007 8.7715 8.1757 7.6446 7.1695 6.7429 6.3587 6.0113 5.4099 4.9094 12.0416 12 3034 11.0612 11.2722 9.4424 9.5802 5.6964 5.7234 5.1486 5.1668 23 20.4558 18.2922 16,4436 14.8568 13.4886 10.3711 8.8832 8.2664 7.7184 7.2297 6.7921 6.3988 6.0442 5,4321 49245 24 21.2434 18.9139 16.9355 15.2470 13.7986 12.5504 11.4693 9.7066 8.9847 7.7843 7.2829 6.8351 6.4338 6.0726 5.7465 5.4509 4.93 71 10.5288 10.6748 8.3481 8.4217 5.1822 5. 1951 25 22.0232 19.5235 17.4131 14.0939 12.7834 116536 9.8226 9.0770 7.8431 7.3300 6.8729 6.4641 6.0971 5.7662 54669 49476 15.6221 15.9828 26 22.7952 20.1210 14.3752 13.0032 11.8258 10.8100 9.1609 8.4881 7.8957 7.3712 6.9061 6.4906 6.1182 5.7831 5.4804 4.9563 17.8768 18.3270 9.9290 10.0266 5.2060 5.2151 27 23.5596 20.7069 16.3296 14.6430 13.2105 11.9867 10.9352 9.2372 8.5478 7.9426 7.4086 6.9352 6.5135 5.7975 5.4919 4.9636 6.1364 6.1520 28 24.3 164 21.2813 18.7641 16.6631 14.8981 13.4062 12.1371 11.0511 10.1161 9.3066 8.6016 7.9844 7.4412 6.9607 6.5335 5.8099 5.5016 5.2228 4.9697 29 25.0658 21.8444 19.1885 16.9837 15.1411 13.5907 12.2777 11.1584 10.1983 9.3696 8.6501 8,0218 7.4701 6.9830 6.5509 6.1656 5.8204 5.5098 5.2292 4.9747 30 25.8077 22.3965 19.6004 17.2920 13.7648 112578 10.2737 9.4269 8.6938 8.0552 6.5660 6.1772 5.8294 5.5168 153725 17.1591 12.4090 13.3317 7.4957 7.6344 7.0027 7.1050 5.2347 5.2582 4.9789 4.9966 40 32.8347 27.3555 23.1148 19.7928 15.0463 11.9246 10.7574 9.7791 8.9511 8.2438 6.6418 6.2335 5.8713 5.5482 50 39.1961 31.4236 25.7298 21.4822 18.2559 15.7619 13.8007 12.2335 10.9617 9.9148 9.0417 83045 7.6752 7.1327 6.6605 6.2463 5.8801 5.5541 5.2623 4.9995 (14.5) YTM I + [(FV - CV)/N] (FV + CV)/2 where I = Interest paid annually in dollars FV = Face value CV = current value (price) N = Number of years until maturity
