1. Below is information about three $10000 par value bonds, each of which pays coupon semiannually. The required rate of return on each bond is 14%.Calculate the value of the bonds and determine whether the bond is selling at discount, premium or par value.BondCoupon Rate (%)Maturity (years) 1852141031615 2. Using the Interpolation Method to calculate the YTM for the below Bonds:> The par value $18000> Coupon Rate 10% every year> Maturity period 10 years> Market Value of bond $21800

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Financial Accounting Intro Concepts Meth/Uses

14th Edition

ISBN:9781285595047

Author:Weil

Publisher:Weil

Chapter11: Notes, Bonds, And Leases

Section: Chapter Questions

Problem 17E

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Question

1. Below is information about three $10000 par value bonds, each of which pays coupon semiannually. The required rate of return on each bond is 14%.

Calculate the value of the bonds and determine whether the bond is selling at discount, premium or par value.

Bond	Coupon Rate (%)	Maturity (years)

1	8	5
2	14	10
3	16	15

2. Using the Interpolation Method to calculate the YTM for the below Bonds:

> The par value $18000

> Coupon Rate 10% every year

> Maturity period 10 years

> Market Value of bond $21800

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Follow-up Question

Coupon rate=8%

Annual coupon=0.08 x 10000=$800

Maturity period=n=5years

Price of bond=Coupon x 1-(1+r)-nr+10000(1+r)n=80 x 1-1.14-50.14+100001.145=$7940.15

Price of bond=$7940.15

Please explain the answer how to get $7940.15. Is it possible to calculate using Vb = I (PVIFA kb%, n ) + M (PVIFkb%, n) to find the value of bond?

Attached together the PVIF & PVIFA table below for references. Thank you!

Period 1%
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
Table A-3 Present Value Interest Factors for One Dollar Discounted at k Percent for n Periods: PVIF kn = 1/(1+k)"
2%
3% 4%
5%
6%
0.9709 0.9615 0.9524 0.9434
8% 9%
10%
11% 12%
0.9259 0.9174 0.9091 0.9009 0.8929
0.8573 0.8417
0.9706 0.9423 0.9151
0.7938 0.7722
0.9610 0.9238 0.8885 0.8548 0.8227 0.7921 0.7629 0.7350 0.7084
0.9515 0.9057 0.8626 0.8219 0.7835 0.7473 0.7130 0.6806 0.6499
0.9901 0.9604
0.9803 0.9612
7%
0.9346
0.9246 0.9070 0.8900 0.8734
0.8890 0.8638 0.8396 0.8163
0.9426
30
35
36
40
50
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 0.3349 0.2751
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 0.2791 0.2218
0.9235 0.8535 0.7894 0.7307 0.6768 0.6274 0.5820 0.5403 0.5019 0.4665 0.4339
0.9143 0.8368 0.7664 0.7026 0.6446 0.5919 0.5439 0.5002 0.4604 0.4241 0.3909
0.9053 0.8203 0.7441 0.6756 0.6139 0.5584 0.5083 0.4632 0.4224 0.3855 0.3522
0.4039 0.3762 0.3506 0.3269 0.3050 0.2326 0.1789 0.1678
0.3606 0.3329 0.3075 0.2843 0.2630 0.1938 0.1443 0.1342
0.3220 0.2946 0.2697 0.2472 0.2267 0.1615 0.1164 0.1074
0.6232
0.8528
0.7284
0.5339 0.4581 0.3936
0.8444 0.7142 0.6050 0.5134 0.4363 0.3714
0.8360 0.7002 0.5874 0.4936 0.4155 0.3503
0.8277 0.6864 0.5703 0.4746 0.3957
0.3305
0.8195 0.6730 0.5537 0.4564 0.3769 0.3118
13%
14% 15%
16% 20% 24%
25%
30%
0.8850 0.8772 0.8696 0.8621 0.8333 0.8065 0.8000 0.7692
0.8264 0.8116 0.7972 0.7831 0.7695 0.7561 0.7432 0.6944 0.6504 0.6400 0.5917
0.7513 0.7312 0.7118 0.6931 0.6750 0.6575 0.6407 0.5787 0.5245 0.5120 0.4552
0.6830 0.6587 0.6355 0.6133 0.5921 0.5718 0.5523 0.4823 0.4230 0.4096 0.3501
0.6209 0.5935 0.5674 0.5428 0.5194 0.4972 0.4761 0.4019 0.3411 0.3277 0.2693
0.5268 0.4751
0.8963 0.8043 0.7224 0.6496 0.5847
0.4289 0.3875 0.3505 0.3173 0.2875 0.2607 0.2366 0.2149 0.1954 0.1346 0.0938 0.0859 0.0558
0.8874 0.7885 0.7014 0.6246 0.5568 0.4970 0.4440 0.3971 0.3555 0.3186 0.2858 0.2567 0.2307 0.2076 0.1869 0.1685 0.1122 0.0757 0.0687 0.0429
0.8787 0.7730 0.6810 0.6006 0.5303 0.4688 0.4150 0.3677 0.3262
0.2897 0.2575 0.2292 0.2042 0.1821 0.1625 0.1452 0.0935 0.0610 0.0550
0.0330
0.8700 0.7579 0.6611 0.5775 0.5051 0.4423 0.3878 0.3405 0.2992
0.1597 0.1413 0.1252 0.0779 0.0492 0.0440 0.0254
0.8613 0.7430 0.6419 0.5553 0.4810 0.4173 0.3624 0.3152 0.2745
0.1401 0.1229 0.1079 0.0649 0.0397 0.0352 0.0195
0.2633 0.2320 0.2046 0.1807
0.2394
0.2090 0.1827 0.1599
0.8114 0.6598
08034 0.6468
0.5375
0.4388 0.3589
0.2942 0.2415 0.1987 0.1637
0.5219 0.4220 0.3418 0.2775 0.2257
0.1839 0.1502
0.5067 0.4057 0.3256 0.2618 0.2109 0.1703 0.1378
0.4919 0.3901 0.3101 0.2470 0.1971 0.1577 0.1264
0.7798 0.6096 0.4776 0.3751 0.2953 0.2330 0.1842 0.1460 0.1160
0.7954 0.6342
0.7876 0.6217
0.2919
0.2519 0.2176
0.1883 0.1631 0.1415
0.3387
0.1229 0.1069 0.0930 0.0541 0.0320 0.0281
0.3166 0.2703 0.2311 0.1978 0.1696 0.1456 0.1252 0.1078 0.0929 0.0002 0.0451 0.0258 0.0225
0.2959 0.2502 02120 0.1799 0.1528 0.1300 0.1108 0.0946 0.0808 0.0691 0.0376 0.0208 0.0180
0.2765 0.2317 0.1945 0.1635 0.1377 0.1161 0.0981 0.0829 0.0703 0.0596 0.0313 0.0168 0.0144
0.2584 0.2145 0.1784 0.1486 0.1240 0.1037 0.0668 0.0728 0.0611 0.0514 0.0261 0.0135 0.0115
0.7419 0.5521 0.4120 0.3083 0.2314 0.1741
0.1314 0.0994 0.0754
0.7059 0.5000 0.3554 0.2534 0.1813 0.1301 0.0937 0.0676 0.0490
0.6989 0.4902 0.3450 0.2437 0.1727 0.1227 0.0875 0.0626 0.0449
0.6717 0.4529 0.3066 0.2083 0.1420 0.0972 0.0668 0.0460 0.0318
0.6060 0.3715 0.2281 0.1407 0.0872 0.0543
0.0213 0.0134
0.0339
0.1351 0.1117 0.0926 0.0768
0.0638 0.0531
0.1228 0.1007 0.0826
0.0680 0.0560 0.0462
0.1117 0.0907 0.0738 0.0601 0.0491 0.0402
0.1015 0.0817 0.0659 0.0532 0.0431 0.0349
0.0588 0.0471
0.0923 0.0736
0.0378 0.0304
0.2621 0.2072
0.2097 0.1594
0.1226
0.0943
0.0725
0.0443 0.0217 0.0109 0.0092
0.0382 0.0181 0.0088 0.0074
0.0329 0.0151 0.0071 0.0059
0.0284 0.0126 0.0057 0.0047
0.0245 0.0105 0.0046 0.0038
0.0573 0.0437 0.0334 0.0256 0.0196 0.0151 0.0116 0.0042 0.0016
0.0356 0.0259 0.0189 0.0139 0.0102 0.0075 0.0055 0.0017 0.0005
0.0323 0.0234 0.0169 0.0123 0.0089 0.0065 0.0048 0.0014
0.0221 0.0154 0.0107 0.0075 0.0053 0.0037 0.0026 0.0007
0.0085 0.0054 0.0035 0.0022 0.0014 0.0009 0.0006
.
0.0012
.
.
.
.
0.0150
0.0116
0.0089
0.0068
0.0053
0.0040
0.0031
0.0024
0.0018
0.0014
.

Period
1
2
3
4
5
6
7
8
9
10
14
15
16
17
18
19
20
3.1473
11 10.368 9.7868 9.2526 8.7605
8.3064 7.8869 7.4987 7.1390 6.8052 6.4951 6.2065 5.9377 5.6869 5.4527 5.2337 5.0286 4.3271 3.7757 3.6564
12 11.255 10.575 9.9540 9.3851 8.8633 8.3838 7.9427
7.5361 7.1607 6.8137
6.4924 6.1944
5.4206 5.1971 4.4392 3.8514 3.7251 3.1903
13 12.134 11.348 10.635 9.9856 9.3936 8.8527 8.3577 7.9038 7.4869 7.1034 6.7499 6.4235
5.5831 5.3423 4.5327 3.9124 3.7801 3.2233
13.004 12.106 11.296 10.563 9.8986 9.2950 8.7455 8.2442 7.7862 7.3667 6.9819 6.6282
5.7245 5.4675 4.6106 3.9616 3.8241 3.2487
13.865
12.849 11.938 11.118 10.380 9.7122 9.1079 8.5595 8.0607 7.6061 7.1909 6.8109
5.8474 5.5755 4.6755 4.0013 3.8503 3.2682
5.9176 5.6603
6.1218 5.8424
6.3025 6.0021
6.4624 6.1422
21
22
Table A-4 Present Value Interest Factors for a One-Dollar Annuity Discounted at k Percent for n Periods: PVIFA[1-1/(1+k)]/k
16%
20%
24%
25%
11%
12%
13%
14% 15%
0.9009 0.8929 0.8850 0.8772 0.8696
1.6901
0.8621 0.8333 0.8065 0.8000
1%
2%
3%
4%
5%
6%
7%
8%
9%
10%
30%
0.9901 0.9804 0.9709 0.9615 0.9524 0.9434 0.9346 0.9259 09174 0.9091
0.7692
1.9704 1.9416 1.9135 1.8861
1.8594 1.8334 1.8000 1.7833 1.7591 1.7355 1.7125
1.6681 1.6467 1.6257 1.6052 1.5278 1.4568 1.4400 1.3609
2.9410 2.8839 2.8286 2.7751 2.7232 2.6730 2.6243 2.5771 2.5313 2.4869 2.4437 2.4018 2.3612 2.3216 2.2832 2.2459 2.1065 1.9813 1.9520 1.8161
3.6299
3.5460 3.4651 3.3872 3.3121 3.2397 3.1699 3.1024 3.0373 2.9745
4.4518 4.3295 4.2124 4.1002 3.9927 3.8897 3.7908 3.6959
3.6048 3.5172
2.9137 2.8550 2.7982 2.5887 2.4043 2.3616 2.1662
3.4331 3.3522 3.2743 2.9906 2.7454 2.6893 2.4356
30
35
3.9020 3.8077 3.7171
4.8534 4.7135 4.5797
36
40
50
5.7955 5.6014
5.4172
5.2421
4.4859 4.3553 4.2305 4.1114
3.9975
3.6847
5.0757 4.9173 4.7665 4.6229
3.8887 3.7845
3.3255 3.0205 2.9514 2.6427
6.7282 6.4720 6.2303 6.0021 5.7864 5.5824 5.3893 5.2064 5.0330 4.8684 4.7122 4.5638 4.4226 4.2883
4.1604 4.0386 3.6046 3.2423 3.1611
2.8021
7.6517 7.3255 7.0197 6.7327
6.4632 6.2098 5.9713 5.7466 5.5348 5.3349 5.1461 4.9676 4.7988 4.6389 4.4873 4.3436 3.8372 3.4212 3.3289 2.9247
8.5660 8.1622
7.7861 7.4353 7.1078 6.8017 6.5152 6.2469 5.9952 5.7590 5.5370 5.3282 5.1317 4.9464 4.7716 4.6065 4.0310 3.5655 3.4631 3.0190
9.4713 8.9826 8.5302 8.1109 7.7217 7.3601 7.0236 6.7101 6.4177 6.1446 5.8892 5.6502 5.4262 5.2161 5.0188 4.8332 4.1925 3.6819 3.5705 3.0915
14.718 13.578 12.561 11.652
10.838 10.106 9.4466 8.8514 8.3126
15.562 14.292 13.166 12.166 11.274 10.477 9.7632
16.398 14.992 13.754 12.659 11.690 10.828
17.226 15.678 14.324 13.134 12.085 11.158
18.046 16.351 14.877 13.590 12.462 11.470
18.857
19.660
20.456 18.292
17.011
17.658
23
16.444
24 21.243 18.914 16.936
22.023 19.523
25
17.413
15.415
15.937
7.8237 7.3792 6.9740
9.1216 8.5436 8.0216 7.5488
10.059 9.3719 8.7556 8.2014
10.336 9.6036 8.9501 8.3649
10.594 9.8181 9.1285 8.5136
14.029 12.821 11.764
14.451 13.163 12.042
14.857 13.489 12.303
15.247 13.799 12.550 11.469 10.529 9.7066
15.622 14.094 12.783 11.654 10.675
10.836
11.061
11.272
9.8226
10.017 9.2922 8.6487 8.0751 7.5620 7.1016 6.6870 6.3125
10.201 9.4424 8.7715 8.1757 7.6446 7.1695 6.7429 6.3587
10.371 9.5802 8.8832 8.2664 7.7184 7.2297 6.7921 6.3988
8.9847 8.3481 7.7843 7.2829 6.8351 6.4338
9.0770 8.4217 7.8431 7.3300 6.8729 6.4641
6.6039 6.2651 5.9542
7.1196 6.7291 6.3729 6.0472
7.7016 7.2497 6.8399 6.4674 6.1280
7.8393 7.3658 6.9380 6.5504 6.1982
7.9633 7.4694 7.0248 6.6231 6.2593
25.808 22.396 19.600 17.292 15.372 13.765 12.409 11.258 10.274
29.409 24.999 21.487 18.665 16.374 14.498 12.948 11.655 10.567
30.108 25.489 21.832 18.908 16.547 14.621 13.035 11.717 10.612
32.835 27.355 23.115 19.793 17.159 15.046 13.332 11.925 10.757
39.196 31.424 25.730 21.482 18.256 15.762 13.801 12.233 10.962
5.6685 4.7296 4.0333 3.8874 3.2832
5.7487 4.7746 4.0591 3.9099 3.2948
5.8178 4.8122 4.0799 3.9279 3.3037
5.8775 4.8435 4.0967 3.9424 3.3105
5.9288 4.8696 4.1103 3.9539 3.3158
5.9731 4.8913 4.1212 3.9631 3.3198
6.0113 4.9094 4.1300 3.9705
3.3230
6.0442 4.9245 4.1371 3.9764 3.3254
6.0726 4.9371 4.1428 3.9811 3.3272
6.0971 4.9476 4.1474 3.9849 3.3286
3.3321
9.4269 8.6938 8.0552
7.4957 7.0027 6.5660 6.1772 4.9789 4.1601 3.9950
9.6442 8.8552 8.1755 7.5856 7.0700 6.6166 6.2153 4.9915 4.1644 3.9984 3.3330
9.6765 8.8786 8.1924 7.5979 7.0790 6.6231 6.2201 4.9929 4.1649 3.9987 3.3331
9.7791 8.9511 8.2438 7.6344 7.1050 6.6418 6.2335 4.9966 4.1659 3.9995
9.9148 9.0417 8.3045 7.6752 7.1327 6.6605 6.2463 4.9995 4.1666 3.9999
3.3332
3.3333

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Follow-up Question

2. Using the Interpolation Method to calculate the YTM for the below Bonds:
> The par value $18000
> Coupon Rate 10% every year
> Maturity period 10 years
> Market Value of bond $21800

Solution

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