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A 30-year maturity, 8% coupon bond paying coupons semiannually is callable in 5 years at a call price of $1100. The bond currently sells at a yield to maturity (YTM) of 7% (3.5% per half-year). What is the yield to call? How does it relate to the YTM? Why?
Bond Price = PV of CFs from it.
Period | CF | PVF @3.5% | Disc CF |
1 | $ 40.00 | 0.9662 | $ 38.65 |
2 | $ 40.00 | 0.9335 | $ 37.34 |
3 | $ 40.00 | 0.9019 | $ 36.08 |
4 | $ 40.00 | 0.8714 | $ 34.86 |
5 | $ 40.00 | 0.8420 | $ 33.68 |
6 | $ 40.00 | 0.8135 | $ 32.54 |
7 | $ 40.00 | 0.7860 | $ 31.44 |
8 | $ 40.00 | 0.7594 | $ 30.38 |
9 | $ 40.00 | 0.7337 | $ 29.35 |
10 | $ 40.00 | 0.7089 | $ 28.36 |
11 | $ 40.00 | 0.6849 | $ 27.40 |
12 | $ 40.00 | 0.6618 | $ 26.47 |
13 | $ 40.00 | 0.6394 | $ 25.58 |
14 | $ 40.00 | 0.6178 | $ 24.71 |
15 | $ 40.00 | 0.5969 | $ 23.88 |
16 | $ 40.00 | 0.5767 | $ 23.07 |
17 | $ 40.00 | 0.5572 | $ 22.29 |
18 | $ 40.00 | 0.5384 | $ 21.53 |
19 | $ 40.00 | 0.5202 | $ 20.81 |
20 | $ 40.00 | 0.5026 | $ 20.10 |
21 | $ 40.00 | 0.4856 | $ 19.42 |
22 | $ 40.00 | 0.4692 | $ 18.77 |
23 | $ 40.00 | 0.4533 | $ 18.13 |
24 | $ 40.00 | 0.4380 | $ 17.52 |
25 | $ 40.00 | 0.4231 | $ 16.93 |
26 | $ 40.00 | 0.4088 | $ 16.35 |
27 | $ 40.00 | 0.3950 | $ 15.80 |
28 | $ 40.00 | 0.3817 | $ 15.27 |
29 | $ 40.00 | 0.3687 | $ 14.75 |
30 | $ 40.00 | 0.3563 | $ 14.25 |
31 | $ 40.00 | 0.3442 | $ 13.77 |
32 | $ 40.00 | 0.3326 | $ 13.30 |
33 | $ 40.00 | 0.3213 | $ 12.85 |
34 | $ 40.00 | 0.3105 | $ 12.42 |
35 | $ 40.00 | 0.3000 | $ 12.00 |
36 | $ 40.00 | 0.2898 | $ 11.59 |
37 | $ 40.00 | 0.2800 | $ 11.20 |
38 | $ 40.00 | 0.2706 | $ 10.82 |
39 | $ 40.00 | 0.2614 | $ 10.46 |
40 | $ 40.00 | 0.2526 | $ 10.10 |
41 | $ 40.00 | 0.2440 | $ 9.76 |
42 | $ 40.00 | 0.2358 | $ 9.43 |
43 | $ 40.00 | 0.2278 | $ 9.11 |
44 | $ 40.00 | 0.2201 | $ 8.80 |
45 | $ 40.00 | 0.2127 | $ 8.51 |
46 | $ 40.00 | 0.2055 | $ 8.22 |
47 | $ 40.00 | 0.1985 | $ 7.94 |
48 | $ 40.00 | 0.1918 | $ 7.67 |
49 | $ 40.00 | 0.1853 | $ 7.41 |
50 | $ 40.00 | 0.1791 | $ 7.16 |
51 | $ 40.00 | 0.1730 | $ 6.92 |
52 | $ 40.00 | 0.1671 | $ 6.69 |
53 | $ 40.00 | 0.1615 | $ 6.46 |
54 | $ 40.00 | 0.1560 | $ 6.24 |
55 | $ 40.00 | 0.1508 | $ 6.03 |
56 | $ 40.00 | 0.1457 | $ 5.83 |
57 | $ 40.00 | 0.1407 | $ 5.63 |
58 | $ 40.00 | 0.1360 | $ 5.44 |
59 | $ 40.00 | 0.1314 | $ 5.26 |
60 | $ 40.00 | 0.1269 | $ 5.08 |
60 | $ 1,000.00 | 0.1269 | $ 126.93 |
Bond Price | $ 1,124.72 |
YTC is the Rate at which PV of Cash inflows are equal to Bond Price. when the bond is called.
Period | CF | [email protected]% | Disc CF | PVF @3% | Disc CF |
0 | $ -1,124.72 | 1.0000 |
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