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A 30-year maturity, 8% coupon bond paying coupons semiannually is callable in 5 years at a...

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?

Solutions

Expert Solution

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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