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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?
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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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