In: Finance
A 20-year 10% semi-annual-coupon bond has a face (and redemption) value of $1,000. Find the price of the bond, assuming a nominal annual interest rate of 12% convertible semiannually
[I am not good at this class so a thorough write out on paper would be most beneficial to me]
Answer: 849.54 [Provided on the homework, but i don't know how to solve]
Period | Discounting
Factor [1/(1.06^period)] |
Discounting
Factor Annuity (Sum of discounting factor & all previous discounting factors) |
1 | 0.943396226 | 0.943396226 |
2 | 0.88999644 | 1.833392666 |
3 | 0.839619283 | 2.673011949 |
4 | 0.792093663 | 3.465105613 |
5 | 0.747258173 | 4.212363786 |
6 | 0.70496054 | 4.917324326 |
7 | 0.665057114 | 5.58238144 |
8 | 0.627412371 | 6.209793811 |
9 | 0.591898464 | 6.801692274 |
10 | 0.558394777 | 7.360087051 |
11 | 0.526787525 | 7.886874577 |
12 | 0.496969364 | 8.38384394 |
13 | 0.468839022 | 8.852682963 |
14 | 0.442300964 | 9.294983927 |
15 | 0.417265061 | 9.712248988 |
16 | 0.393646284 | 10.10589527 |
17 | 0.371364419 | 10.47725969 |
18 | 0.350343791 | 10.82760348 |
19 | 0.33051301 | 11.15811649 |
20 | 0.311804727 | 11.46992122 |
21 | 0.294155403 | 11.76407662 |
22 | 0.277505097 | 12.04158172 |
23 | 0.261797261 | 12.30337898 |
24 | 0.246978548 | 12.55035753 |
25 | 0.232998631 | 12.78335616 |
26 | 0.219810029 | 13.00316619 |
27 | 0.207367952 | 13.21053414 |
28 | 0.195630143 | 13.40616428 |
29 | 0.184556739 | 13.59072102 |
30 | 0.174110131 | 13.76483115 |
31 | 0.16425484 | 13.92908599 |
32 | 0.154957397 | 14.08404339 |
33 | 0.146186223 | 14.23022961 |
34 | 0.137911531 | 14.36814114 |
35 | 0.130105218 | 14.49824636 |
36 | 0.122740772 | 14.62098713 |
37 | 0.115793181 | 14.73678031 |
38 | 0.10923885 | 14.84601916 |
39 | 0.103055519 | 14.94907468 |
40 | 0.097222188 | 15.04629687 |
Coupons pending = Time till maturity = 20 years = 20*2(because smi-annually) = 40 Coupons
Price of Bond = PV of All Coupons + PV of Maturity Value
= [Coupon*Annuity Factor] + [Maturity Value*Discounting Factor]
= [1000*5%*15.04629687] + [1000*0.097222188] = 752.3148 + 97.222 = $849.5368 = $849.54