Question

In: Finance

A 20-year 10% semi-annual-coupon bond has a face (and redemption) value of $1,000. Find the price...

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]

Solutions

Expert Solution

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


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