Question

Kilgore Natural Gas has $1,000 par value bonds outstanding at 12% interest. The bonds will mature in 50 years. Compute the current price of the bonds if the yields to maturity (YTM) is 14 percent. Assume annual coupon payments.

Answer 1

Given,
Face value of bonds	$1,000
Coupon rate	12%
Maturity	50 years
Yield to maturity	14%
Explaination: We know that price of a bond today would be the PV of future cash inflows discounted at the required rate of return i.e. YTM.
Annual cashflow= Coupon payments= $1000*12%= $120
Terminal cashflow= Coupon payments+ Face value= $1000+$120= $1120
Year	Cashflow	Discounting factor @ 14%	PV of cashflows
1	120	0.877192982	105.2631579
2	120	0.769467528	92.33610342
3	120	0.674971516	80.99658194
4	120	0.592080277	71.04963328
5	120	0.519368664	62.32423972
6	120	0.455586548	54.67038572
7	120	0.399637323	47.9564787
8	120	0.350559055	42.06708658
9	120	0.307507943	36.90095314
10	120	0.26974381	32.36925714
11	120	0.236617377	28.39408521
12	120	0.207559102	24.90709229
13	120	0.182069388	21.84832657
14	120	0.15970999	19.16519875
15	120	0.140096482	16.81157785
16	120	0.122891651	14.74699811
17	120	0.107799694	12.93596326
18	120	0.094561135	11.34733619
19	120	0.082948364	9.953803675
20	120	0.072761723	8.731406733
21	120	0.063826073	7.659128713
22	120	0.055987783	6.718533959
23	120	0.04911209	5.893450841
24	120	0.043080781	5.16969372
25	120	0.037790159	4.534819053
26	120	0.033149262	3.97791145
27	120	0.0290783	3.489396009
28	120	0.025507281	3.060873692
29	120	0.022374808	2.684976923
30	120	0.019627024	2.355242915
31	120	0.017216688	2.066002557
32	120	0.015102358	1.812282944
33	120	0.013247682	1.589721881
34	120	0.011620774	1.394492878
35	120	0.010193661	1.223239367
36	120	0.008941808	1.073016988
37	120	0.007843691	0.941242972
38	120	0.006880431	0.82565173
39	120	0.006035466	0.724255904
40	120	0.005294268	0.635312196
41	120	0.004644095	0.5572914
42	120	0.004073768	0.488852105
43	120	0.00357348	0.428817636
44	120	0.003134632	0.376155821
45	120	0.002749677	0.329961247
46	120	0.002411997	0.28943969
47	120	0.002115787	0.253894465
48	120	0.001855954	0.222714443
49	120	0.00162803	0.195363546
50	1120	0.001428096	1.599467632
		Price today	857.35