Question

12- You are interested in purchasing a 30-year, semi-annual bond with a current market price of $1015.75. If the yield to maturity is 6.85% and the face value is $1,000, what must the coupon rate be on the bond? (6.97%) 13- Suppose a 7.75% coupon bond with 15 years to maturity and a face value of $1,000 presently has a yield to maturity of 7.25%. Assuming annual interest payments, what is the price of the bond? ($1,044.83)

Answer 1

Bond Price = PV of CFs from it.

Let X be the semi annual Coupon amount.

Period	CF	[email protected]%	Disc CF
1	X	0.9669	0.9669X
2	X	0.9349	0.9349X
3	X	0.9039	0.9039X
4	X	0.8740	0.874X
5	X	0.8450	0.845X
6	X	0.8170	0.817X
7	X	0.7900	0.79X
8	X	0.7638	0.7638X
9	X	0.7385	0.7385X
10	X	0.7141	0.7141X
11	X	0.6904	0.6904X
12	X	0.6676	0.6676X
13	X	0.6455	0.6455X
14	X	0.6241	0.6241X
15	X	0.6034	0.6034X
16	X	0.5834	0.5834X
17	X	0.5641	0.5641X
18	X	0.5454	0.5454X
19	X	0.5274	0.5274X
20	X	0.5099	0.5099X
21	X	0.4930	0.493X
22	X	0.4767	0.4767X
23	X	0.4609	0.4609X
24	X	0.4456	0.4456X
25	X	0.4309	0.4309X
26	X	0.4166	0.4166X
27	X	0.4028	0.4028X
28	X	0.3895	0.3895X
29	X	0.3766	0.3766X
30	X	0.3641	0.3641X
31	X	0.3521	0.3521X
32	X	0.3404	0.3404X
33	X	0.3291	0.3291X
34	X	0.3182	0.3182X
35	X	0.3077	0.3077X
36	X	0.2975	0.2975X
37	X	0.2876	0.2876X
38	X	0.2781	0.2781X
39	X	0.2689	0.2689X
40	X	0.2600	0.26X
41	X	0.2514	0.2514X
42	X	0.2431	0.2431X
43	X	0.2350	0.235X
44	X	0.2272	0.2272X
45	X	0.2197	0.2197X
46	X	0.2124	0.2124X
47	X	0.2054	0.2054X
48	X	0.1986	0.1986X
49	X	0.1920	0.192X
50	X	0.1857	0.1857X
51	X	0.1795	0.1795X
52	X	0.1736	0.1736X
53	X	0.1678	0.1678X
54	X	0.1623	0.1623X
55	X	0.1569	0.1569X
56	X	0.1517	0.1517X
57	X	0.1467	0.1467X
58	X	0.1418	0.1418X
59	X	0.1371	0.1371X
60	X	0.1326	0.1326X
60	1000	0.1326	132.58
Bond Price			25.3262X + 132.58

Thus 25.3262X+ 132.58 = 1015.75

25.3262X = 1015.75 - 132.58

= 883.17

X = 883.17 / 25.3262

= 34.87

Annual Coupon = 34.87 * 2

= 69.74

Coupon Rate = Coupon AMount / Face Value

= 69.74 / 1000

= 0.0697 i.e 6.97%

Part B:

Price of Bond = PV of CFs from it.

Year	CF	PVF @7.25%	Disc CF
1	$      77.50	0.9324	$      72.26
2	$      77.50	0.8694	$      67.38
3	$      77.50	0.8106	$      62.82
4	$      77.50	0.7558	$      58.58
5	$      77.50	0.7047	$      54.62
6	$      77.50	0.6571	$      50.92
7	$      77.50	0.6127	$      47.48
8	$      77.50	0.5712	$      44.27
9	$      77.50	0.5326	$      41.28
10	$      77.50	0.4966	$      38.49
11	$      77.50	0.4631	$      35.89
12	$      77.50	0.4318	$      33.46
13	$      77.50	0.4026	$      31.20
14	$      77.50	0.3754	$      29.09
15	$      77.50	0.3500	$      27.12
15	$ 1,000.00	0.3500	$    349.98
Bond Price			$ 1,044.83

Pls comment, if any further assistance is required.