Question

Bond P is a premium bond with a coupon of 6.3 percent , a YTM of 6.59 percent, and 19 years to maturity. Bond D is a discount bond with a coupon of 6.3 percent, a YTM of 9.91 percent, and also 19 years to maturity. If interest rates remain unchanged, what is the difference in the prices of these bonds 4 year from now? (i.e., Price of Bond P - Price of Bond D) Note: Corporate bonds pay coupons twice a year.

Answer 1

Price after 4 years = Balance period i.e., 15 years

Price of Bond P

Period	CF	[email protected]%	Disc CF
1	$      31.50	0.9681	$   30.50
2	$      31.50	0.9372	$   29.52
3	$      31.50	0.9073	$   28.58
4	$      31.50	0.8784	$   27.67
5	$      31.50	0.8504	$   26.79
6	$      31.50	0.8232	$   25.93
7	$      31.50	0.7970	$   25.10
8	$      31.50	0.7716	$   24.30
9	$      31.50	0.7469	$   23.53
10	$      31.50	0.7231	$   22.78
11	$      31.50	0.7000	$   22.05
12	$      31.50	0.6777	$   21.35
13	$      31.50	0.6561	$   20.67
14	$      31.50	0.6352	$   20.01
15	$      31.50	0.6149	$   19.37
16	$      31.50	0.5953	$   18.75
17	$      31.50	0.5763	$   18.15
18	$      31.50	0.5579	$   17.57
19	$      31.50	0.5401	$   17.01
20	$      31.50	0.5229	$   16.47
21	$      31.50	0.5062	$   15.95
22	$      31.50	0.4901	$   15.44
23	$      31.50	0.4744	$   14.94
24	$      31.50	0.4593	$   14.47
25	$      31.50	0.4446	$   14.01
26	$      31.50	0.4305	$   13.56
27	$      31.50	0.4167	$   13.13
28	$      31.50	0.4034	$   12.71
29	$      31.50	0.3906	$   12.30
30	$      31.50	0.3781	$   11.91
30	$1,000.00	0.3781	$ 378.11
Price of Bond P	$ 972.63

Price of Bond D

Period	CF	[email protected]%	Disc CF
1	$      31.50	0.9528	$   30.01
2	$      31.50	0.9078	$   28.60
3	$      31.50	0.8649	$   27.25
4	$      31.50	0.8241	$   25.96
5	$      31.50	0.7852	$   24.73
6	$      31.50	0.7481	$   23.57
7	$      31.50	0.7128	$   22.45
8	$      31.50	0.6792	$   21.39
9	$      31.50	0.6471	$   20.38
10	$      31.50	0.6166	$   19.42
11	$      31.50	0.5874	$   18.50
12	$      31.50	0.5597	$   17.63
13	$      31.50	0.5333	$   16.80
14	$      31.50	0.5081	$   16.01
15	$      31.50	0.4841	$   15.25
16	$      31.50	0.4613	$   14.53
17	$      31.50	0.4395	$   13.84
18	$      31.50	0.4187	$   13.19
19	$      31.50	0.3990	$   12.57
20	$      31.50	0.3801	$   11.97
21	$      31.50	0.3622	$   11.41
22	$      31.50	0.3451	$   10.87
23	$      31.50	0.3288	$   10.36
24	$      31.50	0.3133	$     9.87
25	$      31.50	0.2985	$     9.40
26	$      31.50	0.2844	$     8.96
27	$      31.50	0.2710	$     8.54
28	$      31.50	0.2582	$     8.13
29	$      31.50	0.2460	$     7.75
30	$      31.50	0.2344	$     7.38
30	$1,000.00	0.2344	$ 234.37
Price of Bond D	$ 721.10

Difference in price of the bonds = Price of Bond P - Price of Bond D

= $ 972.63 - $ 721.10

= $ 251.53

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