Question

The price of a 30-year bond with an 8% coupon rate and $1,000 par will _____ when the yield rises from 8% to 9%?

A) increase of $103 C) decrease of $103

B) increase of $73 D) decrease of $73

Answer 1

Price of Bond If Coupon rate 8% & YTM is 8%:

$ 1000

If Coupon Rate and YTM are equal Bond Price will be Maturity Value.

Thus Price is $ 1000

Price of Bond If Coupon rate 8% & YTM is 9%:

Price of Bond = PV of CFs from it.

Year	CF	PVF @9%	Disc CF
1	$      80.00	0.9174	$   73.39
2	$      80.00	0.8417	$   67.33
3	$      80.00	0.7722	$   61.77
4	$      80.00	0.7084	$   56.67
5	$      80.00	0.6499	$   51.99
6	$      80.00	0.5963	$   47.70
7	$      80.00	0.5470	$   43.76
8	$      80.00	0.5019	$   40.15
9	$      80.00	0.4604	$   36.83
10	$      80.00	0.4224	$   33.79
11	$      80.00	0.3875	$   31.00
12	$      80.00	0.3555	$   28.44
13	$      80.00	0.3262	$   26.09
14	$      80.00	0.2992	$   23.94
15	$      80.00	0.2745	$   21.96
16	$      80.00	0.2519	$   20.15
17	$      80.00	0.2311	$   18.49
18	$      80.00	0.2120	$   16.96
19	$      80.00	0.1945	$   15.56
20	$      80.00	0.1784	$   14.27
21	$      80.00	0.1637	$   13.10
22	$      80.00	0.1502	$   12.01
23	$      80.00	0.1378	$   11.02
24	$      80.00	0.1264	$   10.11
25	$      80.00	0.1160	$      9.28
26	$      80.00	0.1064	$      8.51
27	$      80.00	0.0976	$      7.81
28	$      80.00	0.0895	$      7.16
29	$      80.00	0.0822	$      6.57
30	$      80.00	0.0754	$      6.03
30	$ 1,000.00	0.0754	$   75.37
Price of Bond			$ 897.26

Diff = $ 1000 - $ 897

If YTM increased from 8% to 9%, Bond Price decreased by $ 103.