Question

With celebrity​ bonds, celebrities raise money by issuing bonds to investors. The royalties from sales of the music are used to pay interest and principal on the bonds. In April of​ 2009, EMI announced that it intended to securitize its back catalogue with the help of the Bank of Scotland. The bond was issued with a coupon rate of 6.7​% and will mature on this day 38 years from now. The yield on the bond issue is currently 6.4%. At what price should this bond trade​ today, assuming a face value of $1,000 and annual​ coupons?

What is the percentage change in price for a zero coupon bond if the yield changes from 6.5​% to 8.5​%? The bond has a face value of $1,000 and it matures in 8 years. Use the price determined from the first​ yield, 6.5%, as the base in the percentage calculation.

Answer 1

Part A:

Value of Bond = PV of CFs from it.

Year	CF	PVF @6.4%	Disc CF
1	$      67.00	0.9398	$      62.97
2	$      67.00	0.8833	$      59.18
3	$      67.00	0.8302	$      55.62
4	$      67.00	0.7802	$      52.28
5	$      67.00	0.7333	$      49.13
6	$      67.00	0.6892	$      46.18
7	$      67.00	0.6478	$      43.40
8	$      67.00	0.6088	$      40.79
9	$      67.00	0.5722	$      38.34
10	$      67.00	0.5378	$      36.03
11	$      67.00	0.5054	$      33.86
12	$      67.00	0.4750	$      31.83
13	$      67.00	0.4464	$      29.91
14	$      67.00	0.4196	$      28.11
15	$      67.00	0.3943	$      26.42
16	$      67.00	0.3706	$      24.83
17	$      67.00	0.3483	$      23.34
18	$      67.00	0.3274	$      21.93
19	$      67.00	0.3077	$      20.62
20	$      67.00	0.2892	$      19.38
21	$      67.00	0.2718	$      18.21
22	$      67.00	0.2554	$      17.11
23	$      67.00	0.2401	$      16.08
24	$      67.00	0.2256	$      15.12
25	$      67.00	0.2121	$      14.21
26	$      67.00	0.1993	$      13.35
27	$      67.00	0.1873	$      12.55
28	$      67.00	0.1760	$      11.80
29	$      67.00	0.1655	$      11.09
30	$      67.00	0.1555	$      10.42
31	$      67.00	0.1462	$        9.79
32	$      67.00	0.1374	$        9.20
33	$      67.00	0.1291	$        8.65
34	$      67.00	0.1213	$        8.13
35	$      67.00	0.1140	$        7.64
36	$      67.00	0.1072	$        7.18
37	$      67.00	0.1007	$        6.75
38	$      67.00	0.0947	$        6.34
38	$1,000.00	0.0947	$      94.67
Value of Bond	$1,042.44

Part B:

Value of Zero Coupon Bond = Maturity Value * PVF (r%, n)

Price @ 6.5%:

= $ 1000 * PVF(6.5%, 8)

= $ 1000 * 0.6042

= $ 604.2

Price @ 8.5%:

= $ 1000 * PVF(8.5%, 8)

= $ 1000 * 0.5207

= $ 520.7

% Change in Price = [ Price @ 8.5% - Price @ 6.5% ] Price @ 6.5%

= [ 520.7 - 604.2 ] / 604.2

= - 83.53 / 604.2

= -0.1383 i.e -13.83%