Question

1. What is the price of a 25-year sovereign bond with a 4.5 per cent yield with annual coupons of 3.5 per cent and a £1,000 face value? How do you define a sovereign bond? Take the above bond in and determine what would be the price of this bond if it paid no coupons? How would you define this type of bond? What would be the benefits for a corporation to issue a bond with no coupons?

Answer 1

Price of a bond = PV of CFs from it.

Year	CF	PVF @4.5%	Disc CF
1	£       35.00	0.9569	£   33.49
2	£       35.00	0.9157	£   32.05
3	£       35.00	0.8763	£   30.67
4	£       35.00	0.8386	£   29.35
5	£       35.00	0.8025	£   28.09
6	£       35.00	0.7679	£   26.88
7	£       35.00	0.7348	£   25.72
8	£       35.00	0.7032	£   24.61
9	£       35.00	0.6729	£   23.55
10	£       35.00	0.6439	£   22.54
11	£       35.00	0.6162	£   21.57
12	£       35.00	0.5897	£   20.64
13	£       35.00	0.5643	£   19.75
14	£       35.00	0.5400	£   18.90
15	£       35.00	0.5167	£   18.09
16	£       35.00	0.4945	£   17.31
17	£       35.00	0.4732	£   16.56
18	£       35.00	0.4528	£   15.85
19	£       35.00	0.4333	£   15.17
20	£       35.00	0.4146	£   14.51
21	£       35.00	0.3968	£   13.89
22	£       35.00	0.3797	£   13.29
23	£       35.00	0.3634	£   12.72
24	£       35.00	0.3477	£   12.17
25	£       35.00	0.3327	£   11.65
25	£ 1,000.00	0.3327	£ 332.73
Price of Bond	£ 851.72

Price of Bond if it doesn't Pay coupon amount = Maturity Value * PVF(r%, n)

= £ 1000 * PVF ( 4.5%, 25 )

= £ 1000 * 0.3327

= £ 332.7

This type of bond is called as Zero Coupon Bond. These type of Bonds will not pay coupon amounts till its maturity. Hence These bonds will be quoted at discount.

Benifit to corporation:

Corporation can differ the payment to later years. This bond not required to pay anything for a period of 25 years other than maturity amount. It will be viable for the corporation facing problems in short term.

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