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Index-linked bonds. Coupon calculation. Q11-Sept 2006, Q7-Apr 2004

A

aika1

Member
Hi,

I am a little bit confused with calculation of the actual coupons on the index-linked bonds:

For instance, past exam September 2006 (q.11).
-On 1 July 2002, the government of a country issued an index-linked bond of
term seven years. Coupons are paid half-yearly in arrears on 1 January and 1
July each year. The annual nominal coupon is 2%. Interest and capital
payments are indexed by reference to the value of an inflation index with a
time lag of eight months.
Date Inflation index
November 2001: 110.0
May 2002: 112.3
November 2002: 113.2
May 2003: 113.8

I understand that to find the actual amount of coupon say for 31/12/2003 we need to multiply coupon=1 by ‘Index May 2003’ and divide by ‘Index November 2001’.
What I don’t understand is why the coupon should be multiplied by 0.8.
The official solution is: 0.8×1× (Index May 2003/Index November 2001)=
0.8×1×113.8/110

However, here is a similar question from April 2004 (q.7).
A government issued a number of index-linked bonds on 1 June 2000 which were redeemed on 1 June 2002. Each bond had a nominal coupon rate of 3% per annum, payable half yearly in arrears, and a nominal redemption price of 100. The actual coupon and redemption payments were indexed according to the increase in the retail price index between 6 months before the bond issue date and 6 months before the coupon or redemption payment dates.
The values of the retail price index in the relevant months were:
Date Retail price index
December 1999: 100
June 2000: 102
December 2000: 107
June 2001: 111
December 2001: 113
June 2002: 118.


In the solution provided the coupon at 1 December 2000 is 1.530 (ie. 1.5×(Index June 2000/Index December 1999), I mean it is not multiplied by any other number, in contrary to the previous example.

My concern and questions then are:
1) If and when we need to multiple the coupon by another number?
2) What is the meaning of 0.8 in the first example, how to interpret it? How it is derived? I mean if it is 8 months ×0.1, then where this 0.1 comes from?

Hope someone can clarify.
Thank you.
 
From the question,

An investor, paying tax at the rate of 20% on coupons only, purchased the
stock on 1 July 2003, just after a coupon payment had been made.

Calculate the price to this investor such that a real net yield of 3% per annum
convertible half yearly is obtained and assuming that the investor holds the
bond to maturity.

0.8 = amount left after 20% tax.
 
I see now, it was so simple :)

Now when I look at your explanation I cannot understand how I could miss tax issue involved. I see that I need to read the problems more carefully in order not to miss any information and don't make silly mistakes.

Thanks a lot! you saved a day for me...
 
I am not following this example well.

I am not able to understand the v/(1+r) factor.

The first coupon payment that the investor receives is on 31st dec 2003. Whereas the increment in the indexation has been effective since May 2003 per annum. So is 1 year being considered as may 2003 to may 2004?

How is the real present value being calculated?

Can someone explain the whole example in detail?

Thanks,
Bijal
 
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