Asia Perpetual Bonds

I need a volunteer mathematician to unravel this one please.

I got bogged down!!!

I want to know a formula to determine how much wealth is lent and how much gets repaid by these bonds. Clearly, since the capital is fixed in currency terms they lose all of the wealth invested on the capital side. But how much wealth gets paid back?

1) If the interest rate never changes and (a) ifAEG% = 0 %, or (b) AEG% is fixed, or (c) AEG% is variable
2) If the true interest rate is fixed
3) If everything is variable

How about a perpetual index-linked to AEG bond paying a fixed true interest rate?
Would those sell?

------------------------------

http://www.asiacreditadvisors.com/uploads/1/0/6/3/10638261/2013-02-25_scmp_perpetual_bonds.pdf

The above item discusses bonds in issue now with no maturity date.

Mathematically, how do these work?

Look at the Maths section of the Ingram Blogs to find out.

Here is a summary:

P% = C% + D% + I%

Where P% in this case would be the interest rate paid on the bond.

So r% = C% + D% + I%

It has three components:
The Capital value repaid C% p.a.
D% p.a. is the rate at which the cost of the interest payments r% (in currency) gets cheaper to pay - this is the rate at which average incomes are rising. So D% = AEG% p.a. This remains fixed until r% changes.
and
I% - the rate of interest (if any) above AEG% p.a.

So how does this work out?
r% = C% + AEG% + (P% - AEG%)
If r% = AEG% we get"
r% = C% + AEG%
So C% = r% - AEG% = 0% p.a.

If r% <> AEG% we get:
0% = C% p.a.

Either way, no capital value is repaid. But r% is not zero.
and r% = AEG% + I%
So I% = r% - AEG%

So we have:
r% = 0% + AEG% + r% - AEG%
Hmmm
0% = 0%

At least the equations are consistent!

Let's try another way.
What happens to the capital value of the bond over time?
It is fixed in money value, so it vanishes over time due to a constantly average income.
Bond issuers LOVE high AEG.
What about the interest paid, what is that worth?

They say that the interest gets adjusted to market rates. What are market rates?
If they have not been distorted than the rate of transfer of wealth from the lender to the investor W% p.a.  is given by I% p.a. x L (the sum invested) - the rate of loss of wealth  = AEG% p.a. x L (the sum invested)

W% = I%.L - AEG%.L = L x (I% - AEG%)

I% = P% - AEG%

So W% = L x (P% - 2 x AEG%)
 or if you prefer:
W% = L x (r% - 2 x AEG%)
If W% p.a. = W/ L x 100% p.a. we get:
W p.a. = W% x L / 100%
W p.a. = L x (r% - 2 x AEG%) x L / 100%

W p.a. =