IRD Determination G3: Yield to Maturity Method for Bonds (worked example)

[Snoopy]

There must be more to this than what our table is showing at first glance. So some of my own thought processes, as I try to get a handle on what is going on, will follow.

That first $70k coupon payment was 'not fully earned' by our investor, because our investor bought into the bond part way through that first shown investment period (on 12-03-1987, which was 64 days before the ex-coupon pay date). Put another way, our investor was only entitled to part of that 'investment coupon payment'. Rather than have our investor refund part of that payment to the previous owner of that bond, 'the bond market' deals with this situation in a different way to the sharemarket.

IF this was a share poised to pay a $70k dividend on the ex-dividend date, THEN as a 'share owner', one would expect the market value of one's shares to drop by $70k after the share ex-dividend date (all other factors in the market being equal). But this isn't what happens on the bond market. Instead, the market prices a bond in such a way that any 'coupon payment' is, in this case, spread across each of the days in the half year between actual coupon payments occurring, on an equal basis. Thus the 'refund' that 'our bond owner' was due to make to 'the previous bond owner' was incorporated into the capital price our new bond owner paid for the bond on market. In this way, the 'income loss', required to be paid back to the former bond owner, by our new bond investor, has been 'adjusted for' by our new bond investor taking an equivalent 'capital loss'. And the way our new investor takes this 'capital loss' on market, is to pay a 'capital premium' above the value for the underlying capital asset.

Thus from an IRD tax 'currently owned bond investor perspective', both 'capital gains and/or losses' and 'coupon payments' get mixed up into one 'payment pot'. How much did our bond investor 'earn' during that 64 day portion of the half year ownership period during which our bond investor made their bond purchase? It is all based on a constant annual rate R which we are told is 16.2308% (this number is too difficult for you plebs reading the IRD documentation to work out. So just accept what we, the IRD, tell you., O.K.?)

All right, I admit the IRD did not actually state that bit in brackets. But that is my take on what was implied. I am calling BS on this 'patronizing position' as espoused by the IRD. In order to calculate this 'constant annual return rate' you need to know the opening capital value of each bond when it was first set up. I had naively assumed that this must have been the same as the capital value paid back at maturity. But this assumption must be wrong (see my post 23). Since we are not given the opening capital value position of the bond, we do not know how much capital was 'lost' at repayment time. And if we don't know how much capital was lost, that means we do not have the information needed to calculate the constant annual return rate 'R' over any time period. Thus we are forced to accept the constant annual return rate figure of 16.2308% figure is 'true', with no way to verify that figure.

Maybe I am reading this whole thing the wrong way. But I think this apparent lack of disclosure by the IRD on this matter in what purports to be an 'explanatory determination' is disgraceful for a worked example that is there to show 'we plebs' how interest income should be distributed over multiple time periods.

From the referenced IRD document:
"In general there is no explicit formula for a yield to maturity in terms of the cashflows."

So what is this then?
https://www.wallstreetmojo.com/yield...y-ytm-formula/

YTM = [C + (F-P)/n] / [(F+P)/2]

SNOOPY