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

[Snoopy]

The next step is to find out how this information relates to the tabulated information in 'Determination G3'.

Below is the first table, exactly as it appears in Determination G3.

Period Ending	Principal Outstanding	Income in Respect of Period	Payments Received at End of Period
15-05-1987	$1,012,500	$28,815	$70,000
15-11-1987	$971,315	$78,826	$70,000
15-05-1988	$980,141	$79,542	$70,000
15-11-1988	$989,638	$80,317	$1,070,000
Total		$267,500	$1,280,000

The periods are split into six monthly intervals, which is a strange thing to do as tax years always have twelve months. Nevertheless I will go with the numbers 'as presented' and see what comes out.

The first period, ending 15-05-1987, represents 64 days (refer post 2) of a half year period over which $70k of interest would be paid to the bondholder, if they had held those bonds for 6 months. But since they only held those bonds for 64days, their share of that interest would be: $70,000 x [64/(365x0.5)]= $24,547.95

The total capital gain held by our investor over the whole investment period was:

($1,280,000 - 4x$70.000) - $1,012,500 = -$12,500 (i.e. a loss)
This represents a loss of -$12,500/[64+1.5x365] = -$20.44 per day

Yet for income tax purposes, we must add (adding a negative number is subtraction) to this $24,547.95, the portion of 'extra capital' our bondholder will get back that has been apportioned to this period: 64x-$20.44=-$1,308.16. So taxable earnings for the initial period reduce to: $24,547.95-$1,308.16=$23,239.79

Now we move on to the three six monthly income periods. Interest income for each of those is $70,000. But once again there is a 'capital adjustment' to be made for each period of: $20.44 x (365/2)= $3,730.30. So taxable earnings for the full six month period add to: $70,000-$3,730.30= $66,269.70

As previously discussed (post 1), all of these adjustments are 'capital' adjustments that change the book value of the capital of the bond remaining for income tax purposes (column 2 in the above table). Using my 'first principles' analysis, I would rewrite the reallocated income table that I have replicated above, as below:

Period Ending	Principal Outstanding (1)	Adjusted Gross Income in Respect of Period	Already Income Incorporated Taxable Capital Loss	Payments Received by End of Period
Day of Opening Investment	$1,012,500
15-05-1987	$1,011,192	$23,240	($1,308m)	$70,000
Income transfer to previous bond owner (2)				($45,452)
15-11-1987	$1,007,462	$66,270	($3,730)	$70,000
15-05-1988	$1,003,731	$66,270	($3,731)	$70,000
15-11-1988	$1,000,000	$66,270	($3,731)	$1,070,000
After Investment matures	$0
Resultant Capital Loss	$12,500
Total		$222,050	($12,500)	$1,234,548

Notes

1/ Capital adjustments period to period are as follows:
@15-05-1987: $1,012,500-$1,308=$1,011,192
@15-11-1987: $1,011,192-$3,730=$1,007,462
@15-05-1988: $1,007,462-$3,730=$1,003,731
@15-11-1988: $1,003,731-$3,730= $1,000,000

2/ Transfer required of income paid to you that belonged to the Previous Bond Owner:$ $70,000-$24,548=$45,452

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There is a obvious juxtaposition between my table above and the IRD table at the head of this post. That being that my table incorporates a 'capital loss', with declared income being lower than the coupon rate income received, whereas the IRD table is showing income higher than the coupon rate received (i.e. our bondholder has received a 'capital gain'). That IRD determination was made on 13th May 1987. So either I am the first person in the 36 years since publication of that document that has picked up the IRD's error, or I have made a mistake ;-P.

Actually I think I have made a mistake. With shares, where if you sell a share ex-dividend, but the registration process is delayed such that you are delivered the dividend in error, you are required to forward on that dividend to the new owner. With bonds it doesn't work like that. I believe that in a bond, interest due is priced in as though it was being accrued daily. So when you sell a bond coming up to the interest due date, you automatically retain your share of the upcoming interest payment. Or more pertinently, the buyer of the bond does not acquire the portion of the interest that was due to you the seller. That means there is no separate 'refund' transaction as shown in my version of the table. And if there is no refund, that means once all transactions have been tallied up, I make a capital gain, not a capital loss. So I will now rework my own version of the table, given these revised assumptions.

SNOOPY