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

[Snoopy]

When all else fails, go back to the original data.

https://www.taxtechnical.ird.govt.nz...20211123023345

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.

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 capital loss)

But the IRD table is showing income higher than the coupon rate received (i.e. our bondholder has received a 'capital gain').

(Note: That IRD determination example was made and published way back on 13th May 1987).

There is something very strange about the above table (taken straight from the referenced IRD document I might add).

"How can one table show both a capital loss and a capital gain for the same set of cashflows?"
This is the question I want answered that I do not understand!

It is quite clear that when we take out the 4x$70k 'coupon payments' our investor has made a capital loss over the investment period of $12,500 (at the cash transactional level).

Yet we also know that the 'deemed constant rate of return. on this investment of 16.2308% is greater than the coupon rate (based on the bond redemption price) of 14%. The only possible way to explain this 'interest rate differential' is that our investor bought the bond at a discount and will make a capital gain. Indeed those last three deemed 'income in respect of period' payments being greater than the coupon rate of $70k would suggest this.

This table above is showing us that the IRD is requiring us, as the new bond holder, to declare a 'capital gain' over an 18month+ period over which we make a net cash loss on our investment. WTF?

At times like this I am tempted to lie on top of my doghouse and just go "woof, woof." Much easier than playing this bond investment game.

Yet 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.

SNOOPY