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

[Snoopy]

Here is the IRD tax document that is used to equalise earnings across reporting periods, with a worked example. This is something you need to understand if you wish to invest in bonds directly.

The following technical tax bulletin is sub-headed 'Determination G3: Yield to maturity method''

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

I have been for a long time curious about how this is done. But I have lacked motivation to find out because frankly, up until the last few months I considered bond investment as offering a fixed interest return for an equity risk. However, I always told myself that when I could buy blue chip(ish) bonds at an interest rate starting with a 7, then I might come back to them. And lo and behold that day is here. Be warned, that as I am writing this I don't really know what I am doing. When you don't exactly know what is going on, I find it best to go back to first principles. That is what I will attempt to do in this thread. The whole purpose of this thread is to try and understand the worked example (not fully explained in the IRD document), so here goes.

We will start with someone else's opinion. Below is how SailorRob sums up the process (from the Oceania thread post 16406)

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As for the tax doc, that's just a simple DCF model where you solve for the net present value to be zero and thus determine the discount rate.

That discount rate is used to determine the income for the tax year. I wouldn't get to bothered about that, the tax is exactly the same, you just pay it on $1 of income the same way as the next $1.

It's just a simple way of calculating the income by determining a yield.

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I do note the clock has just passed 9pm, which is beyond the hour when I write my worst stuff. But Rob's explanation looks like 'accounting speak' taken out of context to me.

For a start nothing is being discounted in this IRD example (cashflows shown in bold). If you look at all the sample calculations, there is no 'time value of money' being considered here. The input cost (what the investment was bought for) is quite clear: $1,012,500 (12-03-1987). The total money received once the investment fully matures is also clear: 70k(15-05-1987)+70k(15-11-1987)+70k(15-05-1988)+70K(15-11-1988)+1,000k(15-11-1998) = $1,280,000 (total over time). The overall 'gain' made (including interest income and taxable capital gain) is $1,280,000 - $1,012,500 = $267,500. The only thing that is being changed is when the income is being recognised. Not the amount of money being recognised.

So back to 'first principles' as I promised. Quoting from the referenced technical tax bulletin:

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Principle

The yield to maturity method apportions the total income or expenditure under a financial arrangement so that—

(a) The amount apportioned in respect of each period between payments represents a constant annual rate R on the amount of the principal outstanding during each period; and
(b) The rate R is such that at the time the financial arrangement is issued or acquired the discounted value of the money to be given and received accumulates to zero.

The amount apportioned to each period is then allocated to income years on a daily basis, in accordance with 'Determination G1'.

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A few words of my own, setting out how I see what is being described. Buying bonds 'at a discount to face value' means that you will get more capital back than you laid out when that bond matures (should you hold it to maturity, which for the propose of this exercise I shall assume you do). This 'extra capital' you get back is subject to tax at your marginal income tax rate, whether you are classed as a 'bond trader' or not. You are also taxed on the bond interest income 'as normal'. Despite the extra capital coming to you in 'one hit', when the bond matures, the 'financial arrangement' rules require you to 'spread this future taxable capital gain out' across the remaining term of the bond.

The actual interest payments are 'set in stone' right at the beginning of when the bond was created. Thus all of the 'equalising adjustments' must be made, for tax purposes, by assuming that you are getting some of the 'extra capital back' you are due BEFORE the bond matures. Thus in the year the bond matures, the capital that is returned to you is declared to be the original capital value of the bond, EVEN THOUGH IN CASH TERMS THIS IS NOT TRUE. In reality you will get all of your bond capital back only when the bond matures, despite having had to declare some of this capital gain as income in previous tax years.

The next step is to find out what the 'Determination G1' referred to is.

SNOOPY