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

[Snow Leopard]

I thought that you had realised where you had gone wrong on your first pass.
But you are totally misunderstanding this and basically nothing in your rework is correct, especially your assumptions.

Sometime tomorrow I will see if we can put you on the path to understanding.

[Snow Leopard]

[All] Bonds are Financial Arrangements but not All Financial Arrangements are Bonds:

If you do a word search on Determination G3 you will not find the word Bond or the word Interest, so amongst the many possibilities this 'Financial Arrangement' between B (the buyer) and S (the seller) could be:

A five year loan with an initial value of $1.5m with 10 semi-yearly payments of $70,000 and a final repayment of $1m that B bought off A;

A unique loan which B & S entered into where the initial value is that $1,012,500 and the repayments are as specified;

The 'Bond' that Snoopy has assumed which B bought from A.

The history of, and precise type of this arrangement is irrelevant, from 12 Mar 1987 to the end on 15 Nov 1988 they all have identical profiles and G3 shows how to correctly calculate the income and make adjustments to the outstanding principal for tax purposes for the periods between payments.

Deciding to throw the method away and calculate the linear income over the entire period of the loan, which is what in a very roundabout way has happened in this post, is a pointless exercise.

Whether such a linear approach is even permitted in some other determination or other, I do not know. But given it is simple and straight-forward I very much doubt it.

[Snoopy]

[All] Bonds are Financial Arrangements but not All Financial Arrangements are Bonds:

If you do a word search on Determination G3 you will not find the word Bond or the word Interest, so amongst the many possibilities this 'Financial Arrangement' between B (the buyer) and S (the seller) could be:

A five year loan with an initial value of $1.5m with 10 semi-yearly payments of $70,000 and a final repayment of $1m that B bought off A;

A unique loan which B & S entered into where the initial value is that $1,012,500 and the repayments are as specified;

The 'Bond' that Snoopy has assumed which B bought from A.

The history of, and precise type of this arrangement is irrelevant, from 12 Mar 1987 to the end on 15 Nov 1988 they all have identical profiles

I have hit the pause button here. All of what the Snow Leopard has written above is correct. And yes I did assume our buyer B, bought the 'bond' (if it was a bond) off an earlier buyer A. But as the Snow Leopard says, the exact history of the story of this 'bond' is irrelevant, provided we know the starting conditions, the ending conditions and the interest payments for the bond (if I am allowed to call it that) for the duration of the investment in question.

and G3 shows how to correctly calculate the income and make adjustments to the outstanding principal for tax purposes for the periods between payments.

I would argue it doesn't show the method used, as the author writes in rather ambiguous terms.
"It will be found that the constant annual rate R is 16.2308% per annum"

I went to my front door mat today, lifted it up, and didn't find anything. So if that isn't proof the IRD is not telling the full story, I don't know what is!

SNOOPY

[Snoopy]

I would argue it doesn't show the method used, as the author writes in rather ambiguous terms.
"It will be found that the constant annual rate R is 16.2308% per annum"

I went to my front door mat today, lifted it up, and didn't find anything. So if that isn't proof the IRD is not telling the full story, I don't know what is!

In an attempt to find the mystery of what has gone on here, I have decided to take 'desperate measures'. That means reading the 'Yield to Maturity' reference document right through, starting at the beginning! Look what I found on page 1:

"The approach adopted is to define a constant annual rate R representing the yield to maturity of all the cash flows in the financial arrangement. Income derived and expenditure incurred is assumed to be compounded on the date of each payment."
"In general there is no explicit formula for a yield to maturity in terms of the cashflows."

It sounds like we have to solve an implicit equation, while selecting a suitable payment period that fits the cash flows (in this case six monthly) to 'simplify' things.

"The yield to maturity is defined as the discount rate at which the cashflows accumulate to zero."

"As part of the method, the amount of income derived or expenditure incurred to be compounded at the end of of each period is calculated as a fraction F multiplied by the principal outstanding during the period. This income derived and expenditure incurred is then added to the principal outstanding for the next period (if one exists). The final payment must equal the principal outstanding during the final period plus the income derived or expenditure incurred during that period."

Hmmm. I am starting to think the solution might be to buy all your managed fund investments through a ;fixed interest manager' and forget about all this stuff!

SNOOPY

[Snow Leopard]

....It sounds like we have to solve an implicit equation.

Iterative methods and a spreadsheet

[Snoopy]

Iterative methods and a spreadsheet

I have found a web reference here that might be useful
https://www.wallstreetmojo.com/yield...y-ytm-formula/

Yield to Maturity Formula

YTM considers the effective yield of the bond, which is based on compounding. The below formula focuses on calculating the approximate yield to maturity, whereas calculating the actual YTM will require trial and error by considering different rates in the current value of the bond until the price matches the actual market price of the bond. Nowadays, computer applications facilitate the easy calculation YTM of the bond.

Yield to Maturity Formula = [C + (F-P)/n] / [(F+P)/2]

Where,

C is the Coupon.
F is the Face Value of the bond.
P is the current market price.
n will be the years to maturity.

SNOOPY

[Snow Leopard]

Iterative methods and a spreadsheet

PM me an email address and I will send this Excel Spreadsheet:

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Molehill >>> Mountain.