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

IRD example (Cashflows shown in bold).

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(15-11-1988) = $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.

Being changed is when the income is being recognised. Not the amount of money being recognised.

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.

Time to create some weekend amusement for the readers. Watching me make a fool of myself trying to calculate the 'yield to maturity' for this example bond.

When the bond is finally repaid it will be with a $1,000k (i.e. million dollar) capital repayment. It is apparent that the interest payments we know about are $70k every six months. We can use these two numbers to work out the annual 'coupon rate' C as follows:

Coupon Rate = ($70k + $70k)/ $1,000k = 14%. Annual coupon payment is $140k

There is no 'market' for the bonds in the example given. So F=P=$1,012,500.

There is one full year to maturity (year ending 30th November), plus a 'fractional year' which measured in days is:
(19+30+31+30+31+31+30+31+15)/ 365 = 0.6795

So the total number of years 'n' is: 1 + 0.6795 = 1.6795

Putting these numbers into the 'yield to maturity' formula gives me:
= [C] / [(2F/2] = C/F = $140k/ $1,0125k = 13.83%

This makes little sense to me (sigh!) I think my working has been undone because I am meant to be working out 'the market price of the bond' when there is no market.

SNOOPY