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## How to do an income unit calculation

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Gengulphus
Lemon Quarter
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### How to do an income unit calculation

I've written the following as a result of knowing that I and others have written such posts before, but failing to find them at all quickly - so I thought an 'instructions' post whose subject says what it's about (rather e.g. than being buried in the middle of a thread about a particular share or HYP) would be a good idea! One request: please keep any responses strictly to the subject of how to do income unit calculations (or accumulation unit calculations as I have in its footnote), and not about such things as whether they're a useful thing to do...

To do an income unit calculation, you need (with in each case the value of the portfolio including both the value of its shareholdings and the value of its cash balance):

* For each time that you added cash to the portfolio, the date, the amount of cash added and the value of the portfolio just before the cash was added.

* For each time that you removed cash from the portfolio, the date, the amount of cash removed and the value of the portfolio just before the cash was removed.

* For each time that the portfolio received a dividend, the date, the cash value of the dividend and the value of the portfolio just before the dividend appeared.

Put them down in date order, recording dividends received in a separate column. If you withdraw dividends from the portfolio, don't record them as cash added to or removed from the portfolio; if you keep them inside the portfolio, do also record them as cash added to the portfolio (*). Also choose a unit value for the initial deposit into the portfolio (it's usual to choose a round number such as £1 or £100) and calculate how many units that makes the initial deposit equal to.

As a small example, imagine a portfolio that was started with a deposit of £20,000 near the start of the 2019/2020 tax year, earned dividends of £150, £200, £250 and £400 in that tax year which it retained inside the portfolio for reinvestment, had another deposit of £20,000 added near the start of the 2020/2021 tax year and earned dividends of £50, £100, £250, £300, £350 and £450 in that tax year which were withdrawn to supplement other income for living expenses. If we select £100 as the initial unit value (so that the initial £20,000 is 200 units), the inputs to the calculation might be:

You then fill in the blanks in that table by working through the rows from top to bottom, doing the following on each row:

1) Divide "Value of portfolio on date, just before cash change" by "Old number of units" to determine the "Unit value".
2) Divide "Cash added (+) or removed (-)" by "Unit value" to determine the "Units added (+) or removed (-)".
3) Add "Units added (+) or removed (-)" to "Old number of units" to determine the "New number of units".
4) If the row has a "Dividends received" value, divide it by the "Old number of units" to determine the "Dividends per unit".
5) Copy this row's "New number of units" into the next row's "Old number of units".

So for the second row, the calculations are: Unit value = £20,100.00/200.0000 = £100.50; Units added or removed = £400.00/£100.50 = 3.9801; New number of units (and third row's Old number of units) = 200.0000+3.9801 = 203.9801, Dividends per unit = £400.00/200.0000 = £2.0000. Then for the third row, they are: Unit value = £19,400.00/203.9801 = £95.11, Units added or removed = £250.00/£95.11 = 2.6286, New number of units (and 4th row's Old number of units) = 203.9801+2.6286 = 206.6087, Dividends per unit = £250.00/203.9801 = £1.2256. And so on, ending up with:

The results of the calculation are:

* The unit values on the specific tabulated dates (and the unit value on any other date can be determined by dividing the portfolio's value on that date by the new number of units for the last tabulated date before it = the old number of units on the first tabulated date after it).

* The totals of the dividends-per-unit values that fall within a time period. For example, the table above indicates dividends per income unit for the 2019/2020 tax year of £2.0000+£1.2256+£0.9680+£0.7190 = £4.9126, and for the 2020/2021 tax year (assuming no more dividends arrive in its remainder) of £0.4752+£0.8553+£0.6652+£0.0950+£0.5702+£0.1901 = £2.8510.

All the row-by-row calculations are completely automatic - i.e. one can program a spreadsheet to automatically calculate the second table above from the first, and for any significant amount of data such a spreadsheet or some other automated calculation is the only sensible way to do them. So the potentially tedious part of the calculation is preparing its inputs - i.e. producing the equivalent of the first table above. For a HYP, a very large fraction of the input data is likely to be the dividend payments, and for that it may well be useful to enter all the dividends for a month (or other period such as a week or a quarter) as a single combined payment arriving midway through the period. The results of the calculation are likely to be slightly different from the fully accurate calculation described above, but only very slightly different. I.e. this is basically a matter of accepting slight inaccuracies to get a big reduction in the amount of input data you need to produce. As a general rule, as you use longer periods, the input data requirements become smaller, but the inaccuracies become larger.

(*) To do an accumulation unit calculation, these instructions change to: If you immediately withdraw dividends from the portfolio, do also record them as cash removed from the portfolio; if you keep them inside the portfolio, don't record them as cash added to or removed from the portfolio. Note that this means that you don't actually need to include anything about dividends kept inside the portfolio in an accumulation unit calculation at all, unless you're curious about the dividends it's earning per accumulation unit (if you are, you can get figures for them by including dividends in the calculation - but note that they're not an extra return on top of the accumulation unit value change, as they are for income units, but instead tell you roughly what part of the accumulation unit value change is due to dividends). Also note that for many (I suspect most) ways of running a portfolio with dividends being withdrawn, they're not being withdrawn immediately - instead, the portfolio owner lets them accumulate within the portfolio and withdraws the accumulated dividends from time to time: don't record the individual dividend payments as cash removed from the portfolio in such cases, because the cash removal by the later withdrawal does that job. (But there are ways of running a portfolio in which dividends are withdrawn immediately - some nominee brokers credit dividends to your bank account as they're received, either as their standard way of doing things or as an option you can choose, and for portfolios held as certificates or in CREST accounts, companies pay dividends directly to you by cheque or bank transfer, bypassing the broker in the case of CREST accounts.)

Gengulphus