From: Ronald Raygun 
Subject: Re: Wages Program
Newsgroups: uk.finance
Date: Sun, 04 Apr 2004 15:17:56 GMT

Alasdair Baxter wrote:

> I am looking for a small program which will calculate my wages.  For
> example, I key in all the relevant details like tax code, week no. tax
> rate, NI rate, etc and it should show my correct net wage.

Prompted by this query, I thought I'd have a look at what would be
involved in cobbling such a program together myself.

The challenge, it seems, lies in getting exactly the same answer as
the one you'd get if using the IR's published tables, instead of an
answer which is, if you like, "more correct" but actually a few pence
off the "official" answer.  The solution therefore involves knowing what
the algorithm is which IR use to compile their tax tables, since clearly
it would be inelegant (not to mention laborious) simply to absorb their
tables into the program.

The pay adjustment tables ("Tables A"), which give the pro rata
weekly or monthly allowance to be deducted from pay to date (or added
to it, in the case of K codes), given the employee's tax code and
the week or month number, appear to have used the following recipe:

If the tax code is 0, the adjustment is 0, whatever the week or month.

Otherwise, for codes 1 to 500, the pay adjustment for the whole year
(i.e. cumulatively in month 12 or week 52) is ten pounds times the code,
plus nine pounds, plus a number of pence, if necessary, to make the total
number of pence divisible by 12 or 52 as the case may be.

For any month or week other than 12 or 52, the cumulative adjustment is
that for the year divided by 12 or 52, times the month or week number.

The 500 increment applied to codes 501 and above is dealt with similarly,
by rounding £5000 up to the next number of pence divisible by 12 or 52.

So far, so good.  The rest, applying the starting, basic, and higher
rate tax rates, should be easy.

But AARGH!  I'm flummoxed by something in the other tables.  Looking at
the "calculator tables", based on the starting/basic and basic/higher
rate boundaries being £1960 and £30500 (these are 2003-04 boundaries,
the 2004-05 tables don't seem to be available yet), it's clear that the
SR table which seeks to apportion £1960 to its monthly or weekly
equivalent is simply £1960 divided by 12 or 52 and rounded up, if not
whole, to the next higher whole pound.  The same is true of table B
(and C, which is the same), you divide £30500 by 12 or 52 and round up
to the next whole pound.

Now, to calculate tax where £1960 < pay <= £30500 (in month 12 or week
52), you should either take 10% of £1960 and add 22% of (pay - £1960),
or else, as they do, you simply take 22% of pay and deduct 12% of £1960,
which is £235.20.

So obviously what they need to do is pro-rate the £235.20 by dividing
it by 12 or 52, and then rounding up to the next whole penny, which in
fact is exactly what they do for the weekly method.  For the monthly
method, however, as it happens, £235.20 is exactly divisible by 12,
giving £19.60.  Thus the entries in the Starting Rate Relief table
should be £19.60 times the month number.  Unfortunately, however, the
table gives one extra penny relief for months 1 and 2 (but not 3), and
also for 4, 5, 7, 8, 10, 11, but not 6, 9, or 12.

It gets worse.  To calculate tax when pay > £30500, you take 40% of
the excess, and add £6474.80 (which is 22% of £30500 minus 12% of £1960).
Now I'd expect the add-on entries in the table which pro-rates £6474.80
to be a 12th of that, rounded up to the next whole penny, but no.  The
figures in the official table are 12p more for months 1, 4, 7, 10, and
25p more for months 2, 5, 8, 11, but correct for months 3, 6, 9, 12.

Why?

Similarly for the weekly scheme, the add-on table figures are off from
the obvious algorithm by 17p in week 1, 35p in week 2, 14p in week 3,
and continuing 32p, 11p, 30p, 8p, 26p, 5p, 23p, 3p, 11p, but then
correct for week 13.  I haven't looked at them all, but it seems the
pattern repeats so that week 14 is 17p out just like week 1; week N is
out by the same amount as week N-13.

I can't quite figure it out.  Any ideas?