Bill said:

This has confused me somewhat Martin, and appears to disagree with the

earlier reply of a flat 19% of ALL of the £100K profits??

Any comment?

It may help you to think of it graphically. Plot Corp Tax vertically

against pre-tax profit horizontally. The relevant curve is a number

of straight line segments all joined up. The first segment goes from

(0,0) to (10000,0), which means that for any profit in the range NIL

to £10k, tax is NIL. The next bit goes from (10k,0) to (50k,9500).

This means that if profit is £50k, CT will be £9500 (which is 19% of

£50k).

Significantly, observe that the slope of the first segment is 0, while

that of the second is 0.2375 (i.e. 9500 divided by 40k).

The official way of calculating marginal relief in the 10k to 50k

band is to presume first that 19% tax is payable on the whole profit,

and then to "correct" this by appling a relief calculated using the

fraction 19/400. What this means is that you take the margin (i.e.

difference) between actual profit and 50k, multiply this by the

official relief fraction, and then subtract this from the would-be

19% of the profit.

So if, for example, the profit is £11k, your first approcimation to

the correct tax is £2090, being 19% of £11k. Then you work out the

margin between £11k and £50k, which is £39k. Multiply this by 19/400

and you get £1852.50, which you subtract from £2090 to get £237.50.

This is the actual tax payable, and also happens to be 23.75% of £1k.

This works for any amount A in the £10k to £50k range, because

0.19*A - (19/400)*(50k-A) = 0.2375*(A-10k)

The third segment goes from where we left off (50k,9500) to (300k,57k).

This segment not only has slope 0.19, but if extended it would pass

through (0,0), so for every point (X,Y) on it, Y is in fact 0.19*X.

The 4th segment goes from (300k,57k) to (1500k,450k), and the 5th

"segment" is a half line, going from (1500k,450k) to infinity with

a 0.3 slope. If extended, (0,0) would also lie on it.

The marginal relief applying to profits between 300k and 1500k again

assumes you start with a "30% on the whole lot" assumption, and then

apply marginal relief using the fraction 11/400 (by multiplying it

by the difference between the profit and 1500k. For any amount P it

is also true that

0.3*P - (11/400)*(1500k-P) = 0.3275*(P-300k) + 0.19*300k

And of course another way to determine the slope of the 4th segment

is simply to divide its height (450k-57k=393k) by its width

(1500k-300k=1200k). 393/1200 = 0.3275.