Sunday, 11 April 2021

Calculating the marginal corporation tax rate in your head using 'rectangles'

This post is not really about tax, I'm just using it as an example of how to use 'rectangles' to simplify and solve maths problems, so is of general application.
From the BBC:

Mr Sunak... said a new small profits rate would maintain the 19% rate for firms with profits of £50,000 or less, meaning that about 70% of companies - 1.4 million businesses - would be "completely unaffected" by the tax rise. And there will be a taper above £50,000, so that only businesses with profits of £250,000 or greater will be taxed at the full 25% rate - about 10% of firms.

Assuming this works the same as the old way (when the lower and upper limits were £300,000 and £1.5 million), you can work out the marginal tax rate on profits between £50,000 and £250,000 as follows:
£50,000 x 19% = £9,500
£250,000 x 25% = £62,500
£62,500 - £9,500 = £53,000
£250,000 - £50,000 = £200,000
£53,000 ÷ £200,000 = 26.5%

Which is a bit tedious.

This morning I tried using 'rectangles' in my head instead. This turns out to be much easier and quicker - there are more steps but the first six require no calculations at all and only take a couple of seconds:

1. The green rectangle is the tax you pay on exactly £50,000 of taxable profits.
2. The yellow rectangle plus the red rectangle is the total additional tax you pay on exactly £250,000 of taxable profits.
3. But they don't officially make you pay the 'red' tax; they make you pay the 'orange' tax in addition to the 'yellow' tax on profits between £50,000 and £250,000.
4. The red and orange rectangles must have the same area.
5. The red rectangle is 6% high and £50,000 wide.
6. The orange rectangle is X% high and £200,000 wide.
7. The orange rectangle is four times as wide, so it's only one quarter as high.
8. X = 6% red height x 1/4 = 1.5%.
9. Total height of yellow plus orange rectangle = 25% + 1.5% = 26.5%.

This is so painfully obvious to me now, why didn't I think of this decades ago, when the marginal rate changed every few years? The relevance of this may seem pretty arcane, but when you have groups of companies, it comes in handy when deciding how to minimise the total tax payable when there's a decision to be made, like surrendering losses or restricting the capital allowance claim this year in exchange for a larger WDA claim in the next year etc.


Unknown said...


Tax cuts and increases in government spending, totally 100% self financing with 100% LVT in place, so there will be a large surplus but nobody will be better off. Any attempts to increase wealth in people's hands will result in rent raises.

Mark Wadsworth said...

The problem will never arise as a national, flat rate UBI does NOT go into higher rents.