Perhaps we should stop using percentages as a way of expressing greater or lesser, increase or decrease or as way of describing the part of something that is occupied by another part. A lot of people don’t really understand percentages – and here I particularly include people who should, because they use them a lot, such as politicians and media folk.
I’m exercised by the Chancellor of the Exchequer’s stated intention of increasing National Insurance payments by 1%. Well, that’s nothing is it? What did I hear the Chancellor say? ‘A penny in the pound’ - why, that’s nothing. The old percentage based Find the Lady trick is being used here. Let’s look at cases:
An employer wishes to increase an employee’s salary by £1000 a year. We’ll assume that the basic salary means that the employee will already be paying 11% N.I. (National Insurance) – so £110 would normally be deducted over the year from that sum. NI is now going to rise by that mere 1%. Employee now pays 12%, that is £120. So the sum the employee has to pay has risen by £10. If what you pay rises from £110 to £120 that is a 9% rise in the year. Mr Chancellor was using the old dodge of referring to the increase in the rate of NI charge.
In this case the employer also has to pay an NI contribution in respect of the employee above and this is calculated on 12.8% of the gross sum paid to that employee. So, in order to pay the extra £1000 to the employee the employer already has to stump up £128. And now the rate is going to go up by … just a penny in the pound … 1%. So 13.8% will have to be paid. No longer £128 but £138. Over the year that’s a 7.8% increase in the employer’s outgoings on this one employee.
And this increase will be applied to the employee’s current salary as well. And to that of everyone else on the payroll.
It’s sums like this, that employers have to do when they consider giving pay rises and, most important to the poor old long-suffering Nation, when they contemplate increasing their staffing. ‘It’s a tax on employment’ say the Chancellor’s critics. You bet it is!
A Beginner’s Guide to Percentages
Please ignore this if you just don’t care for sums
Let’s look at a very common example: Value Added Tax. VAT is levied on most articles that you buy and in the UK is calculated by adding 17.5% of the ‘real’ price to the ‘real’ price of the thing. So something that should cost you £100 ends up costing you £117.50. The £17.50 is the VAT element. That’s easy.
OK suppose you see something in a shop that is priced at £117.50 and you want to see what the VAT element of this is. If you have temporarily forgotten how that £117.50 was arrived at you might well reach for your pocket calculator and work out what is 17.5% of £117.50. So you multiply £117.50 by 0.175 (if you are an advanced mathematician) or you multiply £117.50 by 17.5 and then divide by 100 (if you are not). You find that the VAT element appears to be £20.56 (plus a tiny bit that you ignore). A bit more calculator work tells you that the article must have cost £96.94 before the VAT was added.
But we know that the article’s real price was £100 and now we remember that the VAT element to be added to it was £17.50. So how did the VAT get to be £20.56?
It’s not difficult to work out what to do to get the right answer. Call the original price x. To get the VAT-inclusive price x has to be increased by 17.5% . That is, x was multiplied by 1.175. So, to find what x is you just divide the VAT-inclusive price by 1.175. £117.50 divided by 1.175 gives you £100.
Back in 2009 when the UK Chancellor of the Exchequer reduced VAT from 17.5% to 15% you can imagine the confusion. ‘Well, it’s dropped by 2.5% innit? So if we’re selling something for £85 all we have to do is knock 2.5% off; this gives us £85 minus (get out the calculator) £2.12 if we round it down, which gives us £82.88. Get out the magic marker!
Wrong! The correct VAT inclusive price, after the VAT reduction has been taken into account, is £83.19. It may only be 31 pence that has inadvertently been given to the customer but the VATman will still want his full chunk of the action which is £10.85 so it’s the shop that takes the loss. The only safe way of handling this is first to calculate the ‘real’ price that is contained within the 17.5% VAT inclusive price (divide by 1.175 = £72.34) and then to increase the ‘real’ price by the new VAT figure of 15% (multiply £72.34 by 1.15 = £83.19).
Now, with a General Election just announced, we might well give thought to what happens if, after a new government has been elected, the VAT rate rises to 20%. Oh yes, this is a real possibility. If it happens how do you calculate what the new VAT-inclusive price is? Assume that something was on sale for £240.
You go back to step one above and calculate what the pre-VAT price was. Divide the VAT-inclusive price by 1.175 (VAT is currently 17.5%) and this gives you £204.25 as the pre-VAT price. Now multiply that sum by 1.20 (New VAT being 20%). That’s £245.10. So the VAT increase will cost you £5.10 extra on a £240 purchase.
Don’t be caught out by anyone saying to you, ‘VAT’s gone up by 2.5% so instead of charging you £240 we’ll have to charge you £240 plus 2.5%. That’ll be £246, please’. There’s only a 90 pence difference but it’s your 90 pence! Apply it to a car costing £10,000 and the argument becomes stronger.
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