The maths behind Starmer's Chagos sleight of hand
In exchange for the privilege of ceding sovereign British territory to Mauritius, Sir Keir Starmer has agreed to fork out billions of pounds of taxpayers' money.
Britain is set to pay £101 million per year for 99 years, or a hair under £10 billion in total. Add in all the supplementary payments and inflation and it's closer to £30 billion.
Read the Government press release, however, and we're apparently paying out £3.4 billion. So which number is correct?
The short answer is both of them. The slightly more complicated answer is that it depends on what you're doing.
The longer answer is that Sir Keir is engaged in a mathematical sleight of hand. The £30 billion is what you get if you add up the cash value of every payment, uprating some for inflation at 2 per cent each year.
But if we want to know how much a policy actually costs, we need to remember that £1 today and £1 in 2134 have very different values.
This is partly because of inflation (which decreases the value of money over time), and partly because future payments are 'discounted' to get a present value: if we want to put a single figure on the cost of a policy spread over many years, we need to translate each year's spending into present-day values. Economists refer to this as the net present value of a series of payments.
Conceptually, we can think of this as the sum we'd need to set aside today to fund spending £100 million or so each year for 99 years.
Because the money will earn interest, we don't actually need the full £30 billion. We just need the equivalent net present value. And the net present value of all the payments combined, discounted by around 5 per cent each year, is roughly £3.4 billion.
It's at this point that the sleight of hand has taken place. There's absolutely nothing wrong with using net present values. Generally speaking, they're the best number for economic analysis, letting us compare a series of costs and benefits in today's money.
However, they are very rarely the figures politicians use. And they certainly aren't the numbers deployed when they wish to give the impression of generous spending.
For instance, when the Prime Minister announced £22 billion of investment into carbon capture and storage over 25 years, he didn't break it down by year, discount it, and give a neat present value. Instead, he gave the larger, nominal number.
Quite why, having signed an embarrassingly defeatist treaty set to cost the UK billions over the next century, Sir Keir has suddenly been persuaded of the economist's view on the merits of present value calculations, will have to remain a mystery.
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