Would euro solution be costly for Treasury?

One of the more counter-intuitive predictions in the Office for Budget Responsibility's recent forecasts for the British economy was that the government would borrow £112bn more in the coming five years than it expected in March, but would shell out £22.2bn less than anticipated in interest payments.

Or to put it another way, the OBR assumed that although the UK's public finances were deteriorating, so that that the national debt will be just shy of £1.5 trillion pounds in less than five years, investors would remain unprecedentedly keen to lend to the British Treasury.

And on this scenario, borrowing costs for the British government would remain at or near historic lows.

How plausible is this?

Well it is based on two assumptions.

First that the Bank of England will succeed in bringing down RPI inflation.

Second, that the strong rise in the price of UK government debt over the past few months, the increase in gilt prices, is not anomalous and will be sustained.

Neither assumption is a dead cert.

There are plenty of reasons to fear that investors' love affair with gilts won't be sustained.

In fact, there are 624bn of them - which, on my calculation, is the sterling value of gilt sales, or fund-raising by the government, needed from 2012 to 2016.

Based on the OBR's revised projections for government borrowing, investors are expected to buy astonishing quantities of gilts over the coming five years.

In the current year, the current Treasury expectation is that the Debt Management Office will sell £179bn of gilts - a colossal sum by all historic standards.

And, I calculate that (ignoring the modest amounts that the Treasury may choose to borrow via National Savings or in the form of very short term loans) gilt sales will be an eye-watering £189bn next year, £170bn in 2013/14, £151bn in the following year, and £114bn in 2015/16.

Now the bulk of that borrowing is to fund the government's deficit, rather than to refinance existing debt.

As I have pointed out here before, if the Debt Management Office hadn't done quite such a brilliant job in borrowing for long maturities - such that the average maturity of UK debt is just under 14 years - the UK might well be like Italy in finding it very hard to borrow at any price right now.

But even if we're not on the cusp of going bust, is it likely that - with the Debt Management Office having to sell £624bn of gilts in four years from next April - the interest rate that investors charge to lend to the government will remain near the record lows of this year.

To remind you, it is very hard to find any point in the history of British government borrowing when it has been cheaper for the government to borrow, even though it is also hard to find periods when the public finances have been in worse shape.

So you don't have to be a depressive bear of the UK to fear that the cost of borrowing for the government may rise.

For one thing, the Bank of England might choose to buy no more gilts - once it has completed its latest round of £75bn of gilt buying.

If the Bank were to go on a gilt-free diet, pension funds, banks and other investors would have to collectively buy and hold around £100bn a year more gilts than they've been doing since 2009.

So can that additional demand be created without the price of gilts falling and implied borrowing costs for the government rising?

Worse still, the Bank of England could decide to sell some or all of the £275bn of gilts it will have acquired through quantitative easing.

The Bank would only choose to do that, of course, if it feared that inflation was rearing its ugly head in a serious way.

But if inflation were to become entrenched, gilt prices would tumble independently, because creditors would demand a higher interest rate from the government, to compensate for rising inflation.

Or to put it another way, there is a big inflation risk to the OBR's forecast of falling interest-rate payments by the government.

That said, the Bank of England's current expectation that inflation will fall and stay low may turn out to be right.

But even if the Bank of England's inflation confidence is well founded, there is another reason to fear borrowing costs for the Treasury may rise a fair bit.

It stems from an internal contradiction in the OBR's forecasts.

On the one hand, the OBR admits that its gloomy prognosis of low economic growth and falling living standards in Britain may not be gloomy enough - because that forecast is predicated on an orderly resolution of the eurozone's debt crisis.

But here's the thing (and sorry for springing this on you now): investors have been taking exceptionally low interest rates from the British government precisely because they don't want to lend to Spain or Italy, they don't want to increase their eurozone exposure, and they've got to put their cash somewhere.

UK gilts have been seen as a safe haven in the eurozone storm. And the more intensely that storm has raged, the cheaper it has been for the UK government to borrow (the German and US public sectors have also benefited from this financial boycott of the over-extended parts of the eurozone).

As I mentioned, investors have to put their money somewhere. And the more ghastly it looks across the channel, the more the UK looks like a better bet, and the easier and cheaper it is for the UK government to borrow.

But what if the OBR is right and the eurozone sorts itself out relatively painlessly (please don't facetiously yabber on about porkers defying gravity and whatnot)?

Obviously we should all say hooray - because the UK economy would have dodged the biggest missile heading this way.

However in those glorious circumstances, the price of gilts would almost certainly fall and the borrowing costs for the government would rise - because investors would feel less in need of the safety supposedly offered by gilts.

In fact gilt prices have fallen in the past few days, as hopes have risen that this week's EU summit will see some kind of credible solution to the eurozone mess.

All of which is to say that the UK government's borrowing costs may well rise - though probably not in a lethal way.

According to OBR calculations (which I have reworked, in my sad way), each 1% increase in the interest rate paid by HM Treasury would cost the British taxpayer just under £2bn next year and around £7bn by 2015/16.

Now here is the unsurprising conclusion: only if investors start demanding that the government pay four or five percentage points more to borrow, only if the interest rate were to rise to what Italy has been paying recently, would the UK's big debt become unaffordable.

Which is why the only economic argument that matters is how close the UK is to tumbling from fiscal hero to zero - how close we are to becoming Italy.

That is an argument for another day.

But it may be worth remembering that the aggregate public-sector and private-sector indebtedness of the UK is higher than for any eurozone country, even Greece - and our annual government deficits are significantly greater than those of Spain or Italy.

Although, for the avoidance of doubt, that does not on its own prove that the chancellor's decision to opt for more austerity is right or wrong.