By Mike Baker
BBC News education correspondent
How healthy is the independent school sector?
An instant diagnosis of the latest symptoms suggests it is in the pink.
Student numbers are holding up well, class sizes are smaller than ever, and the long-term decline in boarding has not only levelled out but is even showing signs of growth (and not just because of the appeal of Harry Potter).
But there are some underlying trends that are less rosy.
Some leading members of the independent sector are now warning against complacency.
This week saw publication of the 2006 census from the Independent Schools Council, which covers over 80% of all pupils in independent, fee-charging schools in the UK.
Overall pupil numbers were up, from 504,141 last year to 505,450 this year. That is a tiny increase of just over 0.2%.
However, this is not such a bad result when set against the wider demographic picture that shows a declining number of children of school age. The total number of pupils of primary school age in Britain has been falling by about 50,000 a year for at least the past five years.
So, even maintaining stable numbers is an achievement and suggests a slight improvement in market share.
At the same time, the census showed that class sizes in fee-charging schools had reached a record low. There are now just 9.87 pupils per teacher in these schools, that is about half the ratio in state schools.
So why should the independent sector be worrying? There are several reasons. Firstly, long-term growth relies on the numbers coming in at a young age. These are the children who will be in the independent sector for the next decade.
Yet this was the area showing the largest fall: numbers in nursery sector were down by 0.6% and in the primary age range they were down by 1%.
The second worry is that the cost of private education continues to rise beyond the means of many potential customers.
Although this year saw the lowest increase in average fees for seven years, it was still a whopping 5.7%. That is considerably more than double the rate of inflation.
Like house prices, the cost of private education has been rising so fast, and for so long, that it is hard to see how enough parents can continue to afford it out of earned income to sustain current market share.
The schools would argue, with some justification, that their costs, mainly teachers' salaries, are rising faster than inflation.
They are also aware that there is now strong competition from the state sector in England. The new city academies (however controversial they may be) have state-of-the-art facilities that are beyond the means of most independent schools.
Two successful independent schools - Belvedere Girls and William Hulme's Grammar School - are planning to leave the fee-charging sector to become academies. Others could follow.
Look more closely at the figures and you see that they have achieved this largely due to a big rise in the recruitment of overseas pupils
Specialist secondary schools (now accounting for 75% of the state secondary sector in England) have brought new money, better facilities, and a different ethos into the maintained schools sector. They also permit limited selection of pupils by aptitude.
Uniforms, strong discipline, specialist teaching and curricula, and vastly improved IT equipment have equipped growing numbers of state schools to compete with their fee-charging counterparts.
On top of this, in the last Budget the Chancellor, Gordon Brown, promised to raise per pupil funding in the state sector eventually to a level matching what is now spent in the independent sector.
The independent sector might dismiss these arguments by pointing out that this year's figures show they are still bucking the downward demographic trend.
Yet look more closely at the figures and you see that they have achieved this largely due to a big rise in the recruitment of overseas pupils to the boarding sector.
The increase in new entrants from overseas was 11% or 870 pupils. That alone accounts for the lion's share of the overall increase in all pupils (1,311).
Clearly this is good news for boarding schools involved in the overseas market. There are some very interesting trends.
Recruitment from France, Spain and Germany was up by between 25% and 30%. Low-cost flights and the spread of the International Baccalaureate have played their part here.
Yet without this increase in overseas numbers, the overall numbers in boarding schools would have fallen this year.
The overseas pupil market is an important one. For a start it brings in an estimated £320m in fees each year.
It is also a testament to the international reputation of British private education.
Incidentally, independent boarding schools complain bitterly that the government fails to give them the same sort of support it gives to universities for their overseas recruitment.
Yet overseas markets are volatile, remaining highly sensitive to exchange rates, the health of international economies, visa arrangements, and concerns over unpredictable issues such as terrorism and bird flu.
As Matthew Sherwood of the Economist Intelligence Unit told the Hobsons' international boarding schools conference this week, the world economy is expected to show a gradual slowdown over the next 18 months.
He added that the high level of sterling against the dollar would continue to make a British education relatively expensive to overseas parents.
This conference also heard that Britain was still the world leader in international pupil recruitment but, in cost terms, schools in the UK were looking increasingly expensive compared with the main competitor countries: Australia, the USA and New Zealand.
According to research from Hobsons, average boarding school fees for overseas pupils in the UK are about £19,500, compared with £12,000 in Australia and New Zealand, and £16,000 in the USA.
With around 5% of all pupils coming from overseas, the British independent sector is more reliant on the foreign market than its competitors. This is a sign of its international appeal but also of the risks should pricing or other factors lead to a change in this volatile market.
So the warning signs are there: concerns over the relentless rise in fees, cost pressures from the rise in state sector salaries, a demographic downturn, stronger competition form state schools, and the extent of reliance on overseas pupils.
Some within the sector have alerted schools to the risks.
At its recent annual conference, the general secretary of the Independent Schools Council, Jonathan Shephard, warned that parents would be priced out of the market if fees continued to rise faster than inflation.
Despite the high fees, independent schools rely heavily on families with moderate incomes.
An ISC survey found that almost 10% of independent school pupils lived in postcodes with incomes below the national average. A further 14.5% lived in areas where incomes were only just in line with the national average.
Average fees at day schools are now about £8,000. That means parents need about £12,000 of gross income to pay for each child in private education.
As well as cutting costs, some in the independent sector have argued that it should make itself more indispensable to the state as a way of ensuring its future.
There has been growth in, for example, the sharing of facilities. There is potential for greater sharing of staff and expertise.
Yet most of the suggestions for greater cooperation involve the independent sector taking in the brightest state school pupils.
The real breakthrough might come if the independent sector started to look at what it might offer to pupils with special needs or to those who are, for other reasons, disengaged from the state system.
Then the government might find it indispensable and the private sector could start to find a new role if, or perhaps when, times start to get tougher.
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