London Briefing:Is J Sainsbury destined to enter the record books as Europe's biggest-ever private equity buyout? Or will the would-be bidders walk away when they find the figures do not add up?

The barbarians are certainly at the checkout - shares in Britain's third-largest supermarkets group soared as much as 14 per cent last week as a trio of powerful private equity players admitted they were sizing it up for a bid.

Led by CVC, the trio includes Blackstone and Kohlberg Kravis Roberts, the Wall Street investment firm whose $31 billion buyout of tobacco giant RJR Nabisco in 1989 was immortalised in the book Barbarians at the Gate. KKR was also behind the $6.6 billion buyout of the Toys R Us chain in 2005.

The surge in Sainsbury's share price added more than £1 billion to its stock market value, taking its shares above 500p, their highest level in more than seven years.

Analysts say a bid would have to be pitched at 550p-600p to have any chance of success, valuing the 139-year-old business at more than £10 billion. Include debt and the pension deficit, and its enterprise value rises to £12 billion.

Yet a few years ago, Sainsbury's could have been bought for little more than half that figure. Its sales were on the slide as it paid the price for a disastrous new IT system brought in by former chief executive Sir Peter Davis that left its shelves empty of basic items such as bread and eggs.

Tesco and Asda were sharper at marketing and keener on prices and Sainsbury's customers left in droves.

So why now? Chief executive Justin King, the former Asda executive brought in from Marks & Spencer three years ago, is widely acknowledged to be doing a good job. He is more than halfway towards his target of raising sales at Sainsbury's by £2.5 billion over three years and has now delivered eight consecutive quarters of sales growth.

The timing of the private equity approach says more about the buyout industry than it does about Sainsbury's. The simple fact is that they have more cash than there are targets to spend it on.

While scores of companies have fallen prey to private equity bidders, the buyout players have suffered a number of notable failures - including unsuccessful moves on EMI, ITV, Woolworths and HMV.

Deals that would not have been looked at by the industry a few years ago are now being dusted off. In the case of Sainsbury's, though, it is hard to see how the sums can be made to work. After Friday's surge, its shares are trading on a stratospheric multiple of 48 times historic earnings and 36 times prospective earnings. That compares with around 20 times prospective earnings at Tesco.

It is true that Sainsbury's is sitting on a lucrative property portfolio. In the books at some £5 billion, it could now be worth as much as £7.5 billion. The buyout bidders would sell this off to help finance the deal, but it would leave the supermarket chain struggling to meet costly rental payments on its stores - and at a time when rents are rising.

A big push into non-foods is another key plank of the consortium's strategy for Sainsbury's. It has lagged behind Tesco and Asda in developing its higher-margin non-food business, particularly while King has being concentrating his efforts on revitalising the core grocery operation.

One drawback to this eminently sensible plan is that many of Sainsbury's stores are simply not large enough to carry a full range of clothing, electricals and other non-food ranges. And the investment required to achieve the transformation would be substantial.

Despite all the apparent negatives to a deal, other private equity players are now also circling Sainsbury's, raising the prospect of an auction for the company. The frenzy of rumours has spread to other retailers, both in Britain and the rest of Europe, where French group Carrefour's chain, Metro, is said to be a target. Some believe Sainsbury's will take evasive action by doing its own property deal or even, according to one report, joining forces with Marks & Spencer to achieve the required boost to its non-food business.

So far, Sainsbury's has said little, other than to stress it has not actually received an approach, nor has there been any word from the founding Sainsbury family. Their view will be key to the success of any offer.

All told, the family account for around 20 per cent of the shares, down from 37 per cent three years ago. Apart from the core 13 per cent stake held in a blind trust for Lord Sainsbury, the family holding is fairly widely spread. Other key shareholders are the insurance group Axa, with just over 15 per cent, and the US value-investment firm Brandes, which has just under 10 per cent.

Brandes, which also has a sizeable stake in Marks & Spencer, is a long-time shareholder in Sainsbury but chose the wrong time last week to top-slice its 11 per cent holding. It sold 29 million shares on Wednesday, two days before the price surged on the back of the consortium statement.

Had Brandes waited until Friday, it would made another £15 million. However, the US firm is unlikely to be losing much sleep over its poor timing - it is estimated to be sitting on a profit of as much as £500 million on its remaining 9.77 per cent stake.

Fiona Walsh writes for the Guardian newspaper in London