By Freya Berry

LONDON, March 28 (Reuters) - Buyout firms are finding it harder to take part in mergers and acquisitions as the lure of stronger equity markets persuades more funds seeking to exit assets to try their luck with a public share sale or turn to cash-rich corporate buyers.

Private equity-backed mergers and acquisitions (M&A) fell by almost a third to $55.2 billion from a year ago, Thomson Reuters quarterly data showed on Friday.

European private equity firms accounted for 8 percent of M&A deals in the year to date, down from 10 percent from the same period last year and the lowest since 2011, although the value of private equity-backed deals did rise in the region.

"The bottom line is that in many sectors private equity is struggling to compete with the public markets," said James Simpson, Head of Sponsor M&A at UBS. "Assets that would naturally have come to private equity are going to IPO."

The MSCI World Price Index surged 24 percent last year. That has brought a rash of companies to market as they seek to capitalise on buoyant public interest, limiting the deals available for buyout firms.

Private equity firms are also grappling with asset price inflation.

Valuations have risen, partly due to a scarcity of assets, because of companies turning to IPOs, but also due to a growing amount of undeployed fund capital which leaves private equity funds paying out more as they hunt for ways to spend cash.

A report by Bain & Company this month found that undeployed capital, or dry powder, hit $1 trillion at the end of 2013, pushed up by investors seeking returns in a world of low interest rates.

"Multiples have gone up," Simpson said. "You have to acclimatise to paying bigger prices, and that takes a bit of time."

As well as expensive assets, funds are also shying away from competition with huge corporate cashpiles built up since the financial crisis.

Last year, GlaxoSmithKline scrapped a plan to sell its drinks businesses Lucozade and Ribena in an auction which would have included private equity firms when Japan's Suntory Beverage & Food muscled in.

"Whilst (investors) would continue to say this is a fantastic environment in which to exit businesses, it's actually still proving to be a challenging environment in which to deploy new capital," said Alasdair Warren, head of European Financial Sponsors Group at Goldman Sachs.

"The IPO markets are so strong and the multiples are so high, that it is very difficult for sponsors to compete."

But despite the squeeze, private equity firms are confident that the rush to IPO will not last forever.