Plucking nuggets from its in-depth analysis of free cash flow (FCF) of the food retail sector, Barclays equity research team has cast doubts on the resilience of earnings estimates at the UK supermarkets.As growth in food retail has eroded in the last 15 years, investors and companies have become more interested in cash, inspiring the Barclays team to scrutinise each food retailer to identify outperformers and underperformers.Although the bank acknowledges FCF has its valuation limitations it is much less affected by accounting quirks and a key indicator of dividends.Analysis of FCF as a percentage of sales, or FCF margin, for 2015-16 gives strong scores for Morrison and Booker.Morrison's FCF margin depends to some extent on very positive working capital expectations based on the company's £600m three-year target, which "may indeed be deliverable, but is unlikely to be sustainable indefinitely". Furthermore, Barclays fears that the new Morrison CEO may need to invest more in price, which would put pressure on the EBITDA component."It is unlikely that the FCF yields of these two companies will remain in a high single-digit area - we believe either the equity will be re-rated or our FCF forecasts will come under pressure, or a combination of the two may occur," said Barclays."Given that we have stock rating of 'underweight' on Morrison and 'equal weight' on Sainsbury, we tend to fear that our estimates are more likely to come under pressure."Given that Morrison's new CEO starts work next week - and given continuing high price competition in the sector - we believe there is especially reason to be wary of further price investment/margin erosion in the case of that company."There should be caution on Sainsbury ahead of its reporting of fourth quarter trading statement on 17 March, with Kantar data indicating falling sales but falling fuel prices likely to be a benefit.All of the three of Tesco, Sainsbury and Morrison have enjoyed relatively strong share price performances so far in 2015 - "which could be attributed in part to Tesco's relatively measured approach to price investment, to the slowing sales growth at Aldi and Lidl and the beneficial impact of lower fuel prices" - but petrol prices have started to drift up somewhat from recent lows and the slowing discounter growth is unlikely to continue all the way to zero."For that reason we tend to be quite cautious on the outlook for all three names and we expect both Sainsbury and Morrison... to highlight the continuing tough conditions in the UK market and the likelihood of further price investment."