Some of the UK's largest grocers have been having a hard time of it over the last few years, forcing management teams to rethink their strategies, be it due to the financial crisis, higher food prices (until recently), the advent of digital marketing and distribution strategies or failed adventures overseas, to name just a few of the sector's woes. Despite that, there are those who are keeping the faith. That is how some observers interpreted recent share purchases, on past February 17th, by Tesco's Non-Executive Chairman, Sir Richard Broadbent.On that occasion Broadbent added 10,000 shares to his stake at an individual price of 331.22p a piece, for a total spend of £33,122.Time to leave?Be that as it may, results do matter and shareholders' patience has its limits. Thus, perhaps, Tesco's finance director is set to resign as early as next week, just days before the firm reveals another sharp drop in its profits, next April 16th, the Financial Times reported on Thursday evening, after the close of trading. In its most recent update the firm said it still expected to report full-fiscal year profits within the range of what were then the "current" market expectations, which it saw as being in between £3.16bn to £3.42bn.Significantly, just over a month ago, on February 26th, Oriel Securities downgraded the food retailer to 'add' from 'buy' after the supermarket chain launched £200m of price cuts and said it was stepping up its store revamp programme.High dividend yield not necessarily a good signThe company's plight is highlighted by the fact that its shares are now trading at its lowest levels in at least five years. True, it is not alone, as Sainsbury's or Morrison's price graphs, for example, can attest. However, and as analyst Mike Dennis at Cantor Fitzgerald wrote to clients earlier today: "In contrast to Sainsbury's we believe both Tesco and Morrison's are still trying to cut significant costs and find a credible trading strategy to grow sales." For the year ended on February 28th 2014 consensus pegs the retailer's pre-tax profits at £3.054bn on revenues of £61.163bn, placing the stock on a price-to-earnings multiple of 9.8 times and a dividend yield of 5%, according to data compiled by JCF Factset.As ever, the question now for investors is whether that dividend yield reflects an undervalued stock or whether that pay-out will need to be adjusted downwards.AB