Shares in BP are not far short of having recovered half the fall brought about by the Deepwater Horizon tragedy. There is a growing optimism, both within the company and on the stock market, that the damage from the disaster may not be as bad as had been feared. Some of the $20bn fund ring-fenced to pay for claims arising out of the event may come back to the company.Brokers suggest a value of $10.90 for every barrel of oil sold. Apply this average price to the rest of BP's proven reserves of 16.7m barrels and this suggests that BP's market capitalisation is about $13.5bn below where it should be, or 46p a share. This takes no account of any value at all for the downstream business of refining and selling the stuff on the forecourt. It indicates why BP could prove attractive to a potential predator if the shares remain where they are, the Times suggests.Vodafone shares are trading at 165p, buttressed by the promise to raise dividends by 7% in real terms over the next three years and a yield now standing at 5.4% for the current year.But some analysts are concerned that prospects for the core business are at best sluggish and that any expected payments from US partner Verizon may already be factored into the share price. Long-term, Vodafone remains a firm hold, but there seems little immediate upside suggests the Times.The market really should have seen the mini profit warning from Begbies Traynor Group coming. The company has been flagging up the fact that companies are not going bust at a satisfactory rate for months. The shares, after yesterday's 7% fall, are on about eight times' this year's earnings and look a solid hold for recovery, when the bad times roll around again says the Times.Please note: Digital Look provides a round-up of news, tips and information that is impacting share prices and the market. Digital Look cannot take any responsibility for information provided by third parties. This is for your general information only as not intended to be relied upon by users in making an investment decision or any other decision. Please obtain a copy of the relevant publication and carry out your own research before considering acting on any of this information.