(Sharecast News) - Esure confirmed on Monday that it has received an unsolicited proposal from private equity firm Bain Capital at 280p per share in cash. The insurer is in the advanced stages of discussing the possible offer, which represents a premium of around 37% to the closing price of Esure on Friday and a 29% premium to the volume-weighted average price over the last three months.The company, which put out a statement after its share price rose sharply in early trade, said that it has indicated to Bain that it would be minded to recommend a firm offer at such a price.There is no certainty that an offer will be made and Bain Capital reserves the right to make an offer at any time on reduced terms. It now has until 1700 BST on 10 September to either make a firm offer for Esure or walk away.RBC Capital Markets said it expects this deal to get done, as it noted that the offer price is a touch above its 275p price target for Esure."Although the offer still represents an undemanding multiple (12.2x our 2019E earnings per share forecast), given the backdrop in the UK motor market with softening prices plus a motivated seller of more than 30% of the stock, we believe this offer probably represents the best that Esure can expect for now until the cycle turns."Although Esure traded as high as 288p just a year ago, the mood around UK motor insurance stocks has become far more negative in recent months as pricing begins to soften."RBC noted that Esure chairman's Peter Wood - who has a stake of more than 30% - has been mentioned in the press as being willing to sell."With Peter Wood's stake plus his role as chairman, we believe that the bid is likely to succeed if a firm offer is made at 280p," it said, adding that it does not expect any counter offers to emerge.Meanwhile, Neil Wilson, chief market analyst at Markets.com, said this was always the most likely outcome as we knew that Peter Wood was looking for an exit."And the abrupt departure of the CEO in Jan was probably an indication that something was afoot," Wilson added.Hargreaves Lansdown equity analyst Nicholas Hyett pointed out that Esure shares haven't had a great run recently and said the mooted 280p offer price is actually below where the shares were a year ago."The group's underwriting performance has been unexceptional, and while there have been improvements recently, it's still well off best in class," it said."You only have to glance at what Stephen Hester has done at RSA to see why Bain might be interested though. Like Esure, RSA is in the competitive and price-driven personal insurance industry - but a laser-like focus on underwriting and more focussed approach to investment has seen Hester turn a struggling also ran into a force to be reckoned with in relatively short order. Bain will hope it can deliver the same."At 1513 BST, the shares were up 32% to 268.80p. Fellow insurers Direct Line, Admiral and RSA Insurance all got a boost.