Private equity firm BGH Capital has proposed a A$607.3 million ($431.37 million) buyout of Australia"s Virtus Health (VRT.AX) after acquiring a 10% stake, the fertility services provider said on Tuesday, sending its shares up by more than a third. BGH proposed to pay A$7.10 per share, representing a 36% premium to the stock"s last close, after buying a 9.99% stake at the same price and entering a total return swap agreement with UBS for a further 10%, Virtus Health said. Virtus Health, which has 44 fertility clinics and seven day hospitals across five countries, said it was assessing the proposal. Shares of Virtus soared 34.4% to A$7, their highest since Aug. 30, in a subdued Australian market. BGH did not immediately respond to a request for comment. Virtus said the proposal also provided a cash and scrip alternative to major fertility specialist shareholders and certain other affiliated shareholders, so they can continue to hold an investment in the company. Jefferies is acting as Virtus" financial adviser. ($1 = 1.4079 Australian dollars) Reporting by Nikhil Kurian Nainan in Bengaluru; Editing by Subhranshu Sahu Our Standards: The Thomson Reuters Trust Principles.