Brazilian butt lifts, Hollywood stars and even a former US president all feature in the history of a 75-acre private island that has been listed for sale. Pitanguy Island was once owned by world-renowned plastic surgeon Dr Ivo Pitanguy, the pioneer behind the iconic BBL. He died in 2016 aged 93 and left behind his exclusive abode which his family have been reportedly taking care of since. Located off the coast of Rio de Janeiro, Pitanguy Island is now up for grabs and has a hefty price tag of $100 million (£75 million) – among the world's most expensive private islands. The cosmetic surgeon, beauty and skincare specialist used the retreat as a private space for his family, close friends and a small group of select VIP guests. A number of A-listers and Hollywood stars are said to have visited the island, including Tom Cruise, Katie Holmes, Frank Sinatra and former US president Jimmy Carter, according to Beauchamp Estates, which has listed the island. Dr Pitanguy reshaped the island, adding six Modernist-style bungalows, nine suites as well as a swimming pool.

With panoramic views of the Bay of Kings, a beautiful marine area, there is little this exclusive abode does not have. From lush tropical gardens to a private 400-metre airstrip, the island is kitted out with the best of everything. The island can be reached by helicopter, plane or boat, with a helipad, private airstrip and marina (with enough room for large vessels to dock). The island even has its own forest – complete with trails – as well as three private beaches, natural freshwater springs and a natural aquarium. Sports lovers can enjoy the tennis court and there are golf carts to help the next lucky owner get around.

The collection of bungalows and suites feature modernist white render facades, sleek curved walls, spectacular floor-to-ceiling glazed windows overlooking the ocean and gardens. The architecture is said to be partially inspired by the James Bond lair of Francisco Scaramanga which featured in the 1974 film, The Man with the Golden Gun. With plenty of space for expansions, the new owner could add a 30,000 sq ft mansion on the eastern side of the island, subject to planning approval from the local municipality and the Brazilian Navy. This could add up to $135 million (£100 million) of value to the island.

There is also scope to refurbish or rebuild the current buildings within the existing consented planning and building parameters, as well as upgrades to the helipad, airstrip and private marina. Gary Hersham, founding director of Beauchamp Estates, described the island as 'a unique trophy real estate asset' that 'also offers extraordinary potential'. He said: 'The island could remain an exceptional private retreat for a discerning multimillionaire or billionaire, or could be transformed, subject to planning, into a highly exclusive Necker Island style hospitality resort with 5-star amenities of global relevance.' Kay Louise Smith, super-prime sales broker at Beauchamp Estates added: 'Pitanguy Island is one of the most exclusive private islands in the world, offering a James Bond-inspired lair of striking modernist bungalows and suites, superb amenities and an illustrious celebrity backstory.'

If Pitanguy Island is slightly out of your budget, another one has hit the market for less than the average price of a home in London. Hawk's Nest Cay in Cat Island, the Bahamas, is currently listed for sale for £751,376 – conveniently located near the amenities of Hawk's Nest Resort & Marina. The lucky buyer will be entirely surrounded by panoramic sea views and a tropical setting. According to property portal Rightmove, terraced properties in London are selling for an average of £775,395 – making this an absolute steal in comparison.

Located just minutes from the resort island, Hawk's Nest Cay offers seclusion without complete isolation. 'The island has great elevations all along the southern shore and a few beaches on the northern shore,' according to the online listing. 'Access to the island is just a hop over the beautiful Hawk's Nest Creek from the marina to the island. 'The creek is protected from the ocean waves and has natural deep water so you could easily have a large dock on the island if needed. 'Hawk's Nest and Southern Cat Island is renowned for its incredible fishing and the marina, airstrip and resort on your doorstep make Hawk's Nest Cay the island of choice at a great price.'