Norman Braman, the auto dealership magnate, has just uttered the words every contractor dreams of hearing: “Whatever the cost is, we will be building it, period.”

Sitting with his wife, Irma, on the patio of their Indian Creek Island home, off Miami Beach, he has been outlining their plans to single-handedly fund the design and construction of South Florida’s newest major museum, the Institute of Contemporary Art, Miami. It could be a cultural game changer in a city crowded with four significant private museums, two more on the way and three public ones all focused on contemporary art.