A recent Sotheby’s auction of photographic works known as the Buhl Collection beat the expectations of the collection’s private owners by earning more than $12.3 million. The figure represents the highest ever auction price for a private collection of photographs and a third-highest for a single-owner collection.

Before the December 2012 auction, estimates of the auction’s total take ranged from $8 million to $12.2 million. The majority of the proceeds will benefit...