In my opinion, the perpetual calendar is by far the most useful out of all complication in watch making. Essentially this complication is an analog computer as it calculates or computes the complexities of the calendar independently from the user, taking automatic account of months with 28, 29, 30 and 31 days.
For 2015, Audemars Piguet released a Royal Oak Perpetual Calendar in four different versions, two in stainless steel and two in 18k pink gold.
The the new Royal Oak Perpetual Calendar is now 41mm in case size. The enlarged size has resulted in a Grande Tapisserie dial design that greatly increases the overall aesthetics, balance and legibility of the perpetual calendar indications.
The layout of the dial includes all of the traditional indications of a perpetual calendar watch: day, date, highly detailed astronomical moon, month and leap year. In addition, the 52 weeks of the year are indicated by an outer chapter ring with corresponding central hand, adding another layer of time measurement.
The new automatic caliber 5134 is based on its predecessor, calibre 2120, however it has been enlarged in accordance with the updated 41mm case size. The highly finished 4.31mm thick movement is fully visible through the glare-proof sapphire crystal caseback.
The thinner the movement, the more complex it is to adjust and assemble its parts as it requires extraordinary skills to work on components which are sometimes as thin as a human hair. However all finishing operations are performed by hand in accordance with the highest standards of Haute Horlogerie.
I understand the complexity of manufacturing a watch like this to accommodate a thinner movement and case. However, I think these watches are priced too high for a perpetual calendar, especially when you can buy a Tourbillon complication for the same price from of some of the top tier watch manufacturers. The retails of these watches are $60,900 for the stainless steel versions and $95,700 for the 18k pink gold version.