According to Andrew Schneider a MBA student at George Washington University via the Washington Post.

The cost of delivering a first-class letter:
COST TO USPS 48 cents

Sorting labor 10 cents

Delivery labor 7

Facility/vehicle maintenance 2

Fuel/transportation 1

Buildings, equipment, vehicles 2

Retiree pension/health 2

Misc. expense/First Class 8

Corporate overhead. 16