The cost to replace a central air conditioner is about $5,000. However, this price varies depending on the size of your home and the difficulty of the project. It can cost as much as $12,500 to replace an AC unit. The labor required to remove and dispose of the old system adds to the price. The size of your home, brand of AC unit and ductwork complexity can all raise the cost as well.
Air conditioning and refrigeration are provided through the removal of heat. Heat can be removed through radiation, convection, or conduction. Refrigeration conduction media such as water, air, ice, and chemicals are referred to as refrigerants. A refrigerant is employed either in a heat pump system in which a compressor is used to drive thermodynamic refrigeration cycle, or in a free cooling system which uses pumps to circulate a cool refrigerant (typically water or a glycol mix).
Contact/Relay -- Relays are electronically controlled switches that activate the various components of your HVAC system. They manage everything from the power going to the motor to automatic dampers, humidifiers, etc. Most of them are controlled by the thermostat. The most common failure for a relay is being stuck in the "open" position. Separated from its assigned contact point, it fails to complete the connection and send the message to whatever it was supposed to operate. This failure usually occurs from use over time. Each time a relay connects and sends its signal, the electrical arcing from point to point eventually causes wear and tear.
HVAC System Quality Installation Contractor Checklist -- This checklist identifies all of the steps the contractor has taken for the Energy Star Certification and identifies what work the contractor has done. If the system is later modified, this checklist can help identify what was done to proper Energy Star specifications and what was added later that may not meet the requirements.

Your contractor will do a load calculation to determine the proper central air conditioning unit for your home. This calculation accounts for the climate, size, shape and orientation of your home, as well as its square footage. A professional will also look at the insulation, windows, walls, floors and other materials that compose your home. He/she will then examine any leaks, seals and existing ducts or vents.
R-22 Freon is being phased out & isn't readily available. So the service company may only purchase as needed and the lack of availability would make their cost high. But, as long as they can get it, whatever the cost, unfortunately, is less expensive than replacing the A/C. Which will be the case eventually since it's no longer manufactured or sooner as in my case with a not so old a/c that sprang a leak, that would have been just a repair, but since it uses R-22 the whole unit has to be upgraded(replaced).  
These factors are included in a "Manual J" calculation. Contractors who make these calculations before recommending a size can take a couple of hours collecting the information and making the calculation. If your contractor doesn't do it, there are services that will do it for around $99. If you're feeling particularly on the ball, there are also free online calculators.
7 To test it, turn the thermostat to OFF, reset the power at the disconnect next to the compressor and the main panel. Set the thermostat to a temperature below the room temperature, and then switch it ON. To avoid straining an air conditioner’s compressor, wait at least five minutes between turning it off at the thermostat and turning it back on. You should hear the outdoor compressor run and see the fan turning inside the top. If the fan isn’t turning, look for an overload button or switch to reset (not all types have this).