What you must understand about heating and cooling units is that they have to meet certain codes, which require certain permits and proper installation. The professionals understand the codes and how to expediently go about the process of acquiring permits. However, if you happen to be familiar with the codes and permits, and you already have the knowledge to install your own unit, you still need to consider the cost.
HVAC contractors have the ability to purchase units directly from the manufacturers with which they have contracts. The down side might be that you want a different brand of air conditioner from one that your heating and air conditioning contractor offers. Yet the real problem is that the heating and air conditioning contractor can purchase from his supplier for cheaper. In most all DIY cases that have to do with installing a new HVAC system, your free labor cannot compete with their unit prices.
Of course the decision is yours, but in this case the amount you can save is minimal when all factors are taken into consideration. Your time and labor can save you and your home money in other areas. This just isn't the one.
Here again, you need to be very certain that you know what you are doing. There is not much material written about this type of project because these projects are typically handled during construction where heating and air conditioning contractors get the work.
If you are building your own home, then perhaps ductwork installation is well within your command.
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Problems with Doing-it-Yourself
For the average homeowner, HVAC units are just too technical, require too much industry knowledge, and are just not projects where you can afford to do anything that isn't 100% correct.
The inexperience factor could alone cause air to leak at duct elbows and fittings, leading to poor energy efficiency and higher bills. Some remodeling projects can be done imperfectly and still offer you all you need, whereas HVAC installs and ductwork installation could look correct, but can underperform and you might never even know.