Below are some sample output amounts that you can expect and the amounts you can expect to be saving from a solar system in Tennesse:

In Memphis, a 4kw solar system is expected to produce about 5352 kwh of electricity per year. If the average cost is about $.069/kwh, that equates to about $369/year in electric bill savings.

In Nashville, a 4kw solar system is expected to produce about 5110 kwh of electricity per year. If the average cost is about $.069/kwh, that equates to about $352/year in electric bill savings.

In Knoxville, a 4kw solar system is expected to produce about 4821 kwh of electricity per year. If the average cost is about $.069/kwh, that equates to about $332/year in electric bill savings.

As far as the state level incentives go, there are quite a number of different ones that homeowners are eligible for.
One of them is a TVA production incentive, where you get paid an above market rate for each kilo watt hour of electricity you make.  This can be anywhere form 15 to 20 cents per kwh which is at least double the average retail rate.  Also, there are a few different state grants that your local solar installer in your are will be able to help you out with.  So, go and contact someone who is a professional and make sure to ask them about the status of the local solar incentives, also if there are any regional incentives with your utility company if you are in a co-op.