What Watt?

I am confused by the show with the solar energy people talking about costs. If solar is $6.00 a watt and the power company is 12 cents a kilowatt, I still don't know enough to compare them. My impression is that the total cost of building a solar system is calculated into the cost of generating a watt of power divided by one user. The total cost of a power plant is calculated into the cost of generating a kilowatt (one thousand watts) divided by millions of users. The solar power unit has a defined cost, that after that is recouped the cost of generating power is infinitely smaller still divided by one. Whereas the power plant costs are variable and perpetual. The speaker said the solar unit has an average life of 25 years.
So I am confused by the funny math on that show. It would seem to me that the $10,000 for a solar unit used for 25 years would be cheaper than using the power company. math help please!!
jean