You may think that you don't have any wiring "back there", but you probably do. A floodlight doesn't take much current and can very likely be added to an existing circuit. When we had one installed in our back yard a few years ago, we had it tied to a receptacle under the window in our bedroom. They just added a switch on the inside and a light on the outside. (Makes it easy to change the bulb too since it's right under the window!)

$150 - $200 is about the right price and any electrician should be able to do it.

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