Okay, so, let's do a little seat-of-the-pants math.
According to Nvidia's web site, the (base) GTX 1080 draws (at peak) 180 watts, versus 120 watts for the 960, for a difference of something like 60 watts, give or take.
So: the difference you could expect to see in your power bill would be somewhere in the same neighborhood as if you burned one old-fashioned 60-watt incandescent light bulb, for the same amount of time you're running your PC--up to about 4 hours per day, right?
Bearing in mind that a large number of factors can affect the actual numbers (including the specific model of each GPU, exactly what games you play, any driver-related bugs or weirdnesses, and the cost of electricity in your area,) we should be able to get a rough estimate by checking this handy dandy online calculator:
http://energyusecalculator.com/electricity_incandescent.htm
According to the calculator, one 60-watt light bulb burning for 4 hours per day at 13 cents per kWh (which, per the U.S. Energy Administration, is the current U.S. average, rounded up:
https://www.eia.gov/forecasts/steo/report/electricity.cfm ) could be expected to cost a little under $12 per year.
So, unless the 1080 variant you buy draws substantially more power than the Founder's Edition, or the price for electricity in your area is significantly higher than the U.S. average,
or your computer habits drastically change, I doubt you'd see your power bill for the year go up by more than about $12. Allowing a sizeable margin for error, since I suck at math and could have missed something, figure $20 or less for the year, or an increase of less than $2 per month.