Actually no, I acted like at a zero percent interest rate / zero opportunity cost (which is a little weird) it would take about nine years, and at a typical 30% credit card for your average poor dude was infinity. Everyone will fit somewhere within those bounds.
A reasonable opportunity cost might be 3%, I'm too lazy to bother figuring the time till profit because nine years at zero is already too long.
A few things. First, it costs 250, not 300. Second, an alternative would be much cheaper, but it is non zero. Third, it provides other benefits than just potentially saving money such as a great user interface and apps with which to control it remotely.
So say an alternative is 30, the cost is 220, not 300. That takes several years off your calculation. Then having the benefit of an improved interface is non zero. Even if it takes a long time to pay back I plan on living in my house for a long time, and I liked nice things.
Now if you want to argue about overpriced absurd things, go with their $130 smoke detector or whatever it is. No thanks.
A reasonable opportunity cost might be 3%, I'm too lazy to bother figuring the time till profit because nine years at zero is already too long.