If that is true the Patriots are dumb. We know they are not dumb.
It's called "Net Present Value" (NPV) and it's a tool very familiar to folks who work with money. It's simple, it is the value of a future amount of money expressed as the equivalent value of money today. It's based on the idea that cash in hand today is worth more than an expectation of cash in the future.
It factors in things like inflation, internal rate of return, opportunity costs, a whole bunch of things, but the math is straightforward and well understood. I'd bet Jonathan Kraft can calculate it in his sleep. A more sophisticated analysis (which I'd be very surprised if the Pats aren't doing) would also factor in the risk of being outbid for an RFA tender, etc.
I did some half-assed NPV computations using assumptions I pulled out of thin air, or somewhere the sun don't shine, whatever, just to get an idea of how things might stack up. Using the current prime rate (3.5%) and close approximations to RFA first round tender and CB franchise tag salaries, I came up with an NPV for no extension of about $29,000,000 through 2019. Assuming a three year extension averaging $8.5mm with next yezr unchanged the NPV that I calculated was about $25.8mm cost to the team. Increasing the salary for next year to 8 million made that NPV about 33 million cost to the team. So it looks to me like they can likely find some common ground, if they want to.
Other side, for Butler it means he could be leaving 3 or 4 million on the table, out of a potential 30 million deal, but he assumes the risk of injury eroding that 30 million and quite possibly costing him more than the discount to extend now. One thing is sure, if he extends now he won't ever be frying chicken at Popeye's again, unless it's to show his employees how it's done after he buys the franchise. Basically he can have financial security for life before next season, if he wants. Depends on what he wants.