Let's say you buy a SIM, and you buy $25 of time. Over the first 12 months you'll be charged 12 x $0.99 for 911 service (let's round it up to $12). That leaves $13 of credit = 65 min of local calls. If you paid $30 for the SIM, a total of $55, you're $45 ahead of the guy who took the $100 deal. That $45 would allow another 225 min of local calling. So in year 1, if you use less than 290 min, you'd be ahead buying the SIM. Of course the other guy could have used 465 min (including the free $5, and deducting $12 for 911). In subsequent years, you both have to spend at least $25 - providing another 65 min of local calls. If you use less than 290 min, the remaining time would be carried forward when you top-up.

Which sets up this table for the threshold usage below which buying a SIM would be cheaper (assuming SIM cost = $30).

1 year 290 min (24 min/month)
2 years 355 min (15 min/month)
3 years 420 min (12 min/month)
4 years 485 min (10 min/month) .. etc

But don't forget this ignores the cost of the other phone. If that phone was more than $45 the $100 deal will be better - because you've also spent $100 - but only have 65 min of calls available.

It's also true that buying top-ups as required, rather than having to spend $100 upfront, does mean that the time would carry forward longer - which would reduce the average monthly cost for low-volume users.

Eventually you will have used $100 worth of time. If you take the $100 deal you will pay $100 for that time (and you will also get $5 extra time when you activate the phone). If you buy a SIM you will pay $100 + SIM cost for $100 of time. I've left the 911 fee out - it has the same effect over the same number of months