... it would take Facebook 107.66 years to afford to buy themselves.
Only if their earnings were constant for the next 107.66 years. People expect Facebook's earnings to continue to grow. Apple's earnings, by contrast, are considered mature.
Facebook's earnings are via a controlled ecosystem. You can't maintain higher profits that way. You can have short-term higher profits that way - just not maintain them.
It's not about whether they can be considered an "upstart" it's about whether speculators think they have the potential to make much more money than they already do. Amazon for example has been around for 2 decades and have a PE ratio of 179 because they've put nearly all their profits into investing in new businesses that has a lot of potential to make more money down the road.
Only if their earnings were constant for the next 107.66 years. People expect Facebook's earnings to continue to grow. Apple's earnings, by contrast, are considered mature.