-When is the best time for a new, growing airline to switch from leasing to owning?
When you got a stabilized cashflow. Sufficient money, sure, but above all regular, so you know what to expect and can plan accordingly.
Also, you want to buy an aircraft type you'll keep for a while (recent and/or long lasting).
-Is it better to wait until an airline has enough cash to purchase a new/used aircraft outright?
Not sure about what you mean, but the growth of an airline is a mix of pure growth (through -cheap- leases) and consolidation (through buying). You need to alternate these phases, and they are not necessarily the same for all your fleet types (could be buying your props while still leasing your workhorse, whatever the reason is).
-Is it better to purchase an older aircraft first? How old is too old? How expensive is too expensive?
An aircraft's lease for 6-7 years is usually the same than the price of the a/c upfront. If "old" is 8 years and you plan to keep the plane for 15 more years, then yes, you can buy. If on the opposite it's gap-filler, lease. Note that a/c meant to fly cargo can usually last longer than pax ones: 1°) they earn more money, so the offset with maintenance is different; 2°) cargo doesn't dislike aging planes as pax do.
-Does being a part of an alliance help? How?
Depends for what aspect. Alliances help getting the planes (many suppliers), but they won't as for prices, as min alliance price can sometimes still be quite high. That's why airlines starting in the middle of a GW usually don't enter their alliance right away, as thus they're able to get cheaper prices. Or they rely on other players outside of that alliance.
However once you're settled, have a nice margin etc. and just need replacements, yes, the alliance helps very much.
And the real question:
-Is it worth it to take out a loan to cover the cost of purchased aircraft?
It also depends, it's a strategic matter:
- If you see an opportunity in a prod line (newly released plane still cheap, freed slots, etc.) for a plane you need, yes
- If you need that plane (expiring lease on another same one that would leave your schedules crippled), yes
- If it's just to add one more plane and is only for your own pleasure, no.
Usually, loans are mostly used to order new planes from the manufacturer rather than from the UM: they cover the initial cost and let you time to grow and increase your cashflow for when the planes will be delivered.