I have three different sizes of the Corona Razortooth folding saws, and they are definitely good low budget saws. They work well and I do not regret purchasing any of them.
What I discovered though is that there's an even cheaper saw that performs surprisingly well. It's the Coghlans Sierra Saw. They cost around ten bucks and the first impressions are that it's a pretty low quality flimsy saw. It's about 7 inches long and it looks and feels like junk, but when you actually saw something with it you'll find that it works way better than you would ever think it would.
I suggest getting one and trying it for yourself. For ten bucks you can't go wrong.
There's also a pocket model which is about 4 inches long. It also works really well despite looking and feeling like junk. It's pretty light weight too.
I'm just saying... you would think that these things are garbage, but they actually work very well for what they are. They're very affordable, so it wouldn't hurt to try them for yourself. If you are on a tight budget, they might be your best option anyway. Just don't expect to be able to abuse them as much as you normally would. Treat them for what they are and they shouldn't let you down.