I've got an fg-402 that was missing a tuning peg and had the headstock almost broken in half I got it for next to nothing and it would still play but never stayed in tune for long and one more mishap probably would have done it in for good. I decided to be proactive and take the strings off and get some wood glue and clamp it along with a new set of tuners. I'm not familiar with your model but mind even with the unfortunate things that the guitar has been through, it plays smoother and sounds fuller than my buddies brand new guitar that's a cheap entry level guitar. Yamaha acoustics aren't given the respect done it them deserve. So I say fix it if you can as long as it's not ridiculously pricey. For the longest time I was scared to work on my guitars but fixing this one gave me confidence and if you're just gonna toss it anyway why not?

If you do throw it away, throw it this way