Richard (cyphyr) is right, an animation of that length would be tough to accomplish on reasonably priced home equipment. However I think it could be a little more within reach depending on your budget and scene details. I can say right away though that I am almost certain a render farm would be more affordable than buying the necessary hardware.
That being said, your render time is going to depend heavily on the details of your scene setup, how many shaders are in it, how complex the atmosphere/clouds are, how many object models and populations, whether there is water (reflectivity), etc, etc. For a scene of moderate complexity I believe you may be able to get render time down to around 20-30min/frame for high quality at 720p (1280x720). Going with Richard's figure of approximately 7500 frames (slightly less for 24fps "cinema" framerate, more for 30fps NTSC standard; he's quoting PAL), and assuming you can get it down to 20min/frame, you're still looking at 2500 hours or 104 days of rendering. To get it down to 10 days you would of course need 10 of those machines.
If you have experience building computers (and can thus avoid labor costs for someone else to build it), and you want to buy machines mostly for the purposes of rendering (i.e. they can be very stripped-down, just CPU, motherboard, memory, and storage device in a case with a power supply basically), then I think you could put each machine together for about $800 in parts, not counting the operating system (use Linux, buy TG3 Pro + Anim and you get the linux render node = free OS!). So $8000 for 10 machines to render your animation in 10 days, not counting the time to build them of course.
If you do go this route, probably the best bang-for-your-buck in terms of performance is the new Intel i7-5820K, although the motherboards for it are quite a bit more expensive than for older i7 CPUs at present. Also, don't forget licensing costs.
If you decided to go with a render farm, it's difficult to say for sure, but if you had those 20 min/frame render times and you used Pixel Plow, I'm fairly confident it would be less than $1000 at low priority and would almost certainly be done in less than 10 days. If you needed higher priority, it could be $2500 or so, and definitely done in less than 10.
So basically if this is mostly a one-time thing, then a render farm is going to save you a lot of money. If you plan to keep doing more of these over time, then investing in some hardware might be worthwhile.
- Oshyan