It's actually crazy how much estimates on this vary; however, the general number sits around $60k for the initial capital investment.
To give you an accurate idea of what to expect, I've pulled together as many estimates as I could find as well as my own experience working with home care agencies.
Kenyon Home Care Consulting: $60k averageHome Care How-To: $45k minimum to start an independent agency or $35-48k for a franchisee license plus most of the cost of starting an independent agency.
SeniorServiceBusiness.com: $900 if you're willing to do things extremely cheaply and take the absolute lowest-cost options in every instance.(In my opinion, this number is inaccurate because you'll quickly to have to add other overhead and infrastructure, but it's useful as a reminder that there are low-cost options everywhere to get started.)
Home Care Pulse: $60k for your first six months of operation