The question of cost is a common and early question from prospective clients. As with many such questions, there are many ways to answer.
If you hire your own caregiver, you can certainly reduce the obvious payroll costs, at least initially. Many families that hire individuals on their own, will pay cash and not deduct taxes, pay the employer's share of taxes, have no unemployment or worker's comp insurance and so forth. So initially, this could be quite a bit less.
But what do you have at risk? What are the costs involved if those risks become reality? What if you part ways under unfriendly terms? What if she reports you to the IRS and Department of Labor for failing to pay taxes and overtime. What if she has an accident on the job? What are the costs associated with those risks? What if s/he marries your parent and leaves him/her destitute? What of the Caregiver doesn't want to leave your parent's home? Are you ready to have her evicted?
People either don't think of these things, or think that they won't happen to them. These things do happen and with no experienced management in place, your parent is a 'sitting duck' for abuse, neglect and/or financial exploitation.
Working with a licensed, insured and experienced agency means you will pay a bit more, but what you get for that is true peace of mind. All our caregivers have undergone a fingerprint-based background check, drug screen and multiple other background checks before we would ever consider putting them in someone's home. We also provide training to our caregivers both initially and ongoing. If you don't like the caregiver, we can get you another one. If she needs time off, we have a substitute. We take care of all the taxes, insurance and reporting so you don't have to.
I guess the real question is, can you put a price on your loved one's well-being? For the same reason you don't buy your medicine at a flea market, you should be careful about how you pinch pennies when it comes to home care.