I think your figures are realistic. And yes, you can use your home equity for start up funds. You can also apply for an SBA backed loan. They require that you come to the table with 30% of your own money (the home quity is good). You will also likely need to put your house up as collateral.

However, that in itself will not get you the loan. Experience in the industry is also a big factor. The fact that you love to cook and bake won't mean anything to the bank if you don't have actual experience running a restaraunt or cafe. Then again, if you can buy an existing business that too will make a difference. An existing (hopefully successful) business stands a much better chance than a new start up.

Go for it! Write you business plan first. You must not approach a lender without your completed business plan. Look below for help with that:

http://smallbusinessstartup.biz/plan/