If you can do this, or find a small old cheap house for your kid they will be very happy.
My parents bought a little tiny old house from 1943(barely 1k sq ft) here in JAX about 9 years ago for $70k. They used a low cost HELOC from their house that they paid cash for from the sale of company stock.
The rate on the loan and low property tax and insurance means that they only needed $450 from us to cover those costs. So I lived here up until this year with my brother and they charged us $800 a month, so we each split it, $400 a piece.
Now that I live here by myself, I only pay $400, and they use the cash reserve to cover the difference. Since they don't really need the money, and are helping me save up money for a duplex out of state so that I can move closer to them.