" the value of the transfer would be equal the the closing price of the previous day. And that would be my new cost basis. "
That's exactly correct.
Unfortunately, some brokers (e.g. TD Ameritrade) don't update the internal records correctly so you have to be careful.
I speak from experience.
When I look at my outstanding profit/loss on the position, it is wrong. I have the correct basis recorded in Quicken.
