This a really stupid question and I hesitate to ask because the answer will likely be obvious (once I read your responses; and thank you in advance by the way):

When valuing a callable bond in the binomial tree, and the option is exercised at a particular node…we add the coupon payment to the strike price of the option (say, par or 100 plus a coupon payment) and continue on through the tree. But why? The bond has been called; the issuer has it back. I thought with that transaction, they get the bond and I get my 100/par and go on my merry little way,

But in the tree we treat it as if I deliver the bond AND I get the coupon.

It would appear that we assume the coupon gets paid, even if they call it. Is that reality? If not, why do we add the coupon?