When I was first trying to answer your question I tried to work with the numbers you presented, but I couldn't get them to make any sense unless you used some of the proceeds of the new loan to make additions or improvements to the property. So I took the other approach and simply told you in a general fashion what would increase your basis in the property.
With you second example let's say, for sake of simplicity, that you originally bought the property for $100K, all cash. The value of the property goes up enough that now you can get a $110K loan. You "repay" yourself your original $100K and actually get an additional $5K to put in the bank in addition. Presumably the "missing" $5K got consumed in refinancing costs. You did't pay an additional $5K for the property, you paid an additional $5K to get that $110K loan.
