Bought house for $130k, divorced later, refinanced to remove ex and took out some cash, new mortgage $250. Sold for $440. Profit $170.
Just using your numbers and information alone with no other facts to work with, your profit/gain is $310k. The refi has nothing to do with the cost basis of the property. However, there is a difference between refinancing, and buying the ex out. A buyout changes the cost basis. But only for the half you purchased. The cash out adds another wrinkle into the equation also when it comes to deductible interest on SCH A.
As far as paying tax on the gain, that depends on when purchased, when sold, how long it was y our primary residence, and the "ex" may qualify for the capital gains tax exclusion on the half they sold to you assuming this was in fact a buy out.
Of course, the wrinkles aren't over yet if you live in a community property state. Potential complexity abounds here. Lesson I learned many moons ago; if it was easy, you did it wrong.
