Koch traded Machine $1$ for Machine $2$ when the fair market value of both machines was $$49,400.$ Koch originally purchased Machine $1$ for $$76,200,$ and Machine $1\text{'}$s adjusted basis was $$40,600$ at the time of the exchange. Machine $2\text{'}$s seller purchased it for $$64,400$ and Machine $2\text{'}$s adjusted basis was $$55,600$ at the time of the exchange. What is Koch's adjusted basis in machine $2$ after the exchange?