What would the cost be of visiting an asteroid?
This is something that has already been done, so we already have a point of reference. Hayabusa landed on the asteroid 25143 Itokawa in 2005. The mission was considered a success and a sample was returned to Earth. According to sources from the time, the total mission cost was around 170 million dollars and other sources put the development cost of the spacecraft at around 138 million dollars. There is also a planned Hayabusa 2.