It all comes down to the interpretation of the term old plane. A plane can be called old because it was manufactured many years ago. Yet, if properly maintained and overhauled when needed, flying on it might be as safe as flying on any aircraft coming out of the factory. Now, if the term refers to a plane left unattended for many years, then buying it may not be a good idea since it will require a lot of money to take it back to flying form.