Another dodge is to use a tap as a mandrel. It doesn't need to be a new or sharp tap, but it must be the right thread, of course. Taps are usually made with the shank ground from the same centres that the thread is made, so they can be more precise than studding, and firmer to hold in a collet.
So now you know what to do with all those blunt taps you have been saving up. Aunty Flo is never going to get you a fancy grinder, after all.
Cheers, Tim