Hi there. I am so desperately confused and I need help. I have a 1985 Fuji Allegro (pic attached) that I would like to convert into a single speed. This is my first time doing this. After perusing the forum and consulting Sheldon Brown, I figured that all I would really need to do is remove a chainring and replace the cassette with a BMX freewheel, using some spacers to get a correct chainline. I was hoping I could get this done for under $50.

I went down to my local bike shop and the guy said it would cost me $300, or $250 if I did the work myself. He said my back wheel needs to be replaced because just replacing just the freewheel would cause an incorrect chainline. This price seems absurd, and there's no way I'm putting that type of cash into a $25 garage sale bike.

Anyway, now I'm really confused. How much would this project cost me? What would I need to do/buy to make this a single speed?

Thanks very much!