* The minimum cost of conversion? The price of a used road bike + the cost of a flip flop rear wheel + a cog. If you find the rear wheel used too (which shouldn't be a problem since so many people upgrade their completes right off the bat), I don't think it'll necessarily cost more than an affordable complete.
* If you know what you're looking for in the bike to be converted, you could end up with higher quality parts than the hypothetical new complete.
* How many people buy a complete and stop there? A lot of people will change saddles, handlebars, even wheels etc. on a new complete, same as you might on a 2nd hand bike. All this should be factored into the cost for both alternatives, not just the conversion.
* In my mind there's absolutely no need to "butcher" a roadbike to make a conversion. You can leave the frame as is and save the gearing specific parts for a later deconversion.

I'm not saying conversion is always the way to go. But when someone asks for advice about making a conversion, I think it's more on the point to tell them how to do it in the most sensible manner (which is the advice they actually asked for) that to tell them not to do it period. And if the OP can build a wheel, I should think he has the skills to make this happen. If his dad has all the tools, who knows how many parts he has? Plus to me it makes more sense converting a nice old road frame for street use than buying a new 'trackish' frame, but that's just me.