[mdturnerphys]

That's a good reference point. Cost for infrastructure projects usually isn't linear. I've seen an exponent of .6 used to extrapolate costs.

(3140km/27km)^.6 * $4.75B = $82B. Adjusting for inflation gives you something a bit over the $100B. They probably came up with the number in a similar fashion.

Do you know if your number includes the detectors? They would have contributed significantly to the total cost.