$100 billion for a high-tech structure of 1000km in size? I think you're severely underestimating.
Which is around $175,900 per meter.
(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.