According to the Blue Line Extension Fact Sheet [PDF], there are an expected 24,500 average weekday trips by 2035. Assuming that these begin in 2017 and assuming that the travel time savings is 20 minutes (the total trip time across the 9 stops is 22 minutes) yields an estimate of the annual time saved at 424,667 hours (average travel time to work is 25 minutes in Mecklenberg County). Assuming an hourly wage rate of $27 (household income divided by 2000 hours) and attributing 100% of the wage to the value of time saved yields an annual benefit estimate of about $11.5 million. Note that all of my assumptions are likely generous.
As far as I can tell the annual benefits just cover the "estimated $11.5 million in operating costs." That means that the benefits of lower congestion, stronger neighborhoods, improved environmental quality, etc. would need to cover the $1.7 billion construction costs. If each household in Mecklenberg County is willing to pay $100 annually for these benefits (a round number guess), households grow at 2%, and future benefits are discounted at 2%, the present value of nonmarket benefits is $868 million. This falls short of the construction cost by over $200 million. It would take an annual willingness to pay of $250 per household for the benefit/cost ratio to reach 2.
This is certainly not the best use of a billion dollars.