# Fundamentals of Transportation/Evaluation/Solution

A new transportation project is proposed to the city. This project is a form of "guide wire", where cars can hook to these moving, below-ground wires and be transported for free around town. This project is proven to reduce gas consumption by $5 million in its completion year. The city's preferred contractor says that it will take 10 years to build the thing and cost$470,000 a year, which is "perfect" because benefit would exceed costs by more than $300,000. Knowing that inflation is 3 percent, as an expert evaluator, is this a wise decision? Solution: Convert everything to Present Value and see just how great a deal this is. For the present value of the$5,000,000 benefit (gas reduction):
$P={\frac {F}{\left({1+i}\right)^{n}}}={\frac {\5,000,000}{\left({1+0.03}\right)^{10}}}=\3,720,469.57\,\!$ The benefit in present-day value is $3,720,469.57. For the money (cost) being sent to the contractor, a payment of$470,000 per year, the present value would be:
$P=A\left[{\frac {\left({1+i}\right)^{n}-1}{i\left({1+i}\right)^{n}}}\right]=\470,000\left[{\frac {\left({1+0.03}\right)^{10}-1}{0.03\left({1+0.03}\right)^{10}}}\right]=\4,009,195.33\,\!$ 