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?
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):
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:
![{\displaystyle 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\,\!}](https://wikimedia.org/api/rest_v1/media/math/render/svg/05edfbe0c9b4f1fb384caa4c406748cf75a5108f)
The cost in present-day value is $4,009,195.33. Therefore, this detail, while shiny in appearance at first, is NOT a wise decision, since costs exceed benefits.