Problem statement: The State of Georgia wants to build a new railway from Atlanta to Rome, Georgia. A two-lane highway can be built now for $300 million and can be enlarged adding two more lanes 25 years from now for an additional $350 million to accommodate future growth. An alternative is to construct the four-lane highway (full-sized) now for $400 million. Both alternatives would provide the needed capacity for the 50-year analysis period. Maintenance costs are minimal and can be ignored. At a 6% interest rate, should the two-stage or one-stage construction be selected?
I'm assuming that building the high-way now for $400 is cheaper, but I'm not sure how to do the math.