Suppose that a major city’s main thoroughfare, which is also an interstate highway, will be completely closed to traffic for two years, from January 2014 to December 2015, for reconstruction at a cost of $535 million. If the construction company were to keep the highway open for traffic during construction, the highway reconstruction project would take much longer and be more expensive. Suppose that construction would take four years if the highway were kept open, at a total cost of $800 million. The state department of transportation had to make its decision in 2013, one year before the start of construction (so that the first payment was one year away). So the department of transportation had the following choices:

(i) Close the highway during construction, at an annual cost of $267.5 million per year for two years.

(ii) Keep the highway open during construction, at an annual cost of $200 million per year for four years.

a. Suppose the interest rate is 10%. Calculate the present value of the costs incurred under each plan. Which reconstruction plan is less expensive?

b. Now suppose the interest rate is 80%. Calculate the present value of the costs incurred under each plan. Which reconstruction plan is now less expensive?