1.13. According to a report in the St. Louis (Missouri) Post-

Dispatch, that city’s main thoroughfare, Interstate 64, will be completely closed to traffic for two years, from January 2008 to December 2009, 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 Missouri Department of Transportation had to make its decision in 2007, one year before the start of construction (so that the first payment is one year away). So the Missouri Department of Transportation had the following choices:

(i) Close Interstate 64 during construction, at an annual cost of $267.5 million per year for two years.

(ii) Keep Interstate 64 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?