Question

The Department of Transportation plans to build a temporary bridge to reduce travel time during the three years it will take to renovate the Pulaski Skyway, an important bridge for commuters. The temporary bridge can be put up in a few weeks at a cost of $48 million. At the end of three years, the bridge would be decommissioned and the steel would be sold for scrap. The real net cost of decommissioning would be $3 million, after accounting for scrap sales. Based on estimated time savings and wage rates, fuel savings, and reductions in risks of accidents, department analysts predict that the benefits in real dollars would be $15,900,000 during the first year, $18,900,000 during the second year, and $19,000,000 during the third year. Departmental regulations require use of a real discount rate of 4 percent. (a) Calculate the net present value of the temporary bridge assuming that the benefits are realized at the end of each of the three years. (b) Calculate the net present value of the temporary bridge assuming that the benefits are realized at the beginning of each of the three years. (c) Calculate the net present value of the temporary bridge assuming that the benefits are realized in the middle of each of the three years. (d) Does it make sense for the Department of Transportation to build the temporary bridge?

Answer 1

required investment:

building costs = $48 million

decommissioning costs = $3 (at the end of year 3)

benefits:

year 1 = $15,900,000

year 2 = $18,900,000

year 3 = $19,000,000

discount rate = 4%

I rounded my calculations to the nearest thousand:

a) NPV = -48 + 15,900/1.04 + 18,900/1.04² + 16,000/1.04³ = -$1,013,000

b) NPV = -48 + 15,900 + 18,900/1.04 + 19,000/1.04² - 3/1.04³ = $973,000

c) NPV = -48 + 15,900/1.04⁰°⁵ + 18,900/1.04¹°⁵ + 19,000/1.04²°⁵ - 3,000/1.04³ = -$31,000

d) From a strictly financial point of view and only considering the 3 previous calculations, the project should be rejected. Two out of 3 options yield a negative NPV.