Question

The Department of Public Works and Highways (DPWH) is considering the construction of a new highway through a scenic rural area. The road is expected to cost 60 Million Birr with annual upkeep estimated at 500,000 Birr. The improved accessibility is expected to result in additional income from tourists of 7.5 Million Birr per year. The road is expected to have a useful life of 25 years. If the rate of interest is 15%, should the road be constructed?

Answer 1

Here,

Initial cost = 60 million

Annual Cost = 500,000 = 0.5 million

Annual Revenue = 7.5 million

Net Annual Revenue = 7.5 - 0.5 = 7 million

Interest rate = 15%

Net Present Value = - 60 + 7/(1+.15) + 7/((1+.15)^(2))+ 7/((1+.15)^(3))+ 7/((1+.15)^(4))+ 7/((1+.15)^(5))+ 7/((1+.15)^(6)) + 7/((1+.15)^(7))+ 7/((1+.15)^(8))+ 7/((1+.15)^(9))+ 7/((1+.15)^(10))+ 7/((1+.15)^(11))+ 7/((1+.15)^(12)) + 7/((1+.15)^(13)) + 7/((1+.15)^(14)) + 7/((1+.15)^(15))+ 7/((1+.15)^(16))+ 7/((1+.15)^(17))+ 7/((1+.15)^(18))+ 7/((1+.15)^(19))+ 7/((1+.15)^(20))+ 7/((1+.15)^(21))+ 7/((1+.15)^(22))+ 7/((1+.15)^(23))+ 7/((1+.15)^(24))+ 7/((1+.15)^(25))

Net Present Value = -14.75 million

Hence the road shouldnt be constructed, as NPV is negative