With an installed capacity in excess of 11,000 MW, the Belo Monte dam complex on the Xingu River in Brazil will be the world’s third largest hydroelectric dam. The project is expected to cost $16 billion and will begin producing electricity upon completion by the end of 2019 after the 5-year construction period. Even though the dam will provide clean energy for millions of people, environmentalists are sharply opposed. They say it will devastate wildlife and the livelihoods of 40,000 people who live in the area to be flooded. Assume that the funding will occur evenly over the 5-year construction period (i.e., $3.2 billion per year), and that the disbenefits will be $66,000 for each displaced person and $1 billion for wildlife destruction. Further, assume the disbenefits will occur

Question

evenly through the 5-year construction period and the benefits will begin in 2020 and continue indefinitely. At a discount rate of 8% per year, use the B/C ratio to determine the minimum annual benefits required to economically justify the project.

What will be an ideal response?

Answer 1

Convert annual benefits in years 6 through infinity to an A value in years 1 through 5.
B = (A/0.08)(A/F,8%,5)
D = [40,000(66,000) + 1,000,000,000]/5 = $0.728 billion per year for 5 years
C = 16/5 = $3.2 billion per year for 5 years
1.0 = (B – D)/C
1.0 = [(A/0.08)(A/F,8%,5) – 0.728]/3.2
1.0 = [(A/0.08)(0.17046) – 0.728]/3.2
3.2 = (0.17046)A/0.08 – 0.728
A = $1.8435 billion per year