In 2012, Brazil began construction of the Belo Monte hydroelectric dam on the Xi

Question

In 2012, Brazil began construction of the Belo Monte hydroelectric dam on the Xingu River (which feeds the Amazon River). The project is funded by a consortium of investors and is expected to cost $11 billion. It will begin producing electricity in 2017. 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 period from 2012 through 2016 at $2.2 billion per year. The disbenefits are estimated to be $100,000 for each displaced person and $1 billion for wildlife destruction. Assume that the disbenefits will occur evenly through the 5-year construction period and anticipated benefits will begin at the end of 2017 and continue indefinitely. Use an interest rate of 8% per year to determine what the equivalent annual benefits must be to ensure a B/C ratio of at least 1.0

Explanation / Answer

Solution:

Let B indicate $ billion

First, convert annual benefits denote as A in year 6 through infinity to A value in years 1 through 5.

B = (A/0.08) (A/F, 8%, 5)

D = [40,000 (100,000) + 1B]/5 per year for 5 years

C = 11B/5

C = $2.2B per year for 5 years

B/C ratio = 1

(B – D)/C = 1 or (Benefits – Disbenefits)/Costs = 1

[(A/0.08) (A/F, 8%, 5*) – 1B]/2.2B = 1

[(A/0.08) (0.17046) – 1B]/2.2B = 1

0.17046 (A/0.08) – 1B = 2.2B

2.13075A – 1B = 2.2B

3.2B = 2.13075A

A = $1.5018 billion per year

Hence, the equivalent annual benefits must be to ensure a B/C ratio of at least 1.0 is $1.5018 billion per year

*A/F, 8%, 5 = [i/[(1 + i)^n-1]

*A/F, 8%, 5 = [0.08/(1.08)^5-1]

*A/F, 8%, 5 = [0.08/0.469328]

*A/F, 8%, 5 = 0.17046

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