A clean water project in developing country would a?ect the health of a village of 500 people (100 children, 300 workers, and 100 elderly people). The project's immediate implementation would cost $70, 000. It has been estimated that the project would improve the health of workers so that workers can work an extra 200 hours per year, starting next year, 2013. Five years down the road (in 2018) the central government will clean up all the water of the entire country for "free".
The village produces only one good: meat, which is sold in the world market for $4 per pound. The production function for annual meat output is: Y = 10 ∗Kˆ(1/2) ∗ Lˆ(1/2), where Y is output of meat in pounds, K is capital and L is labor measured in worker hours.
The village's capital stock is constant at 1, 000 every year and a worker's annual labor hours are 1, 500. The current interest rate is stable at 8% and is projected to increase to 10% in 3 years (in 2016). Use CBA and investigate whether to implement the clean water project or not. Carefully describe every step in your analysis.
(a) HINTS: Calculate the current annual output of the village in $s
(b) Calculate the annual output of the village if the water project would be installed in $s
(c) Calculate the "extra" output due to the water project. Think carefully about the time horizon that extra bene?ts are realized and properly discount these bene?t streams. Use the appropriate discount factors.
(d) What is the present value of bene?ts and what is the present value of costs (all in $).
(e) If you make assumptions, carefully describe them and explain why you make such an assumption!