Question

The dam currently providing irrigation water to farmers in Happy Valley cost $100 million to build, and the valley currently produces 15 million kilos of sugar per annum which sells at the world price of $1 per kilo. The height of the dam can be raised at a cost of $8 million in order to provide more irrigation water to farmers. It is estimated that, as a result of the extra water supplied in this way, sugar production would rise to 15.5 million kilos per annum in perpetuity (ie. forever), without any increase in the levels of other inputs such as fertilizer, labour, equipment etc. Using a 10% rate of discount, what is the net present value, as indicated by the project benefit-cost analysis, of raising the height of the dam?

Please show excel sheet with formulas. I know annual benefit is 500000, PV is 5000000, and NPV is 3000000 but I am confused how to get these values.

Answer 1

We are given,

Cost of increasing the height of dam = $8 million.

Annual benefit = 1 times * (15.5 million - 15 million) = $0.5 million (perpetuity)

Discount rate = 10%

PV of benefit = Annual benefit / Discount rate

Present Value of benefit = 500,000 / 0.10 = $5 million

NPV = PV of inflow - PV of outflow

NPV = 5 million - 8 million = -$3 million.

Hence, the NPV of raising the height of the dam is -$3 million. Therefore, this project is not feasible as NPV is less than 0.

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