The local W ater Authority is planning to construct a new water treat m ent plan

Question

The local Water Authority is planning to construct a new water treatment plant to cater for increasing water supply demand. The initial capital cost of the project is estimated to be $900,000. The annual operating cost of the plant is $15,000 annually starting at the beginning of year 2. The estimated return from the project is estimated is estimated to be $ 20,000 received annually from the end of year 3. The residual value of the plant is $100,000 at the end of year 20. The evaluation period of the project is 20 years. Assuming a discount rate of 4% estimate the net present value (NPV) of the project and the benefit cost ratio. (All discount tables are in the appendix)

Explanation / Answer

This is for the cash flows from year 1 onwards ...

PV = -15000/(1.04) - 15000/(1.04^2) + 5000/(1.04^3) + 5000/(1.04^4) +......+ 5000/(1.04^19) + 120000/(1.04^20)
PV = -14423.077 - 13868.3432 + [5000/(1.04^3)]* [ 1 + 1/(1.04^1) + ... + 1/(1.04^16) ] + 54766.4335
PV = 26475.013344 + 4444.982 * [ 1 + 1/(1.04^1) + ... + 1/(1.04^16) ]
PV = 26475.013344 + 4444.982 * [ (1/ 1.04 )^ 17 - 1 ] / [ (1/1.04) - 1 ]

so.. PV = 26475.013344 + 56239.22362 = 82714.237

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