Please show details of the problem 11. If higher voltage transmission lines are

Question

Please show details of the problem

11. If higher voltage transmission lines are used, the initial capital cost will increase by $250,000, but transmission losses will be reduced throughout the 30-year life of the project. The optimistic, most likely, and pessimistic projections for annual savings are $25,000, $20,000, and $13,000. Al estimates are "real," i.e., inflation adjusted, and the real MARR is 6%. What is the NPV under the most optimistic projection of annual savings? Under the most likely projection of savings? Under the pessimistic assumption? a. Optimistic NPV Most Likely NPV Pessimistic NPV b. Use the beta probability distribution to calculate the expected value of NPV. That is, attach a probability of 2/3 to the most likely outcome and a probability of 1/6 to both the pessimistic and optimistic outcomes. Does the expected value of NPV equal the NPV for the most likely outcome? Why or why not? c.

Explanation / Answer

Expected Value of NPV = $20708

Requirement c:

Expected NPV = $20708

Most likely NPV = $25297

The expected NPV does not equal thw NPV for the most likely outcome. This is because of the reason that the probability assigned to most likely scenario is not one.

Requirement a: Optimistic Most Likely Pessimistic Annual Savings 25000 20000 13000 PVAF(6%, 30) 13.764831 13.764831 13.764831 PV of Annual Savings 344120.775 275296.62 178942.8 Incremental Initial Cost -250000 -250000 -250000 NPV 94121 25297 -71057 Requirement b: Expected Value of NPV: Optimistic Most Likely Pessimistic NPV 94120.775 25296.62 -71057.197 Probability 0.166666667 0.666666667 0.1666667 Expected Value of NPV 15687 16864 -11843 20708

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