If a better motor fluid is used, the capital cost will increase by 350, but fluid losses will be reduced through the 30 year life of the project. The optimistic, most likely, and pessimistic projections are 35, 30 and 23. All estimates are inflation adjusted and the real MARR is 4%.

a. What is the NPV under the "most optimistic" projection of annual savings? Under "most likely" projection savings? Under "Pessimistic assumption"?

b. Does the expected value of the NPV equal the NPV for the most likely outcome? why or why not?

c. Using the beta probability distribution to calculate the expected value of NPV. Attach a probability of 2/3 to the most likely outcome and a probability of 1/6 to both the pessimistic and optimistic outcomes.