My personal answer:

(1) E[R]=$49640000, [R]=$40487040

(2) E[R]=3*$49640000=$148920000, [R]=$40487040

(3) 3.0441 million

If there's something wrong with my answer, please point it out. Thanks!

2. An oil company is drilling a series of new wells on the perimeter of a producing oil field. About 20% of the new wells will be dry holes (i.e. the production will be 0 barrels per day). Even if a new well strikes oil, there is still uncertainty about the amount of oil produced. Of the new wells that strike oil, 40% produce only 1,000 barrels a day (low yield) and 60% produce 5,000 barrels per day (high yield). (1) Suppose the oil price is $50 per barrel. What is the expected value and standard deviation of the annual revenue of an oil well (assume the well produces oil on 365 days per year)? (2) If the company plans to dig 3 wells, and the outcome of the 3 wells are independent of each other (i.e. the p between every two wells is 0), what is the expected value and standard deviation of the average annual revenue from the 3 wells? (3) Suppose the incremental cash flows of digging and operating a well under the three possible scenarios are as follows. Using a 20% annual discount rate, what is the expected value of the NPV of one well? Year 0 Dry -150M 0 1 2-19 20 Low Yield -150M -13M 5M 5M High Yield -150M -10M 80M 5M 0 0