Consider an investment with uncertain cash flows. The initial cost of the investment is $10,000 in year zero. You estimate three scenarios for the following five years: Most likely case: The project will generate $2,500 in year 1 and it will increase by $500 each year until year 5. Optimistic case: The project will generate $4,000 in year 1 and it will increase by 10% each year until year 5. Pessimistic case: The project will generate $1,500 in year 1 and it will decrease by 5% each year until year 5. a) (10 points) Using properties of Beta distribution, calculate expected value (E[An])and variance (V ar(An)) for each years cash flows (for n = 1, 2, 3, 4, 5). b) (5 points) Assuming that periodical cash flows are independent, determine the expected value and the standard deviation of the present worth for this investment using a yearly interest rate of 15% compounded annually. c) (10 points) Using normal approximation, find the net present worth at risk (VaR) with a 95% confidence level for the duration of the project. ((1.645) = 0.05, where () is the cumulative density function for a standard normal random variable).