POSCO Steel is considering a major investment in a new plant with a capacity of 1 million tons. It is anticipated that the plant will cost $ 1 billion to build and generate expected after-tax cashflows of $ 100 million a year for 20 years. There is substantial uncertainty about these expected cash flows the standard deviation in annual cash flows is 40% - and the cost of capital is 10%. As CEO of the company, you are concerned about the risk and you are considering an alternative plan. You will invest in a smaller plant with a capacity of 500,000 tons, which will cost $ 500 million to build and generate expected cashflows of $ 50 million a year for 20 years. However, you will have the ability to double the capacity and the expected annual cashflows for the remaining project life anytime over the next 5 years by spending an extra $ 500 million. You can assume that the cost of capital remains 10% and that the treasury bond rate is 3%. Should you invest in this alternative plan? Support your answer with numerical analysis.