2. A project requires $150 million investment. If you invest today, the present value of future cash flow is worth $180 million. You can wait for one year to observe the demand of the market; however, you forgo the cashflow in year 

1. Assume if the demand is high, there will be a cash flow of $22 million in year 1 and the present value of future cash flows at the end of year 1 is $220 million; if the demand is low, there will be a cash flow of $12 million in year 1 and the present value of future cash flows at the end of year 1 is $120 million. You need to use risk-neutral valuation method to decide either invest today and start to collect the cash flow or delay it for one year. Annual risk-free rate is 3%. Show your work to get full credit. Keep four decimals. 

(a). What's the risk-neutral probability of high demand? (10 points) 

(b). What's the value of timing option? (10 points) 

(c). Do you want to wait for one year or invest today? Why? (10 points)