Problem 5: A tech company is considering investing in a new plant. Here are the relevant factors: The project will cost $210 million immediately for design. The design stage will take a year. After that, the firm could invest $400 million to complete the second (preparation) phase of the project or discontinue the project. (Option 1 expires at the end of one year from now, i.e., the end of year 1) If the firm chooses to continue, then it has a two-year window during which it can invest an additional $800 million to build the plant. (Option 3 expires at the end of four years from now) The present value of the plant if it existed today is $1,000 million. Use the continuous time version of binomial option pricing model to value the firm's options, meaning the values of a, u and d are determined using the exponential function. Note: The decision hinges on several contingencies in the future. So you must draw a lattice that highlights the underlying asset's future values, and correspondingly, another lattice that provides the payoffs if the firm exercise its option to invest at specific decision nodes. Part A: Assume: (a) The volatility of the underlying asset's returns is 40%; and (b) the risk free rate is 8% per annum. (i) What is the value of this business opportunity? (ii) Should the firm spend $210 million immediately for design? Part B: Assume: (a) The volatility of the underlying asset's returns is 40%; and (b) the risk free rate is 10% per annum. (i) What is the value of this business opportunity? (ii) Should the firm spend $210 million immediately for design? Part C: Assume: (a) The volatility of the underlying asset's returns is 60%; and (b) the risk free rate is 8% per annum. What is the value of this business opportunity? (11) Should the firm spend $210 million immediately for design?