A Silicon Valley start-up company faces an opportunity to invest in an R&D project that will revolutionize the way consumers use telephones. intern et and TV. Suppose a project has two phases. where the first phase (R&D) has a one-year expiration that costs $50 million. The second phase (testing and product development) last three years and requires $70 million. Due to fast-changing technology in TV market, the volatility of the project return can vary in each phase of investment - 20% during the first phase and 30% during the second phase. The risk-free rate for the next five years is 6%. If the product is available today. the value of the project would be $100 million.
(a) Determine the underlying asset lattice (how the project value changes over time).
(b) Determine the value of this compound option.