Suppose if you spend $1 million today on a research project, there is a 30% chance of success at year-end and a 70% chance of failure. In the event of failure, you can decide to invest another $1 million to continue the project. If you do invest, the probability of success at the end of the second year is 40% and the probability of failure is 60%. If the project fails again, you can invest another $1 million but the probability of success falls to 20% and the probability of failure is %80. Conditional on success at any stage, the investment is expected to generate cash ?ows worth $4 million. Assume the investment risk is diversi?able and the risk-free rate is 0%.
(a): Draw the binomial tree and payoffs for each node.
(b): What is the NPV of the opportunity if you always have to reinvest in the event of failure?
(c): What is the NPV of the opportunity when you have the option to decide whether to re-invest if the venutre has failed? (Hint: work backwards to ?nd optimal strategy