1. Brian Inc has successfully tested a protype of an advanced computer chip. The CEO of the company has agreed to further develop the chip for commercialization. It is expected that the full development will take four years to complete with annual developments cost (paid at the end of the year) $8 million. The probability of project success is 20%. If development is successful and the CEO decides to proceed with commercialization, the factory to produce the chip can be built immediately at a cost of $875 million. The commercialized chip will generate profits of $90 million at the end of every year in perpetuity. Assume that the current four-year risk-free interest rate is 7% per year, and the yield on a perpetual risk-free bond will be 12%, 10%, 7%, or 5% in five years. Assume that the risk-neutral probability of each possible rate is the same. What is the value today of this project and should it be accepted? (5 marks).

2. The price of a one-year call option for Lynas Inc. with a $40 strike price is $ 18.5. The current stock price of the firm is $50 per share, and the one-year risk-free interest rate is 10%. Is there an arbitrage opportunity if the price of an identical put option is selling for $6.00? If there is, how much of riskless profit you would earn by exploiting this opportunity? Clearly show what you must do to exploit this opportunity. (3 marks)