Question $1$:

You are estimating the cashflows for a project. You find that, if implemented today, the project costs $$105$ million and generates positive cash flows over the next five years. If the economic situation improves $(30\%$ probability$),$ the project generates annually $$35$ million. If the economic situation remains the same $(50\%$ probability$),$ the project generates annually $$30$ million. If the economic situation deteriorates $(20\%$ probability$),$ the project generates annually $$22$ million cash flow in each of the following five years. The cost of capital for the project is $7\mathrm{.}5\%,$ and the risk$-$free rate is $1\mathrm{.}5\%.$

Now you have a real option to wait for one year and then implement the project. If the project is implemented next year, the project cost goes up to $$110$ million, but you will know the economic situation with certainty. As a result, you will not implement the project if the NPV is negative. Assuming that nothing else changes even if you wait for a year, find out the value of this real option of implementing the project after waiting for a year. Do you exercise the real option?