Problem $1(10$ Points$]$

Tropical Sweets is considering a project that will cost $$70$ million and will generate expected cash flows of $$30$ million per year for three years. The cost of capital for this type of project is $10$ percent and the risk$-$free rate is $6$ percent. After discussions with the marketing department, you learn that there is a $40$ percent chance of high demand, with future cash flows of $$45$ million per year. There is a $20$ percent chance of average demand, with cash flows of $$30$ million per year. If demand is low $($a $40$ percent chance$),$ cash flows will be only $$15$ million per year.

a$.$ What is the expected NPV$?$

b$.$ Now suppose this project has an investment timing option, since it can be delayed for a year. The cost will still be $$70$ million at the end of the year, and the cash flows for the scenarios will still last three years. However, Tropical Sweets will know the level of demand, and will implement the project only if it adds value to the company. Use decision tree analysis to calculate the NPV of the project with the investment timing option.