A company is considering to take a $3$ year project with $$30$ million initial cost. If the demand is high, the project will generate cash flow of $$20$ million each year. If the demand is average, the project will generate cash flow of $$15$ million each year. If the demand is low, the project will generate cash flow of $$5$ million each year. The cost of capital for the project is $10\%.$ The probability of high demand, average demand, and low demand are $20\%,60\%$ and $20\%$ respectively. The company can also choose to wait for $1$ year until it knows which demand conditions and set of cash flow will occur. Assuming if we wait, the up$-$front cost, cash flows and risk will stay the same, except they will be shifted ahead by a year. What is the expected NPV if a firm is waiting for $1$ year using decision tree analysis. Risk free rate$=5\%.$