$3\mathrm{.}24$ Reconsider the research$-$and$-$development decision in Figure $3\mathrm{.}32.$ If you decide to continue the project, you will have to come up with the $$2$ million this year $($Year $1).$ Then there will be a year of waiting $($Year $2)$ before you know if the patent is granted. If you decide to license the technology, you would receive the $$25$ million distributed as $$5$ million per year beginning in Year $3.$ On the other hand, if you decide to sell the product directly, you will have to invest $$5$ million in each of Years $3$ and $4($to make up the total investment of $$10$ million$).$ Your net proceeds from selling the product, then, would be evenly distributed over Years $5$ through $9.$

Assuming an interest rate of $15\%,$ calculate the NPV at the end of each branch of the decision tree.