Northern Distributors expects a $17\%$ rate of return on their investments. They are considering a $15-$year project which will cost them $$100,000$ immediately, $$10,000$ each year for years $2$ to $6,$ $ $20\mathrm{.}000$ each year for years $7$ to $11$ and $$25,000$ each year for the years $12$ to $15$ of the project. Should they take on the project if it will return $$30,000$ at the end of each year for the first $3$ years, $$40,000$ at the end of each year in the next $4$ years, and $$60,000$ at the end of each year for the last $8$ years?

a$)$ Prepare a fully documented timeline of all cash flows

b$)$ Calculate the NPV of the project.