Your boss has asked you to analyze a new project. You estimate that the project will generate a

cash flow of $$3$ million in one year. The cash flow is then expected to grow at $25\%$ per year for

the next $5$ years $($from t $=1$ to t $=2,$ from t $=2$ to t $=3,$ from t $=3$ to t $=4,$ from t $=4$ to t $=5$

and from t $=5$ to t $=6)$ and to remain constant, equal to the cash flow in year $6,$ forever after

that.

The cost of capital is $12\%.$

a$.$ Draw the timeline, showing the cash flows at t $=1,2,3,4,5,6,7$ and $8.$

b$.$ Suppose the firm requires an IRR of at least $18\%$ for each project it invests in$.$ What is the

maximum amount that the firm would invest in the project today $($t $=0)$ in order to meet the

$18\%$ IRR target?

c$.$ Suppose the firm invests the amount calculated in part b$.$

i$.$ What is the NPV of the project?

ii$.$ What is the Profitability Index for the project?