$3-(38$ points$)$ You are a financial analyst for CloudSoft Corp. The company is considering three software projects: Project Stratus, Project Cumulus, and Project Cirrus.

Cash Flow Projections $($in thousands$)$:

Project Stratus $(5-$year duration$)$:

Year Inflows Outflows

Y$00180$

Y$15020$

Y$26025$

Y$37030$

Y$45522$

Y$56024$

Project Cumulus $(4-$year duration$)$:

Year Inflows Outflows

Y$00150$

Y$13010$

Y$24012$

Y$34514$

Y$43813$

Project Cirrus $(6-$year duration$)$:

Year Inflows Outflows

Y$0090$

Y$14015$

Y$24216$

Y$34517$

Y$44818$

Y$55020$

Y$65222$

a$.$ Calculate the NPV for each project given a rate of return of $18\%.$

b$.$ Rank the projects based on their NPV$.$ Which one should CloudSoft Corp. prioritize?

c$.$ For Project Stratus and Project Cirrus, determine the year in which each project breaks even based on cumulative net cash flows. Which project has a quicker return on investment?

d$.$ How would your recommendation change if the company's required rate of return suddenly increased to $20\%?$ Calculate and analyze the new NPVs for each project.