$1.$ XYZ Manufacturing Company is considering expanding its operations by investing in one of two potential projects: Project A or Project B$.$ Both projects require an initial investment of $$3$ million. The cash flows for each project are as follows:

Project A: Year $1$: $$500,000$ Year $2$: $$800,000$ Year $3$: $$1,200,000$ Year $4$: $$1,500,000$ Year $5$: $$1,800,000$

Project B: Year $1$: $$400,000$ Year $2$: $$900,000$ Year $3$: $$1,300,000$ Year $4$: $$1,700,000$ Year $5$: $$2,100,000$

The company's cost of capital is $12\%.$

$1.$ Calculate the Net Present Value $($NPV$)$ for each project.

$2.$ Construct the NPV profile for Projects A and B$.$

$3.$ Analyze the NPV profiles to determine which project offers the highest potential value for XYZ Manufacturing Company.