You work in Lululemon Athletica's corporate finance and treasury department and your manager, the chief financial officer $($CFO$)$ for Lululemon Athletica, has just handed you the estimated cash flows for two proposed projects. Project A involves adding a new item to the firm's fabric line. It would take some time to build up the market for this product, so the cash inflows would increase over time. Project B involves an add$-$on to an existing line, and its cash flows would decrease over time. Both projects have four$-$year lives because Lululemon is planning to introduce an entirely new line of sport wear at that time.

The following are the net cash flow estimates $($in thousands of dollars$)$:

The CFO also made subjective risk assessments of each project and concluded that the projects both have risk characteristics that are similar to the firm's average project. Lululemon's required rate of return is $11$ percent. You must now determine whether one or both projects should be accepted.

$(1)$ Define the term net present value $($NPV$)$ and its rationale. What is the NPV of each project at the given cost of capital, and which project or projects should be accepted if they are independent? Mutually exclusive?

$(2)$ Would the NPVs change if the required rate of return changed?

$(3)$ Calculate each project$$s IRR and evaluate which projects should be accepted if they are independent? Mutually exclusive?