A firm is considering two mutually exclusive projects. Project A has an initial cost of $$150,000($CF$0=-150,000)$ and produces positive after$-$tax cash inflows of $$50,000$ a year at the end of each of the next $3$ years. Project B has an initial cost of $$80,000($CF$0=-80,000)$ and produces after$-$tax cash inflows of $$40,000$ a year at the end of the next $2$ years. If we assume that both projects can be replaced to repeat. The company$$s cost of capital is $8\%.$ What is the most profitable project?

$(1)$ Use the Replacement Chain Approach. Note: Repeat Project A for $2$ times and repeat Project B for $3$ times.

$(2)$ Use the Equivalent Annual Annuity $($EAA$)$ analysis.