Lucy Inc. is considering investing in a project which will cost $$150,000$ today and produce the following after$-$tax cash flows: year $1$$$10,000$; year $2$$$50,000$; year $3$$$75,000$; year $4$$$100,000.$ The risk of the project requires a return of $$12\%.$

What is the IRR of this project? Based on IRR rule, should Lucy Inc. take on this project?