XYZ Corporation is planning to invest in a new project that involves an initial outlay of $$800,000.$ The expected cash inflows are as follows: $$100,000$ in Year $1,$ $$200,000$ in Year $2,$ $$300,000$ in Year $3,$ and $$400,000$ in Year $4.$ However, the project will also incur additional costs of $$150,000$ in Year $2$ and $$100,000$ in Year $4.$ Compute the IRR for this investment.