Joseph was evaluating the feasibility of a project that has an initial investment of $$195,000$ and subsequent investments of $$165,000$ in the $1$st and $2$nd years. From the $3$rd year onwards, it will generate cost savings of $$250,000$ every year for $9$ years.

a$.$ If the project has a terminal value of $$100,000,$ what is the Internal Rate of Return $($IRR$)?$ b$.$ Should the project be accepted if the company's cost of capital is $23\mathrm{.}00\%?$