$(12$ points$)$ Hawar is an all$-$equity firm with a current share price of $$7\mathrm{.}50$ and $10$ million shares outstanding. The cost of capital for this unlevered firm is $10\%.$ Suppose Hawar are evaluating a project that requires an investment of $$22$ million today and provides free cash flow of $$2$ million per year in perpetuity. This investment has the same business risk as Hawar's existing projects. The corporate tax rate is $40\%.$

$(1)$ Imagine the firm proposes to raise $$22$ million to do the new project by issuing equity. What is the NPV of this project?

$(2)$ Alternatively, imagine that the firm finances the project with $$22$ million of permanent debt at a debt cost of capital of $6\%.$ What is the NPV of the project in this case?

$(3)$ What will the share price be once the firm announces taking this project based on financing choice in $(2)?$