TerraCorp is about to open up a new branch. It will cost $$35$M today to set up$,$ and will result in $$9$M in EBIT per year for the next $8$ years, starting one year from today. TerraCorp is going to borrow $$20$M of the startup costs for $8$ years, at a rate of $3\mathrm{.}2\%.$ EarthCo, a firm with very similar operations, has a levered cost of equity of $15\%,$ a debt$-$to$-$equity ratio of $2,$ and a cost of debt of $6\%.$ The corporate tax rate is $25\%.$

a$)$ What is TerraCorp$$s cost of unlevered equity?

b$)$ What is the present value of the tax shield from TerraCorp$$s debt?

c$)$ What is the APV value of this project?