Black Kettle Industries is not growing earnings and faces a tax rate of $35\%.$ The firm$$s EBIT is a perpetuity of $$100,000,000$ and it makes annual interest payments of $$40,000,000$ on its outstanding debt of $$600,000,000.$ Its shares currently trade at $$38\mathrm{.}50.$

a$)$ If a company with the same business risk as Black Kettle, but is completely financed with equity, uses a WACC of $9\%,$ how many shares of Black Kettle are there?

b$)$ Assuming the firm can borrow at the same rate its debt is currently financed at$,$ what is Black Kettle's WACC?

c$)$ With reference to the static tradeoff theory, briefly explain why different industries would be expected to have different optimal capital structures