P$12\mathrm{.}11$ Unlevering the Cost of Capital for a Company with Warrants #$1$: A company has $100,000$ shares of common stock and $10,000$ warrants outstanding. Each warrant has the right to purchase three shares of the company's stock at the end of five years at $$9$ per share. The value of a warrant is $$3\mathrm{.}50$ per warrant, and the company's stock price is $$8$ per share. The standard deviation of the stock's annual return is $30\%.$ The company has a continuously compounded dividend yield of $6\%.$ The company has $$100,000$ of outstanding debt that has an $8\%$ cost of capital. The company's common equity cost of capital is $15\%,$ and the risk$-$free rate is $5\%.$ The company's income tax rate is $40\%$ on all income.

a$.$ Ignore the warrants and calculate the company's unlevered cost of capital and weighted average cost of capital, assuming that the company's current capital structure $($without the warrants$)$ represents its longrun capital structure, and that the discount rate for interest tax shields is the unlevered cost of capital.

b$.$ Using these same assumptions, calculate the company's unlevered cost of capital and weighted average cost of capital, but now include the effect of the warrants.