Suppose the corporate tax rate is $25\%.$ Consider a firm that earns $ $1000\mathrm{.}00$ before interest and taxes each year with no risk. The$$ firm's capital expenditures equal its depreciation expenses each$$ year, and it will have no changes to its net working capital. The$$ risk$-$free interest rate is $5\%.$

a$.$ Suppose the firm has no debt and pays out its net income as a dividend each year. What is the value of the$$ firm's equity?

b$.$ Suppose instead the firm makes interest payments of $ $500\mathrm{.}00$ per year. What is the value of$$ equity? What is the value of$$ debt?

c$.$ What is the difference between the total value of the firm with leverage and without$$ leverage?

d$.$ The difference in $($c$)$ is equal to what percentage of the value of the$$ debt?