$8.$ Alice Corporations has two divisions. The one in the high$-$risk industry has a beta of $1\mathrm{.}5$ and can be financed optimally in line with others in the industry at $25\%$ debt and $75\%$ equity. The low risk division has a beta of $\mathrm{.}8$ and based on industry averages, can be financed optimally at $50\%$ debt and $50\%$ equity. Assuming the risk$-$free rate of return on $10-$year government securities is $2\mathrm{.}7\%$ and the market risk premium is $5\%.$ What is the estimated cost of common equity for the high$-$risk division?

$9.$ Continuing from the prior problem, what is the estimated after$-$tax cost of equity for$10.$ Still working with Alice Corporation and the information from the prior two prob$-$lems, assume that the after$-$tax cost of debt for the high$-$risk division is $6\%$ and the after$-$tax costs of debt for the low$-$risk division is $5\%.$ What are the weighted average divisional costs of capital for each division? the low$-$risk division?