Alan Mills Co has a capital structure consisting of $40\%$ debt and $60\%$ common equity.

They have $$15$ million in available cash $($reinvested profits$)$ to use for capital projects.

Their common shares are selling for $$30\mathrm{.}00$ each. Dividends for next year $($D$1)$ will be $$1\mathrm{.}50$ per

share, and a growth rate of $9\%$ is expected. Underwriting costs for the issue of new shares will be

$$3\mathrm{.}00$ per share.

Up to $$20$ million in bonds can be issued at $11\%$; any amounts greater than this will have to yield

$13\%.$

The corporate tax rate is $34\%.$

Required complete in order, inputting only the answer for the bolded required:

a$)$ Calculate the initial weighted average cost of capital. Use one decimal and do not use $\%.$

For example, for $5\mathrm{.}2\%$ put $5\mathrm{.}2$

b$)$ At what size capital structure will the firm run out of retained earnings?

c$)$ What will be the marginal cost of capital immediately after that point?

d$)$ At what size capital structure will there be a change in the cost of debt?

e$)$ What will be the marginal cost of capital immediately after that point?