Rubenstein Bros. Clothing is expecting to pay an annual dividend per share of $$1\mathrm{.}05$ out of annual earnings per share of $$3\mathrm{.}75.$ Currently, Rubenstein Bros.$\text{'}$ stock is selling for $$31\mathrm{.}00$ per share. Adhering to the company's target capital structure, the firm has $$15$ million in total invested capital, of which $35\%$ is funded by debt. Assume that the firm's book value of equity equals its market value. In past years, the firm has earned a return on equity $($ROE$)$ of $18\%,$ which is expected to continue this year and into the foreseeable future.

Based on this information, what long$-$run growth rate can the firm be expected to maintain? $($Hint: g $=$ Retention rate $\backslash$times ROE.$)$ Do not round intermediate calculations. Round your answer to two decimal places.

$\%$

What is the stock's required return? Do not round intermediate calculations. Round your answer to two decimal places.

$\%$

If the firm changed its dividend policy and paid an annual dividend of $$2\mathrm{.}10$ per share, financial analysts would predict that the change in policy will have no effect on the firm's stock price or ROE. Therefore, what must the firm's new expected long$-$run growth rate? Do not round intermediate calculations. Round your answer to two decimal places.

$\%$

If this plan is implemented, what must the firm's required return be$?$ Do not round intermediate calculations. Round your answer to two decimal places.

$\%$

Suppose instead that the firm has decided to proceed with its original plan of disbursing $$1\mathrm{.}05$ per share to shareholders, but the firm intends to do so in the form of a stock dividend rather than a cash dividend. The firm will allot new shares based on the current stock price of $$31\mathrm{.}00.$ In other words, for every $$31\mathrm{.}00$ in dividends due to shareholders, a share of stock will be issued. How large will the stock dividend be relative to the firm's current market capitalization? $($Hint: Remember market capitalization $=$ P$0\backslash$times number of shares outstanding.$)$ Do not round intermediate calculations. Round your answer to two decimal places.

$\%$

If the plan in part d is implemented, how many new shares of stock will be issued? Do not round intermediate calculations. Round your answer to the nearest whole number.

shares

If the plan in part d is implemented, by how much will the company's earnings per share be diluted? Do not round intermediate calculations. Round your answer to the nearest cent.

$

per share