$24)$ Optimal capital structure $(15$ points$)$

Ham & Cheese Inc. paid an annual dividend of $$6/$share this year. The firm$$s common stock dividends grow at a consistent rate of $2$ percent per year. Common stockholders currently require an annual return of $12\%$ per year on their investment.

The company currently has a $50\%$ debt $-50\%$ equity capital structure. The firm$$s CEO believes that by increasing debt, the company can leverage a higher return for shareholders. He is considering changing the capital structure to $60\%$ debt $40\%$ equity, if such change would benefit the shareholders.

The firm estimates that if it increases the debt ratio, it will be able to increase its dividend growth to $3$ percent per year, and this growth can be sustained indefinitely thereafter. Due to a higher level of debt, the firm$$s common stockholders will require a higher annual return of $14\mathrm{.}5\%$ per year on their stock investment.

Given the above information:

$($a$)$ Find the firm$$s stock price under the current capital structure $(5$ points$)$

$($b$)$ Find the firm$$s stock price under the proposed capital structure $(5$ points$)$

$($c$)$ Given your answers to part $($a$)$ and $($b$),$ explain why the company should or should not change its capital structure $(5$ points$)$