You are given the following details about Facts of Life pc$.$

Breakdown of activities by percentage of total annual company turnover:

Department stores:

$30\%$

Clothing:

$24\%$

Building materials:

$20\%$

Hotels and catering:

$16\%$

Electronics:

$10\%$

Current share price:

Average annual share price growth over the past five years:

Conglomerate sector average annual share price growth over the past five years:

Level of gearing based on market values $($debt$/$debt $+$ equity$)$:

Conglomerate sector gearing level based on market values $($debt$/$debt $+$ equity$)$:

$2\mathrm{.}34$

$5\%$

$9\%$

$23\%$

$52\%$

The directors of the company were given share options by its remuneration committee five years ago. In one years time the share options will allow each director to buy $100,000$ shares in the company at a price of $2\mathrm{.}00.$ The directors' average annual salary currently stands at $200,000$ on a five$-$year rolling contract basis, while average salaries in the conglomerate sector are $150,000$ and tend to be three$-$year rolling contracts.

$($a$)$ Using the above information to illustrate your answer, critically discuss the extent to which Facts of Life pic can be said to be suffering from the agency problem.

$($b$)$

Discuss how the issues you have identified in part $($a$)$ can be addressed in order to reduce the agency problem.