Q is a quoted airline company that operates a network of intercontinental flights. Q has $100$ million shares in issue and the company has a market capitalisation of $$1\mathrm{.}1$ billion.

Q$\text{'}$s board plans to acquire $100\%$ of L$,$ a quoted hotel company. L owns hotels in many of the countries that are served by Q$\text{'}$s flights. Q$\text{'}$s directors believe that doing so will enable Q to offer holiday packages as well as flights and so will be more profitable.

L has $50$ million shares in issue and the company has a market capitalisation of $$0\mathrm{.}5$ billion. Q$\text{'}$s board plans to issue $50$ million new shares and exchange one new share for each of L$\text{'}$s existing shares.

Each of Q$\text{'}$s directors is remunerated with a salary and a percentage of Q$\text{'}$s annual profit.

$(1)$ Evaluate the planned acquisition of L as a means of creating growth for Q$.$

$($ii$)$ Evaluate the agency implications for Q$\text{'}$s shareholders of the proposal by Q$\text{'}$s directors to acquire L$...$

$($iii$)$ Discuss the possibility that L$\text{'}$s directors will advise L$\text{'}$s shareholders to reject Q$\text{'}$s proposal once it has been announced