Question $7(20$ Marks$)$

$($i$)$ Your friend has recently just started a firm with $900,000$ shares. He believes that to expand the firm and fulfill his vision, he requires capital injection to the tune of Gh $\backslash (\backslash$varnothing $800,000\backslash ).$ Should he get the capital, he believes the firm can generate approximately Gh $\backslash (750,000\backslash )$ in earnings $5$ years from today. You did some basic research that places your friend's firm in a P$/$E bracket of $20.$ If the new investor is hoping to annex a $\backslash (45\backslash \%\backslash )$ return on his investment into your friend's business, your friend wants to have clarity on a few things such as:

a$.$ What is the pre and post$-$money valuation of the firm?

b$.$ What proportion of the firm must he give to the new investor on account of the capital injection?

c$.$ How many additional shares must your friend issue for the new investor?