$($c$)$ ALM would like to increase the dividend by $$0\mathrm{.}40.$ It is considering issuing new shares to finance existing projects. This will free up capital to pay the higher dividend. If the cost of issuing new shares is $5\%,$ demonstrate what impact this would have on shareholders' wealth at the end of the year $($note: new shareholders are not entitled to the dividend$).($ans: $$1\mathrm{.}63)$

Solution:

After an increase in the dividend, each existing shareholder would receive

$$0\mathrm{.}15+$$$0\mathrm{.}4=$$$0\mathrm{.}55$

To pay for the increase in dividend, we need to raise $$0\mathrm{.}4100m=$$$40m$

Assume the number of new shares to be issued is $"n"$; since we have new shareholders, the three projects in the firm will be distributed across existing and new shareholders.

$p=\frac{150}{100+n}$

However, there are two unknown variables in one equation. To solve it$,$ we need to find a second equation. The share price paid by the new shareholder should equal the firm's price.

$p($ new issuance $)=\frac{\frac{40}{0\mathrm{.}95}}{n}$

Solve simultaneous equations. W find: $n=39\mathrm{.}02,p=$$$1\mathrm{.}08$

Total Shareholder Wealth $($existing$)=$$$1\mathrm{.}08+$$$0\mathrm{.}55=$$$1\mathrm{.}63$

How do i find the number of shares issued and the new price per share