Z Ltd has on issue $2$ million ordinary shares and $1$ million convertible preference shares of $$0\mathrm{.}50$ each. The holders of the preference shares have the right to convert into ordinary shares at the rate of two preference shares for one ordinary share at a future date. The following figures have been extracted from the statement of profit and loss and other comprehensive income of Z Ltd for the year ending $30$ June $2024.$

Profit after income tax $$290000$

Dividends:

$$ Ordinary $($$$160000)$

$$ Preference $($$ $20000)$

Increase in retained earnings $$110000$

REQUIRED

Calculate the diluted earnings per share for Z Ltd for the year ending $30$ June $2024$