Hanson Co$.$ had $200,000$ ordinary shares, $20,000$ shares of convertible preference shares, and $$1,000,000$ of $10\%$ convertible bonds outstanding during $2011.$ The preference shares are convertible into $40,000$ ordinary shares. During $2011,$ Hanson paid dividends of $$1\mathrm{.}20$ per share on the ordinary shares and $$4$ per share on the preference shares. Each $$1,000$ bond is convertible into $45$ ordinary shares. The net income for $2011$ was $$800,000$ and the income tax rate was $30\%.$

Diluted earnings per share for $2011$ is $($rounded to the nearest penny$)$

Question $13$ options:

$$3\mathrm{.}33.$

$$3\mathrm{.}05.$

$$2\mathrm{.}81.$

$$2\mathrm{.}77$