$**$Solve this problem by using the formula to calculate diluted EPS. Show step by step work to reach the answer, and explain why the given information do not suffice to calculate dilutive eps.$**$ Thank you!

In the fiscal year $2021,$ Horizon Enterprises reported having $400,000$ shares of common stock and $40,000$ shares of $5\%$ cumulative preferred stock on the books. The par value for each preferred share was set at $$100.$ Throughout the year, Horizon opted not to distribute dividends.

For the year ending on December $31,2021,$ Horizon Enterprises announced a net income totaling $$3$ million, with an income tax rate fixed at $30\%.$ On the first day of the year, Horizon awarded $8,000$ stock options to its senior management team, where each option allowed the bearer to purchase $25$ shares of common stock at a fixed price of $$25$ per share. These options were set to vest following a period of one year. Over the course of $2021,$ the average market price for the common stock was $$28$ per share.

Based on the information provided, calculate the diluted earnings per share $($EPS$)$ for Horizon Enterprises in $2021,$ rounded to the nearest cent.

a$.$ $$5\mathrm{.}65$

b$.$ $$7\mathrm{.}05$

c$.$ $$6\mathrm{.}25$

d$.$ The information given does not suffice to calculate the diluted eps. $($answer$)$