On December $31,2017,$ Berclair Inc. had $200$ million shares of common stock and $3$ million shares of $9\%,$ $$100$ par value cumulative preferred stock issued and outstanding. On March $1,2018,$ Berclair purchased $24$ million shares of its common stock as treasury stock. Berclair issued a $5\%$ common stock dividend on July $1,2018.$ Four million treasury shares were sold on October $1.$ Net income for the year ended December $31,2018,$ was $$150$ million.

Also outstanding at December $31$ were $30$ million incentive stock options granted to key executives on September $13,2013.$ The options were exercisable as of September $13,2017,$ for $30$ million common shares at an exercise price of $$56$ per share. During $2018,$ the market price of the common shares averaged $$70$ per share. The options were exercised on September $1,2018.$

Required:

Compute Berclair's diluted earnings per share for the year ended December $31,2018.$ Be clear on the calculations.