I am confused when should I add back preferred dividends when computing diluted

Question

I am confused when should I add back preferred dividends when computing diluted EPS.

At December 31, 2010, Sager Co. had 1,200,000 shares of common stock outstanding. In addition, Sager had 450,000 shares of preferred stock which were convertible into 750,000 shares of common stock. During 2011, Sager paid $600,000 cash dividends on the common stock and $400,000 cash dividends on the preferred stock. Net income for 2011 was $3,400,000 and the income tax rate was 40%. The diluted earnings per share for 2011 is

In this question I added back $400,000 back to net income. However, the solution manual showed they I wasn't suppose to add it back. Why is that?

                           Correct solution:       (3,400,000) / (1,200,000 + 750,000) = $1.74.

Explanation / Answer

Preferred dividend should not be added back because if we take net income then preferred stock dividend should not be added back but when we take earning for equity shareholders then would be added preferred dividend.

so solution is :

Diluted earning per share = 3400000/1950000 = 1.74

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