For the year ended 31 December 2009, Bright-Warm Utility Company had net income of $1,750,000. The company had an average of 500,000 shares of common stock outstanding, 20,000 shares of convertible preferred, and no other potentially dilutive securities. Each share of preferred pays a dividend of $10 per share, and each is convertible into five shares of the company’s common stock. Calculate the company’s basic and diluted EPS.

(Institute)

Institute, CFA. 2016 CFA Level I Volume 3 Financial Reporting and Analysis. CFA Institute, 07/2015. VitalBook file.

The citation provided is a guideline. Please check each citation for accuracy before use.

My solution to the problem:

Basic EPS= (1,750,000-200,000)/(500,000+20,000)

But, the solution in the book is:

Basic EPS= (1,750,000-200,000)/(500,000)

Why is it that prefered stocks are not taken into denominator? It doesn’t make sense to pay out dividend and yet not take into account the prefered stock in weighted average number of shares.

Basic EPS is only taking common equity into account. Basic EPS = (Earnings - Preferred Divs)/Common Shares

The Diluted EPS would be = (1,750,000)/(500,000+(20000*5)) = 2.9166.

The explination for this is: Preferred shares act similarly to debt, meaning they are not typically sharing in the profits of the firm and are a fixed ($10/shr in this case) cost. For basic EPS once you pay the expense the remaining earnings are allocated to common shareholders.

For diluted, you are assuming the shares are converted into common equity, so you no longer need to pay the $10/shr but you convert to common that is your new denominator. Keep in mind if the calculated dilutive EPS > Basic EPS, the actual dilutive EPS number will = Basic EPS. The dilutive EPS number can NEVER be higher than the Basic EPS.

Because its basic eps, you are only looking at ordinary shares and any income associated or relevant to these ordinary shares. thats why the numerator deducts the dividends associated with preferred shares and the denominator excludes the preferred shares as well. whats left is completely related to ordinary shares.

Yawyyyork explained it explicitly. Preferred shares are like debt, and once you have paid the debtor, there is no reason for them to benefit from the profit of the firm, that is why we exclude them from the calculation of the Basic EPS. However, in the diluted EPS, we are assuming that the debt (prefered shares) is now converted to common equity, which means we dont have to pay them the preferred dividend again, i.e., Net income + {Prefered dividend - Prefered Dividend} as your nominator. You can see that the prefered dividend cancel each other out, so you’re left with only the Net Income as your nomination. Now in your denominator, because you have converted the prefered stocks into equity, they have the right to benefit from the profit of the firm, which is why we added the converted prefered shares stock to the denominator to get the Diluted EPS.

Like Yawyyyork stated as well, if the Diluted EPS > Basic EPS, then the Basic EPS is referred to as the Diluted EPS, and we say the Prefered Stocks are Antidilitive.