## What is Diluted EPS? How is it calculated?

Part2: Diluted Earnings Per Share (Diluted EPS)

Diluted EPS is one which is calculated after all the convertible securities are converted into common stock. If a company has convertible securities (that is, if the company has complex capital structure), its basic EPS is greater than diluted EPS. And, if a company has a simple capital structure, its basic EPS is equal to diluted EPS.

Calculating diluted EPS

There are three scenarios that arises while calculating diluted EPS: (1) Convertible Preferred Stock, (2) Convertible Debt, and (3) Employee Stock Options. Let’s discuss them in detail.

(1) Diluted EPS for a company with convertible preferred stock outstanding

When a company has convertible preferred stock, EPS is derived using if-converted method – what EPS would have been if all the convertibles were been converted into common stock at the beginning of the period. If the convertibles were been converted, then there would not be any outstanding convertible securities; instead there would be additional common shares outstanding. Hence, if such conversion had happened, the company would not have paid any preferred stock dividend.

Formula to calculated diluted EPS

Net Income / (Weighted average common shares outstanding + New common shares that would have been issued after conversion)

Example

For the year ended December 31, 2000, let’s say, Company A had a net income of \$3,500,000 with 500,000 average common shares outstanding and 50,000 convertible preferred stock which has the option of converting into 5 common shares each. Dividend paid on preferred stock is \$10/share. Calculate Basic EPS and Diluted EPS.

 Components Basic EPS Diluted EPS (if-converted method) Net Income 3,500,000 3,500,000 Preferred Dividend 500,000 0 Weighted Average Shares Outstanding 1,000,000 1,000,000 If converted 0 250,000

Basic EPS

(3,500,000 – 500,000) / 1,000,000 = \$3.00

Diluted EPS

3,500,000 / (1,000,000 + 250,000) = \$2.80

(2) Diluted EPS for a company with convertible debt outstanding

In this case, the diluted EPS is calculated using the same if-converted method as above – if the convertible debts were converted, these debt securities would no longer exist. Instead additional common shares would be outstanding. Hence, if such conversion had happened, the company would not have paid any interest on the debt.

Formula to calculate the diluted EPS

(Net Income + After-tax interest on the convertible debt – Preferred dividend) / Weighted average common shares outstanding + New common shares after conversion)

Example

Let’s say, a company reported a net income of \$3,500,000 for the year ended December 31, 2000, with 1,000,000 common shares outstanding, \$100,000 of 6% convertible bonds that are convertible into 20,000 common shares. Assuming a tax rate of 30%, calculate their basic and diluted EPS

 Components Basic EPS Diluted EPS (if-converted method) Net Income 3,500,000 3,500,000 After-Tax Interest 0 4,200 Preferred Dividends 0 0 Weighted Average Common Shares Outstanding 1,000,000 1,000,000 If converted 0 20,000

Basic EPS

3,500,000 / 1,000,000 = \$3.5

Diluted EPS

If the convertible bonds were converted, then there would be only common shares outstanding – an additional 20,000 shares would be outstanding. Also, since the conversion had taken place, no debt interest of \$6,000 (6% x \$100,000) need to be paid on the bond. Hence, 6,000 x (1 – 30%) = 4,200 gets added on an after-tax basis. Therefore,

Diluted EPS = (3,500,000 + 4,200) / (1,000,000 + 20,000) = \$3.45

(3) Diluted EPS for a company with stock options, warrants or equivalent

In this case, diluted EPS is computed using treasury stock method – what EPS would have been if the stock options were been exercised and the company had utilized the cash to purchase treasury stock. When the options are exercised, the options are no longer outstanding; instead the company receives cash with additional common shares outstanding. Further, we need to calculate the number of common shares outstanding to adjust the shares that could have been bought with the cash received through exercising the options.

Formula

(Net income – Preferred dividends) / (Weighted average number of common shares outstanding + Additional shares because of options exercise – Shares purchased with the cash received)

Example

Let’s say, Company A reported a net income of \$3,500,000 with 1,000,000 common shares outstanding, 50,000 options outstanding with an exercise price of \$30. Over a period of time, the market price of the stock has increased to \$50. Calculate basic and diluted EPS

 Components Basic Diluted EPS (Treasury Stock) Net Income 3,500,000 3,500,000 Preferred Dividend 0 0 Weighted Average Common Shares Outstanding 1,000,000 1,000,000 If converted 0 20,000

Basic EPS

3,500,000 / 1,000,000 = \$3.5

Diluted EPS

Cash received (exercising options) = \$50,000 x 30 = \$1,500,000

Additional Common Shares Outstanding = 50,000 (because options were been exercised)

Treasury Stock purchased = 1,500,000 / \$50 = 30,000

Net new common shares = 50,000 – 30,000 = 20,000

3,500,000 / (1,000,000 + 20,000) = \$3.43