 ## Calculating Basic and Dilutive Earnings-per-Share (EPS) for CFA Level 1

You need to have a firm grasp on how to calculate both basic and diluted EPS under both simple and complex capital structures. Expect at least a few exam questions: one requiring the use of the Diluted EPS equation, another using the basic EPS calculation, and perhaps others testing your general understanding of dilutive vs. non-dilutive securities. This section also introduces the common-size income statement which could be used on the exam.

Why is Earnings-per-share important?

Earnings per share is one of the most commonly used measures of corporate performance. EPS is reported for common stock. We can use both Basic EPS and Dilutive EPS depending on the capital structure of the firm.

## Understanding and Calculating Basic EPS

A firm has a simple capital structure when it has no dilutive securities, or securities that can be converted into common stock. A simple capital structure would only have a mix of common stock, nonconvertible debt, & nonconvertible preferred stock.

Firms with a simple capital structure are only required to report basic EPS.  Where the Basic EPS is calculated as: In our calculation we subtract preferred dividends because EPS is defined as the per-share earnings available to common shareholders. That is also why we DON’T subtract common dividend payments.

In the denominator, the weighted average number of common shares outstanding over a year depends on either a daily or monthly average which can be affected by stock splits/share repurchases. For example if a company with 5,000 shares outstanding at the beginning of the year issues an additional 4,000 shares on Oct 1, the weighted average would be (5,000 + (0.25*4000)) = 6,000 shares.  If a company were to buy back shares we would use the same methodology but exclude those shares from the date they were reacquired.

### Dealing with Stock Splits and Stock Dividends when calculating EPS

In our full CFA Level 1 material we cover stock dividends and stock splits within more detail in the corporate finance section.

A stock split refers to dividing each preexisting share into a specific number of new, post-split shares. After a 3:1 split, a holder of 100 previous shares would now hold 300 shares.

A stock dividend refers to the firm issuing additional shares to its shareholders in an amount proportional to their current holdings. So if you own 200 shares and a 5% stock dividend is paid, you would receive an additional 10 shares.

Neither stock splits nor stock dividends will change the percentage of the company a shareholder owns.

For both methods, you will need to be able to adjust the weighted number of shares outstanding. To do this we adjust all of the shares outstanding prior to the split or dividend. So in our previous example, where the company had 5,000 shares outstanding at the beginning of the year, a 5% stock dividend would cause us to adjust the total shares outstanding by 5% (5,000 * 1.05) = 5250. The split or dividend would not cause us to adjust the additional 4000 shares issued in October after the split. So our weighted average in this example would be 6,250.

## Dilutive EPS

A complex capital structure is one which contains potentially dilutive securities such as options, warrants, and convertible stocks and bonds. Dilutive securities are defined as anything that would decrease EPS if exercised or converted. Anti-dilutive securities are the opposite—they would increase EPS.  Note that firms with a complex capital structure must report both Basic and Dilutive EPS.

Basically, because there is the potential for dilutive securities to increase the number of shares outstanding we need to adjust our basic EPS calculation for the potential dilution.

We calculate diluted EPS as: When calculating this EPS on the CFA Level 1 exam we have to evaluate the impact of each potentially dilutive security separately to determine if in fact it is dilutive. If the security is anti-dilutive we ignore it in our calculation.

So:

• If convertible preferred stock is dilutive (i.e. EPS will fall if converted to common stock) we include those shares in our denominator, but must then add back in convertible preferred dividends as income available to common shareholders
• Similarly, if the convertible bonds are dilutive we would ignore any interest expense on those bonds by adding the after-tax interest expense back in to the numerator[i]

Any dilutive security is weighted in the denominator only by the portion of the year that the dilutive security was outstanding.

### Treasury Stock Method

On the exam this is most likely to be tested with options or warrants.

An option or warrant is dilutive if its exercise price > weighted average share price for the year.

When this is true, we use the treasury stock method to calculate the number of shares to include in the denominator.

The treasury stock method assumes that any funds received by company from the exercise of options would be used to hypothetically purchase shares of a company’s common stock at the average market price. So the net number of shares to add to the denominator is the number of new shares created by exercising the options minus the number of shares the company could hypothetically buy back using the proceeds of the option exercise.

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[i] We only use the after-tax value here because any interest a company pays on bonds is usually tax deductible.