Level 1 CFA® Exam:
Earnings Per Share
To be able to compute earnings per share, we need at least to know net income and the number of shares outstanding. However, to compute EPS (earnings per share) we usually don’t use the number of shares at the beginning of the period or at the end but we rather use the WACSO (weighted average of common shares outstanding) during the period.
The table provides information about a company:
| shares outstanding on 1 January | 8 million |
| shares issued on 1 June | 3 million |
What is the value of the company’s WACSO?
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As we dealt with WACSO, we can now proceed to discuss different types of earnings per share.
We distinguish 2 types of earnings per share, namely:
- basic earnings per share (basic EPS), and
- diluted earnings per share (diluted EPS).
Basic EPS is given by the formula presented below and it is equal to net income less preferred dividends divided by weighted average common shares outstanding. In other words, we divide what is left to common shareholders after preferred dividends are paid by the number of common shares.
The following table presents information about Pro, Ltd. company:
| net income for year ended 31 Dec 2022 | USD 10 million |
| paid preferred dividend | USD 0.5 million |
| common dividends | USD 2 million |
| shares outstanding on 1 Jan 2022 | 8 million |
| shares issued on 1 July 2022 | 3 million |
What is the value of the company’s basic EPS?
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If a company has a complex capital structure and issues potentially dilutive financial instruments, diluted earnings per share must be calculated.
Potentially dilutive financial instruments include:
- convertible preferred shares,
- convertible preferred debt, and
- options.
Let’s calculate diluted EPS if there are convertible preferred stocks outstanding. Convertible preferred stocks are preferred stocks that can be exchanged for common stocks.
For convertible preferred stock, the if-converted method is used. The if-converted method tells us what would happen to EPS if we had converted the convertible preferred stock into common shares at the beginning of the period. Have a look at the formula to be used in your level 1 CFA exam:
Under the if-converted method (in comparison to basic EPS calculations):
- preferred dividends are not subtracted in the numerator because preferred stocks are assumed to be converted,
- weighted average number of shares outstanding in the denominator is increased by new shares from converting preferred stocks.
The table presents information about Pro, Ltd. company:
| net income for year ended 31 Dec 2022 | USD 10 million |
| paid preferred dividend | USD 0.5 million |
| common dividends | USD 2 million |
| shares outstanding on 1 Jan 2022 | 8 million |
| shares outstanding on 31 Dec 2022 | 8 million |
| convertible preferred shares | 300,000 |
The company did not issue any shares throughout the year. Each convertible preferred share is convertible into two common shares. What is the value of the company’s basic and diluted EPS?
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Now we’ll learn how to compute diluted EPS if there is a convertible debt outstanding. A convertible bond gives the bondholder the right to exchange the bond for a specific number of the company’s common shares. For convertible debt, the if-converted method is also used.
The if-converted method tells us what would happen to EPS if we had converted the convertible debt into common shares at the beginning of the period. Have a look at the formula to be used in your level 1 CFA exam:
Under the if-converted method (in comparison to basic EPS calculations):
- after-tax interest on convertible debt is added in the numerator because the company will pay less interest if the debt is converted,
- weighted average number of shares outstanding in the denominator is increased by new shares from converting convertible debt.
Pay attention to 3 things here:
- As in the case of calculating diluted EPS for convertible preferred stocks, the formula assumes that debt is converted at the beginning of the year.
- In the formula we ADD after-tax interest on convertible debt to net income because net income from the income statement takes into account the interest on debt. However, in the if-converted method, we assume that convertible debt was converted and no interest on it was paid.
- Finally, we should remember to subtract preferred dividends in the numerator because the formula takes into account convertible bonds only. Of course, if the company has both convertible preferred stock and debt, we should recognize the impact of both types of instruments when computing diluted EPS.
The table presents information about Pro, Ltd. company:
| net income for year ended 31 Dec 2022 | USD 10 million |
| paid preferred dividend | USD 0.5 million |
| common dividends | USD 2 million |
| shares outstanding on 1 Jan 2022 | 8 million |
| shares outstanding on 31 Dec 2022 | 8 million |
| convertible bonds | 40,000 |
The company did not issue any shares throughout the year. Each convertible bond is convertible into 20 common shares. The interest on convertible debt amounts to USD 350,000 and the tax rate equals 20%. What is the value of the company’s basic and diluted EPS?
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Finally, it’s time we computed diluted EPS if the company has options outstanding. For options, the treasury stock method is used. The term 'treasury stock method' is used only by U.S. GAAP.
Nevertheless, IFRS recommend the same procedures for calculating EPS in the case of options.
The treasury stock method tells us what would happen to EPS if we had converted stock options into common shares. Have a look at the formula to be used in your level 1 CFA exam:
As you can see only the denominator is adjusted for options. The numerator remains the same as in the case of basic EPS. But what exactly happens in the denominator?
We add new shares issued at option exercise but we also subtract the number of shares that the company could repurchase for proceeds from share issuance at option exercise. Note that if the options were outstanding for less than one year, we have to adjust the number of 'new shares' proportionately.
By the way, shares that a company repurchases are called treasury stock, hence the name under U.S. GAAP 'treasury stock method'.
The table presents information about Pro, Ltd. company:
| net income for year ended 31 Dec 2022 | USD 10 million |
| paid preferred dividend | USD 0.5 million |
| common dividends | USD 2 million |
| shares outstanding on 1 Jan 2022 | 8 million |
| shares outstanding on 31 Dec 2022 | 8 million |
| options outstanding at the beginning of the year | 40,000 |
The company did not issue any new shares or granted options throughout the year. Each option gives a right to buy one common share for USD 20. The average price of the company’s shares during the year amounted to USD 50. What is the value of the company’s diluted EPS?
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Dilutive securities are securities that, if included in the diluted EPS calculation, would result in EPS lower than the company’s basic EPS.
On the other hand, antidilutive securities are securities that, if included in the diluted EPS calculation, would result in EPS higher than the company’s basic EPS.
Remember that antidilutive securities are not used for the calculation of diluted EPS and for this reason diluted EPS is always lower than basic EPS. We will illustrate this point by the following example.
The table presents information about Anti, Co. company:
| net income for year ended 31 Dec 2022 | USD 1 million |
| preferred dividends | USD 200,000 |
| shares outstanding on 1 Jan 2022 | 3 million |
| shares outstanding on 31 Dec 2022 | 3 million |
| convertible preferred shares | 50,000 |
The company did not issue any shares throughout the year. Each convertible preferred share is convertible into two common shares. What is the value of the company’s basic and diluted EPS?
(...)
- We distinguish 2 types of earnings per share: basic earnings per share (basic EPS) and diluted earnings per share (diluted EPS).
- If a company has a complex capital structure and issues potentially dilutive financial instruments, diluted earnings per share must be calculated.
- Potentially dilutive financial instruments include convertible preferred shares, convertible preferred debt, and options.
- The if-converted method tells us what would happen to EPS if we had converted the convertible preferred stock (or convertible preferred debt) into common shares at the beginning of the period.
- The treasury stock method tells us what would happen to EPS if we had converted stock options into common shares.
- Dilutive securities are securities that, if included in the diluted EPS calculation, would result in EPS lower than the company’s basic EPS.
- Antidilutive securities are securities that, if included in the diluted EPS calculation, would result in EPS higher than the company’s basic EPS.
- Antidilutive securities are not used for the calculation of diluted EPS and for this reason diluted EPS is always lower than basic EPS.