Diluted EPS Formula (Table of Contents)
Diluted EPS Formula
Where,
Convertible Securities = Convertible preferred shares + Convertible debt + Stock options + warrants
Examples
Suppose Company ABC has the following structure of shares and dilutive securities at the end of a fiscal year:
- Weighted average Common shares outstanding: 800,000
- Convertible preferred shares: 10,000, convertible into 5 shares of common stock each and paying dividend of $10 per share
- Convertible Debt: $20,000 of 5% bonds convertible into 5,000 shares
- Stock Options outstanding at the beginning of the year: 10,000 with the exercise price of $45 (Average market price of company shares during the year was $55 per share)
- Net Income before preferred dividend=$2,000,000, tax rate 25%
| Particulars ($) | Basic EPS | Diluted EPS |
| Net income | 20,00,000 | 20,00,000 |
| Less: Preferred Dividend | 1,00,000 | – |
| Add: After-tax cost of interest | – | 750 |
| Numerator | 19,00,000 | 20,00,750 |
| Weighted average number of common shares outstanding | 8,00,000 | 8,00,000 |
| Additional shares issued if preferred shares converted | – | 50,000 |
| Additional shares issued if debt converted | 5,000 | |
| Additional shares issued If options exercised (in-the-money) | – | 1,818 |
| Denominator | 8,00,000 | 8,56,818 |
| EPS | 2.38 | 2.34 |
Diluted EPS Formula= Net Income(Before Preferred Dividends)+After Tax Cost of Interest / (Common Shares Outstanding +Additional Shares Against Exercise of Convertible Securities)
- Diluted EPS = (20,00,000 + 750) / (8,00,000 + 50,000 + 5,000 + 1,818)
- Diluted EPS = 20,00,750 / 8,56,818
- Diluted EPS = 2.34
Explanation of Diluted EPS Formula
- Definition: Diluted EPS represents a company’s earnings performance (income per share) assuming all its dilutive convertible securities are exercised. Convertible securities could be preferred shares, debentures, unexercised stock options and warrants. Diluted EPS considers what would happen if the dilutive securities are exercised by the holder. Since dilutive securities effectively increase the number of shares outstanding, EPS falls.
- Dilutive vs Antidilutive securities: Each of these convertible securities needs to be dilutive which means that their inclusion in the computation of diluted EPS should not yield a higher EPS value as compared to basic EPS.
For example, consider Company AD has the following structure of shares and convertible securities at the end of a fiscal year:
- Weighted average Common shares outstanding: 800,000
- Convertible preferred shares: 10,000, convertible into 3 shares of common stock of each and paying dividend of $10 per share
- Net Income before preferred dividend=$2,000,000
| Particulars ($) | Basic EPS | Diluted EPS if converted |
| Net income | 20,00,000 | 20,00,000 |
| Less: Preferred Dividend | 1,00,000 | – |
| Numerator | 19,00,000 | 20,00,000 |
| Weighted average number of common shares outstanding | 8,00,000 | 8,00,000 |
| Additional shares issued if preferred shares converted | – | 30,000 |
| Denominator | 8,00,000 | 8,30,000 |
| EPS | 2.38 | 2.41 |
Diluted EPS Formula = Net Income(Before Preferred Dividends)+After Tax Cost of Interest / (Common Shares Outstanding +Additional Shares Against Exercise of Convertible Securities)
- Diluted EPS = (20,00,000 + 0) / (8,00,000 + 30,000)
- Diluted EPS = 20,00,000 / 8,30,000
- Diluted EPS = 2.41
Since Diluted EPS (if preferred are converted) exceeds basic EPS, these convertible preferred shares are antidilutive and hence, will not be included in the computation of diluted EPS. Hence, diluted EPS is always less than or equal to basic EPS.
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- Computation for convertible preferred shares/debentures: In these cases, diluted EPS is calculated using the if-converted method which assumed that the securities had been converted at the beginning of the year.
For preferred shares, after conversion, there would be no preferred shares outstanding, hence no preferred dividends would be given an additional common shares would be issued which would increase common shares outstanding value. Consider the above example of company ABC assuming only convertible preferred shares are there and other convertibles are absent. The computation would be as follows:
| Particulars | Basic EPS | Diluted EPS |
| Net income | 20,00,000 | 20,00,000 |
| Less: Preferred Dividend | 1,00,000 | – |
| Numerator | 19,00,000 | 20,00,000 |
| Weighted average number of common shares outstanding | 8,00,000 | 8,00,000 |
| Additional shares issued if preferred shares converted | – | 50,000 |
| Denominator | 8,00,000 | 8,50,000 |
| EPS | 2.38 | 2.35 |
Diluted EPS Formula = Net Income(Before Preferred Dividends)+After Tax Cost of Interest / (Common Shares Outstanding +Additional Shares Against Exercise of Convertible Securities)
- Diluted EPS = (20,00,000 + 0) / (8,00,000 + 50,000)
- Diluted EPS = 20,00,000 / 8,50,000
- Diluted EPS = 2.35
For convertible debentures, if conversion takes place, there would be additional common shares while company will not pay any interest on the convertible debt meaning thereby that net income will increase by post-tax amount of interest payment. Consider the above example of company ABC assuming only convertible debt are there and other convertibles are absent. The computation would be as follows:
| Particulars | Basic EPS | Diluted EPS |
| Net income | 20,00,000 | 20,00,000 |
| Add: After tax cost of interest
(20,000*0.05*(1-0.25))*** |
– | 750 |
| Numerator | 20,00,000 | 20,00,750 |
| Weighted average number of common shares outstanding | 8,00,000 | 8,00,000 |
| Additional shares issued if debt converted | – | 5,000 |
| Denominator | 8,00,000 | 8,05,000 |
| EPS | 2.50 | 2.49 |
*** Tax rate-25%, interest rate-5%, debt-$20,000
Diluted EPS Formula = Net Income(Before Preferred Dividends)+After Tax Cost of Interest / (Common Shares Outstanding +Additional Shares Against Exercise of Convertible Securities)
- Diluted EPS = (20,00,000 + 750) / (8,00,000 + 5,000)
- Diluted EPS = 20,00,750 / 8,05,000
- Diluted EPS = 2.49
- Computation for stock options and warrants: Under IFRS, shares outstanding is calculated by increased for an excess of a number of new converted shares over and above the no of “inferred” shares that would have to be issued at the average market price of the period for receiving the conversion proceeds. Consider the above example of company ABC assuming only unexercised stock options are there and other convertibles are absent. The computation would be as follows:
| Increase in shares outstanding | |
| Proceeds from option exercise (10,000*45) | $4,50,000 |
| New shares issued proceeds @$55 per share for receiving same proceeds (inferred shares) (450,000/55) | 8,182 |
| Actual shares issued under options | 10,000 |
| Dilutive shares from options | 1,818 |
Dilutive shares from options = Actual shares – New shares issued
- Dilutive shares from options = 10,000 – 8,182
- Dilutive shares from options = 1,818
| Particulars | Basic EPS | Diluted EPS |
| Net income | 20,00,000 | 20,00,000 |
| Numerator | 20,00,000 | 20,00,000 |
| Weighted average number of common shares outstanding | 8,00,000 | 8,00,000 |
| Additional shares issued If options exercised | – | 1,818 |
| Denominator | 8,00,000 | 8,01,818 |
| EPS | 2.50 | 2.49 |
Diluted EPS Formula = Net Income(Before Preferred Dividends)+After Tax Cost of Interest / (Common Shares Outstanding +Additional Shares Against Exercise of Convertible Securities)
- Diluted EPS = (20,00,000 + 0) / (8,00,000 + 1,818)
- Diluted EPS = 20,00,000 / 8,01,818
- Diluted EPS = 2.49
Only in-the-money options may be considered for dilution since they are most likely to be exercised. The options are considered in-the-money if the exercise price is lower than the average market price during the specified period used for computing EPS.
Significance and Use of Diluted EPS Formula
- Complex capital structure and conservatism: Most companies have a complex capital structure consisting of securities having conversion option for which the companies are committed to issuing additional shares in future. Complex capital structure is specially maintained to lower the cost of capital. For example, financial institutions lending convertible debt would charge a lower interest than otherwise equivalent non-convertible debt. When assessing a company’s financial health, however, it is more appropriate to take the more conservative diluted EPS assuming all conversions are exercised although it is unlikely that all conversions will take place simultaneously.
- The difference in basic and diluted EPS: Most analysts and investors are critical of a big difference in basic and diluted EPS. Effectively, this means that the company has a very complex capital structure and significant commitments should the exercise materialize. Another point to note is the actual difference figure. A $0.1 difference between the two EPS may not be as significant in case of $10 million outstanding shares as in case of $10 billion outstanding shares. In the former case, $1 million is not available to exist, investors, while in the latter case it is $1000 million.
- Diluted EPS vs Basic EPS for comparison: For a simple capital structure with no conversion options, diluted EPS and basic EPS are same. When comparing with a complex capital structure, it is more appropriate to use Diluted EPS to facilitate “apple to apple” comparison across time and peers
- Impact on company’s P/E and other valuation measures: Diluted EPS adversely impacts P/E ratio, so shareholders generally dislike companies issuing dilutive securities. Again, analysts find it is less cumbersome to calculate P/E by using a total market cap in the numerator and total earnings in the denominator in case of a complex capital structure rather than check for each and every conversion in the financial statements.
Diluted EPS Formula Calculator
You can use the following Diluted EPS Formula Calculator
| Net Income | |
| After Tax Cost of Interest | |
| Common Shares Outstanding | |
| Additional shares issued if preferred shares converted | |
| Additional shares issued if debt converted | |
| Additional shares issued If options exercised (in-the-money) | |
| Diluted EPS Formula = | |
| Diluted EPS Formula = |
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Diluted EPS Formula in Excel (With Excel Template)
Here we will do the same example of the Diluted EPS formula in Excel. It is very easy and simple.
You can easily calculate the Diluted EPS using Formula in the template provided.
Example #1
Example #2
Example #3
Example #4
Example #5.1
Example #5.2
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