# Diluted Earnings Per Share

Diluted EPS is a variant of earnings per share which represents the worst-case scenario with respect to per share profitability, and is calculated by assuming all convertible financial instruments of the company are converted to its common stock.

Diluted EPS is different from basic EPS which equals earnings attributable to common shareholders divided by weighted average number of outstanding common shares. It is called diluted EPS because increase in weighted average number of outstanding common shares (the denominator) relative to earnings (the numerator) reduces the ratio and dilutes earnings.

A company’s capital structure may include instruments entitling their holders to claim a specific number of the company’s common shares either at their choice or upon occurrence of any contingency. Such convertible instruments include stock options, stock warrants, convertible bonds, convertible preferred stock, etc.

If there are no dilutive convertible instruments, the company's diluted EPS equals its basic EPS.

## Formula and Calculation

$$ Diluted\ Earnings\ Per\ Share \\ = \frac{Net\ Income − Preferred\ Dividends}{Weighted\ Average\ Number\ of\ Dilutive\ Common\ Shares} $$

Weighted average number of dilutive common shares represents the time-weighted average number of maximum possible outstanding common shares. Only such convertible instruments are considered in calculation of diluted EPS which tend to lower the EPS below basic EPS. Instruments that increase numerator by a percentage higher than relevant percentage increase in the denominator, thereby resulting in increased EPS when compared to basic EPS, are anti-dilutive and are not considered when calculating diluted EPS.

## Example

You work as Technical Accounting Manager at Machu Picchu Tours. You asked your assistant to calculate EPS for the company. He did pretty good job with the basic EPS, but is overwhelmed by the complexity of diluted EPS. He came up with the following figures and is looking forward to your input:

Net income | 8,000,000 |

Preferred dividends | 1,000,000 |

Weighted average number of shares | 500,000 |

Stock options (each convertible to 2 shares, at below market price) | 50,000 |

5,000; 10% bonds, each convertible to 20 shares | 5,000,000 |

**Solution:**

$$ Diluted\ Earnings\ Per\ Share \\ = \frac{8,000,000 − 1,000,000 + 5,000,000 × 10\%}{500,000 + 50,000 × 2 + 5,000 × 20} \\ = $10.71 $$

The numerator represents net income of $8,000,000 minus the preferred dividends amounting to $1,000,000 plus the interest expense on convertible bond of $500,000 (= $5,000,000 × 10%). The interest expense is added because in calculation of diluted EPS it is assumed that conversion takes place at the start of the year, and in event of such conversion the interest expense on convertible bond will not be incurred.

The denominator represent weighted average number of dilutive common shares of 500,000 plus 100,000 additional shares on account of exercise of stock options (= 50,000 × 2) plus 100,000 more shares issued on account of conversion of the convertible bond (= 5,000 × 20).