Earnings per Share and Dilution

Two companies earn identical $100m of net income this year. One has 50 million shares outstanding, the other has 200 million. The first earns $2.00 for every share; the second earns $0.50. Same company profitability, wildly different per-share value, purely because of how the ownership pie is sliced. Earnings per share (EPS) exists to make profit comparable per unit of ownership, which is the number that actually maps onto a share price.

$$\text{Basic EPS} = \frac{\text{Net Income} - \text{Preferred Dividends}}{\text{Weighted Average Shares Outstanding}}.$$

Preferred dividends are subtracted first because that income belongs to preferred holders, not common shareholders. The share count is weighted average because share counts change mid-year — a buyback or a new issuance partway through the year should only count for the fraction of the year it was actually outstanding.

Where dilution comes in

Basic EPS uses only shares currently outstanding. Diluted EPS asks a harder, forward-looking question: what if every option, warrant, restricted stock unit and convertible bond that could become common stock actually did? Employee stock options, executive compensation packages and convertible debt all represent claims that can turn into new shares, and every new share created dilutes the ownership — and the earnings — that existing shareholders lay claim to.

$$\text{Diluted EPS} = \frac{\text{Net Income} - \text{Preferred Dividends} + \text{Interest saved on converted debt}}{\text{Weighted Average Shares} + \text{Dilutive Securities (treasury-stock/if-converted method)}}.$$

In words: if a convertible bond converts, the company no longer pays interest on it, so that saved interest is added back to the numerator, while the new shares that bond would create are added to the denominator. The result is always lower than or equal to basic EPS — dilution can only shrink the per-share pie, never grow it.

A worked example

A company reports net income of $80m and has 40 million basic shares outstanding, giving $\text{Basic EPS} = 80/40 = 2.00$, i.e. $2.00. It also has employee stock options exercisable at prices well below the current share price, which under the treasury-stock method translate into a net 3 million additional shares, plus a convertible bond that would add 2 million shares and, if converted, would eliminate $1m of after-tax interest expense the company currently pays on it.

$$\text{Diluted EPS} = \frac{80 + 1}{40 + 3 + 2} = \frac{81}{45} \approx 1.80.$$

That works out to $1.80, 10% lower than basic EPS of $2.00 — the gap purely reflects claims on future shares that haven't been exercised yet but realistically will be, given they're profitable to exercise at current prices.