Basic EPS and the weighted average number of shares

What is basic EPS?

Basic EPS is the profit earned for each ordinary share. Take net income, remove what belongs to preferred dividends , and divide by the average number of common shares outstanding during the year.

$$EPS = \frac{NI - D_p}{W}$$

Only preferred dividends come off: cumulative preferred for the period whether declared or not, non-cumulative only if declared. Common dividends are a use of profit, not a deduction from it.

A company with a simple capital structure has no securities that could turn into common shares (only common and non-convertible preferred), so its diluted EPS equals its basic EPS. A complex capital structure contains convertibles, options or warrants, so diluted EPS can be lower (next lesson).

Capital structure

• Simple Know the idea only common stock and non-convertible preferred
  • Diluted EPS = basic EPS there is nothing to dilute
• Complex Know the idea convertibles, options or warrants outstanding
  • Diluted EPS at or below basic EPS next lesson

How do you weight the shares?

Weight every change in the share count by the part of the year it was outstanding. The result is the weighted average number of shares .

$$W = \sum \text{shares} \times \frac{\text{months outstanding}}{12}$$

Weighted average shares

• Events that add or remove money Memorize time-weight from the date
  • New issue for cash adds shares from the issue date
  • Buyback removes shares from the buyback date
• Events with no cash Memorize restate to the start of the year, and prior years
  • Stock split an n-for-1 multiplies the count by n
  • Stock dividend 10% stock dividend multiplies by 1.10

Questions give you the shares and ask for EPS, or give EPS and ask for earnings, preferred dividends or shares.

What about splits and stock dividends?

Restate them: apply the split to every share outstanding before it, for the whole year, and to prior-year figures too. A stock split or stock dividend gives shareholders more shares for the same assets, so no money comes in and nothing is time-weighted.

Say Halden also did a 2-for-1 split on 1 July. Every share that existed before the split doubles as if the split had happened on 1 January: (2.0 + 0.45) × 2 = 4.9 million. The October buyback came after the split, so its 0.3 million are already post-split shares and are not doubled: 4.9 − 0.075 = 4.825 million, and EPS is 3.6 ÷ 4.825 = USD 0.75. Last year’s reported EPS is halved for comparison. A 10% stock dividend multiplies the count by 1.10.

Exam tip No cash in, no time-weighting. Splits and stock dividends restate; issues and buybacks weight.

Go deeper EPS growth that comes from buybacks

A company that repurchases shares shrinks the denominator, so EPS can grow even when net income is flat. Compare EPS growth with net income growth. If EPS grows much faster, ask whether the buyback was funded by debt (raising interest costs) or by cash that could have been invested in the business.

Go deeper Cumulative versus non-cumulative preferred

Cumulative preferred accumulates unpaid dividends as an obligation to the holders, so the current-year amount is deducted from net income even if the board declared nothing. Non-cumulative preferred holders lose a skipped dividend, so only a declared dividend is deducted. Dividends in arrears from earlier years are not deducted again in the current year’s EPS.