Basic vs. Diluted Weighted Average Number of Shares

Whilst perusing the financial statements of firms while performing an analysis, often the EPS is listed in two forms: basic EPS (sometimes just "EPS"), and diluted EPS. Basic EPS is calculated as:

 EPS=\frac{\text{Net Income}}{\text{weighted average number of shares}}

Diluted EPS takes a little more work. With the diluted EPS, the weighted average number of shares is adjusted by the number of shares that would result from converting any dilutive securities to common shares. This adjustment is then adjusted again to adjust for any shares that could be purchased on the open market from the proceeds of the conversion, based on the average share price for the fiscal period. The total list of dilutive securities is vast, but as an example, here are some things to look for:

  • Convertible bonds
  • Convertible preferreds
  • Outstanding warrants
  • Employee options

It should be noted that the treatment of dilution for different types of securities is not the same across the board. For example, proceeds of warrants and options are used to repurchase common stock, but there are no proceeds from convertible preferreds; however convertible preferreds would impact the preferred dividends that are paid, which would also affect the net income.

An example would probably best illustrate the conversion. Say we were reviewing the financial statements for FirmCorp., and their 2011 annual statement had the following information:

  • Net Income: $123,555,000
  • Weighted Average Number of Shares Outstanding (WANS): 591,223,552
  • Series A Warrants: 5,533,000 outstanding, convertible to 5 common shares each at a price of $3.00/share ($15.00 total per warrant)
  • Average share price for the period: $5.23

Our basic EPS calculation is simple:

     \begin{align*} \text{EPS}_{\text{basic}} & =\frac{\$123,555,000}{591,223,552} \\ & = \$0.21 \end{align*}

To calculate the diluted EPS, we have to adjust the weighted average number of shares. From the above, we have 5,533,000 outstanding warrants, and each warrant can be converted to 5 shares at a cost of $3.00/share. If we were to convert all of the warrants, two things would result:

     \begin{align*} \text{NumShares} & =5,533,000 \times 5 \\ &= 27,665,000\\ \text{CashInflow} & =5,533,000 \times 5 \times \$3.00\\ & =\$82,995,000 \\ \end{align*}

In the above, NumShares is the change in shares by converting all of the warrants, and CashInflow is the money received by converting the warrants. The proceeds from CashInflow would then be used to purchase any shares outstanding from the open market:

     \begin{align*} \text{ShareBuyback} & =\frac{\$82,995,000}{\$5.23}\\ &=15,869,025 \end{align*}

Our weighted average number of shares is then adjusted as follows:

     \begin{align*} \text{WANS}_{diluted} & =\text{WANS}+\text{NumShares}-\text{ShareBuyback} \\ & =591,223,552+27,665,000-15,869,025 \\ & =603,019,527 \end{align*}

And our diluted EPS is then calculated as:

     \begin{align*} EPS_{diluted} & =\frac{\$123,555,000}{603,019,527} \\ & =\$0.20 \end{align*}

With the above explanation in mind, why does this matter? I’ve tossed the notion of basic vs. diluted EPS around in my evaluations, but as of late I have settled on basic EPS. Diluted EPS shows you the EPS if dilutive securities were converted to common shares. However, at the time of publishing the financial statements, the dilutive securities were not converted, and hence did not dilute the EPS. That said, I see little point in evaluating diluted EPS for a fiscal period that has already closed.

However, diluted EPS does give you a preview of the associated internal risks of the company’s financials. By reviewing financial statements, one can determine any potential future impacts if the shares were to be diluted. When analysts post EPS projections, they are often doing so based on the basic EPS; if you are performing a forward-looking evaluation on P/E, P/BV, P/E×P/BV, dividend payout ratio, etc., knowing what could happen if the weighted average number of shares were diluted may have a material impact on your analysis. So at the very least, diluted EPS can serve as a bellwether to potential negative impacts when analyzing a firms.

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