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Price/earnings ratio is defined as:

P/E = Share Price / Earnings per Share

If we multiply both the numerator and the denominator with the number of shares, we get:

P/E = Market Capitalization / Net Income

However, wikipedia says:

Some people mistakenly use the formula market capitalization / net income to calculate the P/E ratio. This formula often gives the same answer as market price / earnings per share, but if new capital has been issued it gives the wrong answer, as market capitalization = market price × current number of shares whereas earnings per share= net income / weighted average number of shares.

Can someone please give a simple example of how this second formula can be incorrect, how the formula can be corrected, and under what circumstances the formula would be correct.

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    The close votes that have accumulated on this question are inappropriate. This is not an accounting question. P/E ratios are used by individual investors to make decisions. This question is on-topic.
    – Chris W. Rea
    Dec 27, 2018 at 17:58

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The issue is the P/E is generally based on the earnings per share where the number of shares used in the calculation is a weighted average. That weighted average takes into account fluctuations in the number of outstanding shares.

The problem with the 2nd formula is that it only works if net income = EPS * number of shares. That is only true if number of shares = the weighted average. If the number of shares has changed, then the calculation will be off.

Example:

Share Price = $42.00
EPS         =  $2.34
P/E         =  17.95

But 

Weighted Shares = 1,100,000
Current shares  = 1,200,000

So 

Net Income = EPS*Weighted Shares = $2,574,000
Market Cap = Current Price*Current shares = $50,400,000

Therefore by the proposed formula MC/NI

MC/NI = 19.58

which doesn't equal 17.95

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  • Could you give a toy example of how this changes the calculation?
    – matthiash
    Dec 28, 2018 at 9:48
  • just added an example
    – mhoran_psprep
    Dec 28, 2018 at 12:02
  • So if a company has 800000 shares at the beginning of the year, and issues an additional 400000 shares after the first quarter, then the weighted average number of shares that year will be 1100000. Am I right?
    – matthiash
    Dec 28, 2018 at 14:35
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    @matthiash: No, weighting by time is not the correct weighting. You need weighting by earnings to get the same results. The relation Net Income = EPS*Weighted Shares becomes true (and trivially so!) when you use Weighted Share Count = Net Income / EPS as the definition.
    – Ben Voigt
    Dec 28, 2018 at 15:05
  • There's also a difference between shares authorized and shares issued.
    – quid
    Dec 28, 2018 at 17:02

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