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| Math Central | Quandaries & Queries |
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Question from Arul: A corporation with 5,000,000 shares of publicly listed stock reported total earnings of $7.20 per share for the first 9 months of operation. During the final quarter the number of publicly listed shares was increased to 10,000,000 shares, and fourth quarter earnings were reported as $1.25 per share. What are the average annual earnings per share based on the number of shares at the end of the year? |
Arul,
Two ways to look at this:
- All shares considered equivalent: There are 10 000 000 shares at the end of the year. The earnings are $7.20×5000000+$1.25×10000000 =$48500000. So the average is $48500000/10000000 =$4.85.
- Earnings are pro-rated: Original 5000000 shares earned $7.20 + $1.25 = $8.45 each during the year. The 5000000 recently issued shares earned $1.25 each during the year. So total earnings was $8.45×5000000+$1.25×5000000 =$48500000. Average is $4.85 again.
So it doesn't really matter which approach you used: the average earnings per share is the total earnings through the year for all shares, divided by the number of shares at the end of the year.
Stephen.
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