SEARCH HOME
 Math Central Quandaries & Queries
 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:

1. 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. 2. 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.

Math Central is supported by the University of Regina and The Pacific Institute for the Mathematical Sciences.