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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?

Stupid question: shouldn't we multiply the earnings by the number of months since they have more "weight"? For example: (7.2*5m*9)+(1.25*10m*3)/10m? I know this yields the wrong answer, but I'm trying to understand reasoning.

Should we not consider that the average 7.2 is the average of first 3 quarters? We cannot simply take the avg of first 3 and last quarter to find the annual average.

It is not the way we can calculate the average that is important, but the total earnings divided by total number of shares. It is not right to use the approach with average earnings for each quarter because the number of shares has been changed for the 4th quarter. The simplest and the right way to answer the question is to find total earnings and divide the result by the total number of shares, as outlined in this post above:

scthakur wrote:

Average earnings per share at the end of the year = total earnings by the end of the year divided by total number of shares at the end of the year.

Total earnings by the end of the year = 5*7.20 + 10*1.25 Total shares at the end of the year = 10

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?

This may be real simple but I am missing something with the verbage was increased to.

The OA is 4.85

Soln : 5 *7.20 + 10*1.25 / 10 = 4.85

I am thinking it should either be 5 *7.20 + 10*1.25 / 15 = 3.2

(or)

5 *7.20 + 5*1.25 / 10 = 4.225

EPS at the year end = Total earnings for the year/no of shares outstanding at the end of year EPS at the year end = (5 *7.20 + 10*1.25) / 10 EPS at the year end = 4.85
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First term (7.2/2) finds what the earnings for the first 3 quarters would have been if there were twice as many shares outstanding (5k to 10k shares), and the second term is the last quarter's earnings.

Last edited by Zanini on 10 Dec 2010, 07:37, edited 1 time in total.

Total earnings for the first three quarters (E1) = 5*10^6*7.2*9/12 Total earnings for the last quarter (E2) = 10*10^6*1.25*3/12 Total earnings = E1+E2 Total earnings per share = (E1+E2)/10*10^6 = 3.0125

Can someone please point out the mistake in my solution?

Total earnings for the first three quarters (E1) = 5*10^6*7.2*9/12 Total earnings for the last quarter (E2) = 10*10^6*1.25*3/12 Total earnings = E1+E2 Total earnings per share = (E1+E2)/10*10^6 = 3.0125

Can someone please point out the mistake in my solution?

I am not really following how you came up with the E1 and E2 variables. The question is much easier than you made it. EPS1 + EPS2 is the correct train of thought, but finding the two variables is very simple. EPS1 = Earnings per Share over the first 3 quarters, and EPS2 = Earnings per share over quarter 4. Since they want to know what EPS for the year would be if there were 10k shares all year, you can use the given $1.25 for EPS2. To find EPS1, pretend that there were 10k shares instead of the 5k shares used to come up with the $7.20 figure. That means that the $7.20 figure will be cut in half since there are double the shares. So, EPS1 = $3.60. $3.60 + $1.25 = $4.85

I think their use of the word "average" in the last sentence of the question might have thrown you off.

Total earnings for the first three quarters (E1) = 5*10^6*7.2*9/12 Total earnings for the last quarter (E2) = 10*10^6*1.25*3/12 Total earnings = E1+E2 Total earnings per share = (E1+E2)/10*10^6 = 3.0125

Can someone please point out the mistake in my solution?

Check the solution below:

A corporation with 5,000,000 shares of publicly traded stock reported total earnings of $7.20 per share for the first 9 months of operation. If during the final quarter, the number of publicly listed shares was increased to 10,000,000, and fourth quarter earnings were reported at $1.25 per share, what are the average annual earnings per share based on the number of shares at the end of the year? A. 1.75 B. 2.40 C. 3.15 D. 3.60 E. 4.85

Earnings for 9 months - \(5*7.2=36\); Earnings for 4th quarter - \(10*1.25=12.5\);

Total earning for a year - \(36+12.5=48.5\);

The average annual earnings per share - \(\frac{48.5}{10}=4.85\).

Can someone explain to me why we don't use WEIGHTED AVERAGE ? It makes sense since the shares have been priced at 7.20 for the first 9 months and 1.25 for the next 3. Shouldn't it be weighted more to the first 9 months for the annual price per share??

Can someone explain to me why we don't use WEIGHTED AVERAGE ? It makes sense since the shares have been priced at 7.20 for the first 9 months and 1.25 for the next 3. Shouldn't it be weighted more to the first 9 months for the annual price per share??

The $7.20 is already weighted in a sense. It isn't the average quarterly earnings over the first 3 quarters, it is the TOTAL eps over the entire first 3 quarters. Therefore, it can be added to the last quarter's EPS without having to weight the two figures. If $7.20 was the average QUARTERLY earnings for the first three quarters, then you would weight it accordingly.

Hope I was able to word that in a way that makes sense.

Last edited by Zanini on 10 Dec 2010, 08:32, edited 1 time in total.

Can someone explain to me why we don't use WEIGHTED AVERAGE ? It makes sense since the shares have been priced at 7.20 for the first 9 months and 1.25 for the next 3. Shouldn't it be weighted more to the first 9 months for the annual price per share??

7.2 is not a price per share it's earnings of per share for the first 9 months of operation.

So, earnings for 9 months - \(5*7.2=36\);

During the final quarter, the number of publicly listed shares was increased to 10, so earnings for 4th quarter - \(10*1.25=12.5\);

Total earning for a year - \(36+12.5=48.5\);

The average annual earnings per share - \(\frac{48.5}{10}=4.85\).

This is definitely a difficult one. It took me 5 minutes to arrive at the solution. Hope its not wrong Difficull: Maybe I haven't seen this type of question in the OG?

Solution: Since we have to consider average earnings for complete one year we can simplify the problem by removing training zeros from the original numbers. so we consider 5 as the number of shares for 9 months and 10 as the # of shares for 3 months. Tot earning with 5 shares = 5 * 7.2 Tot earning with 10 shares = 10 * 1.25 Tot share on which the earnings per share needs to be calculated = 10 the months don't have any relevance except that they sum up to 1 year ( they do not form aprt of calculation as such)

Guys, why do you need complex equations? My peasant's approach to biz: "5,000,000 shares of publicly traded stock reported total earnings of $7.20 per share for the first 9 months of operation" >> if we double number of share and decrease by two times earnings per share, the result won't change.

However, such trick will allow to utilize really easy math: 10 mln shares in total, $3.6/share in first 9 months + $1.25/share in last 3 months = $4.85 per share annually.

Easy, efficient (took like 30 sec) and error-resistant

I don't understand why wouldn't you consider number of months for EPS calculation. Moreover, even for average how does denominator arrive to 10? I mean 10 is only for the last quarter.
_________________

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Lot of folks who are good at math will get tricked by the weighted average concept. But that approach leads to 3.01 as the answer which was not given as a choice. You might have lost 60 secs by the time you arrived at the wrong answer. But then, you will re-read the question and possibly attempt the total earnings/shares approach to arrive at 4.85. If you are good with your variations, you should be able to get the correct answer in 2 mins though.

The moment 3.01 is not in the answer list, don't get confused, but look for alternate approaches or meanings to the question.