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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 - \(\frac{48.5}{10}=4.85\).

Hope it's clear.

Bunuel, I understand that the total of shares of the whole year is 10m, because of the "increased to 10m" term.

However, I don't know why "increased to 10m in the 4th quarter" means that the # of shares in the 4th quarter totaled 10m. I interpreted that the # of shares was increased to 10m FROM 5m (the existing 5m shares of the first 9 months), therefore in the 4th quarter the # of shares traded was only 10 - 5 = 5m, not 10m. I think "increased TO x", means there exists a y < x such that the delta (x - y) is the amount noted as "increased to x".

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 - \(\frac{48.5}{10}=4.85\).

Hope it's clear.

Bunuel, I understand that the total of shares of the whole year is 10m, because of the "increased to 10m" term.

However, I don't know why "increased to 10m in the 4th quarter" means that the # of shares in the 4th quarter totaled 10m. I interpreted that the # of shares was increased to 10m FROM 5m (the existing 5m shares of the first 9 months), therefore in the 4th quarter the # of shares traded was only 10 - 5 = 5m, not 10m. I think "increased TO x", means there exists a y < x such that the delta (x - y) is the amount noted as "increased to x".

Please help me clarify.

Thanks!

Not sure I understand your question.

Yes, the number of shares increased from 5,000,000 to 10,000,000 in 4th quarter. We are also told that in the 4th quarter earnings were at $1.25 per share, so in the 4th quarter total earning were 1.25*10,000,000.
_________________

Bunuel, I understand that the total of shares of the whole year is 10m, because of the "increased to 10m" term.

However, I don't know why "increased to 10m in the 4th quarter" means that the # of shares in the 4th quarter totaled 10m. I interpreted that the # of shares was increased to 10m FROM 5m (the existing 5m shares of the first 9 months), therefore in the 4th quarter the # of shares traded was only 10 - 5 = 5m, not 10m. I think "increased TO x", means there exists a y < x such that the delta (x - y) is the amount noted as "increased to x".

Please help me clarify.

Thanks!

Not sure I understand your question.

Yes, the number of shares increased from 5,000,000 to 10,000,000 in 4th quarter. We are also told that in the 4th quarter earnings were at $1.25 per share, so in the 4th quarter total earning were 1.25*10,000,000.

I meant "increased from 5 to 10 in Q4" means that there are only 5mil shares traded in Q4 (as the first 5mil are traded in first 3 Q already). So in Q4 it should be 5 * 1.25 = 7.25, not 10 * 1.25. It's just the wording issue: "target number X" (10mil) = something already there (5mil in first 3Qs) + the "increased to" part (5mil in Q4). So in this case the "increased to" part is 5mil only.

Bunuel, I understand that the total of shares of the whole year is 10m, because of the "increased to 10m" term.

However, I don't know why "increased to 10m in the 4th quarter" means that the # of shares in the 4th quarter totaled 10m. I interpreted that the # of shares was increased to 10m FROM 5m (the existing 5m shares of the first 9 months), therefore in the 4th quarter the # of shares traded was only 10 - 5 = 5m, not 10m. I think "increased TO x", means there exists a y < x such that the delta (x - y) is the amount noted as "increased to x".

Please help me clarify.

Thanks!

Not sure I understand your question.

Yes, the number of shares increased from 5,000,000 to 10,000,000 in 4th quarter. We are also told that in the 4th quarter earnings were at $1.25 per share, so in the 4th quarter total earning were 1.25*10,000,000.

I meant "increased from 5 to 10 in Q4" means that there are only 5mil shares traded in Q4 (as the first 5mil are traded in first 3 Q already). So in Q4 it should be 5 * 1.25 = 7.25, not 10 * 1.25. It's just the wording issue: "target number X" (10mil) = something already there (5mil in first 3Qs) + the "increased to" part (5mil in Q4). So in this case the "increased to" part is 5mil only.

5,000,000 shares were not sold (traded), they earned some amount for the first 9 months as a dividend, the same with 10,000,000 shares.
_________________

OK, so can "the number of publicly listed shares was increased to 10,000,000 shares" be understood as there were 5mil listed already. And then that number (5mil) was increased to 10 mil. Therefore there were 5mil additional shares. Sorry but I'm a bit confused with the wording...

OK, so can "the number of publicly listed shares was increased to 10,000,000 shares" be understood as there were 5mil listed already. And then that number (5mil) was increased to 10 mil. Therefore there were 5mil additional shares. Sorry but I'm a bit confused with the wording...

Again, we had 5,000,000 shares and each earned $7.20 per share for the first 9 months. Then we bought additional 5,000,000 shares, so we had 10,000,000 shares and each earned 1.25 per share in the 4th quarter.
_________________

as per the question "the 9 months earning is 7.2 per share had it been 7.2/share/month then you were justified in multiplying it by 9 and same principle for the last quarter. the question states: 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. so the 9 months earning is 5*7.2 you do not need to multiply this by 9 again and likewise for the next 3 months I hope this helps

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 - \(\frac{48.5}{10}=4.85\).

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 - \(\frac{48.5}{10}=4.85\).

Answer: E.

Hope it helps.

Where does 10 come from?

10 is the number of shares after the increase: "the number of publicly listed shares was increased to 10,000,000".

During final quarter number of shares were 10 million and EPS for final quarer was $1.25. it would have been $2.50 had the number of shares been 5 million and so EPS for whole year would be $9.70 ($7.20+$2.50). but number of shares doubled at the end of the year and hence EPS for whole year would be halved and thus is the answer E i.e. $4.85.