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M03-27

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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

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New post 16 Sep 2014, 00:21
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Official Solution:

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


The earnings for the first 9 months in millions of dollars - \(5*7.2=36\);

The earnings for the 4th quarter in millions of dollars - \(10*1.25=12.5\) (since in the 4th quarter the number of publicly listed shares was increased to 10,000,000);

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

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


Answer: E
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Re: M03-27 [#permalink]

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New post 30 May 2015, 17:58
Bunuel wrote:
Official Solution:

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


The earnings for the first 9 months in millions of dollars - \(5*7.2=36\);

The earnings for the 4th quarter in millions of dollars - \(10*1.25=12.5\) (since in the 4th quarter the number of publicly listed shares was increased to 10,000,000);

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

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


Answer: E


Bunuel, I have a doubt about the solution presented based on the wording of the question.

For the first 9 months, the average share price for 5 * 10^6 shares was 7.2. So the weighted contribution for this bit should be 5*7.2*9 = 324

Similarly, for the last quarter, it should be 10*1.25*3 = 37.5.

Total = 324+37.5 = 361.5, average for the entire year = 361.5/12 = 30.125 * 10^6 $ as total earnings.

Now per the question, 'what are the average annual earnings per share based on the number of shares at the end of the year', should be:

30.125*10^6/(5+10)*10^6 = 2.0083
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Re: M03-27 [#permalink]

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New post 31 May 2015, 06:16
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Engr2012 wrote:
Bunuel wrote:
Official Solution:

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


The earnings for the first 9 months in millions of dollars - \(5*7.2=36\);

The earnings for the 4th quarter in millions of dollars - \(10*1.25=12.5\) (since in the 4th quarter the number of publicly listed shares was increased to 10,000,000);

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

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


Answer: E


Bunuel, I have a doubt about the solution presented based on the wording of the question.

For the first 9 months, the average share price for 5 * 10^6 shares was 7.2. So the weighted contribution for this bit should be 5*7.2*9 = 324

Similarly, for the last quarter, it should be 10*1.25*3 = 37.5.

Total = 324+37.5 = 361.5, average for the entire year = 361.5/12 = 30.125 * 10^6 $ as total earnings.

Now per the question, 'what are the average annual earnings per share based on the number of shares at the end of the year', should be:

30.125*10^6/(5+10)*10^6 = 2.0083


That's not correct. Total for 9 months was 5*7.2=36, not 5*7.2*9.
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Re: M03-27 [#permalink]

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New post 31 May 2015, 06:35
Bunuel, shouldnt it be a weighted average instead of the regular average that you have calculated?
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New post 31 May 2015, 06:40
Engr2012 wrote:
Bunuel, shouldnt it be a weighted average instead of the regular average that you have calculated?


We ARE calculating weighted average.

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.
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Re: M03-27 [#permalink]

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New post 02 Jun 2015, 04:17
Sorry for the stupid question.
I too am not too clear why we don't multiply 9 for the months that it was at 7.2 and 3 for the remaining 3 months that it was at 1.25.


Bunuel wrote:
Engr2012 wrote:
Bunuel, shouldnt it be a weighted average instead of the regular average that you have calculated?


We ARE calculating weighted average.

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.
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Re: M03-27 [#permalink]

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New post 02 Jun 2015, 04:39
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kelvind13 wrote:
Sorry for the stupid question.
I too am not too clear why we don't multiply 9 for the months that it was at 7.2 and 3 for the remaining 3 months that it was at 1.25.


Bunuel wrote:
Engr2012 wrote:
Bunuel, shouldnt it be a weighted average instead of the regular average that you have calculated?


We ARE calculating weighted average.

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.


Because earnings of $7.20 per share is not per month, it's for 9 months.
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Re: M03-27 [#permalink]

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New post 05 Jun 2015, 19:35
the question says that the earnings in the 4th qtr was increased to 10000000. doesnt that mean that the earnings were 5000000 ?? (10000000 - 5000000). the 10000000 was the increased amt and the 5000000 was the increase.because it was increased to 10000000 not increased by 10000000. in that case the average will be 5*10^6 *1.25 = 625000. so the average will be (36000000+625000)/10000000 = 3.66 answer choice D. kindly clarify.
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M03-27 [#permalink]

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New post 12 Jun 2015, 07:54
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RAJINI123 wrote:
the question says that the earnings in the 4th qtr was increased to 10000000. doesnt that mean that the earnings were 5000000 ?? (10000000 - 5000000). the 10000000 was the increased amt and the 5000000 was the increase.because it was increased to 10000000 not increased by 10000000. in that case the average will be 5*10^6 *1.25 = 625000. so the average will be (36000000+625000)/10000000 = 3.66 answer choice D. kindly clarify.



Hi RAJINI123,

For the first 9 months you have 5M shares which had total earnings of $7.20 each. So that's 5M * $7.20 = $36M
For the final 3 months the number of shares has increased to 10M. So you now have 10M shares which are all earning for that time, not just the 5M extra shares. So the total earnings at $1.25 a share works out at 10M * $1.25 = $12.5M.
Total earnings for the year are now $36M + $12.5M = $48.5M
At the end of the year you have 10M shares so the earnings per share are $48.5M/10M = $4.85

I hope that helps.

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Re: M03-27 [#permalink]

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New post 24 Jun 2015, 08:27
There is a more simple solution:

For the first 3 quarters, Earning per share (EPS) was 7.20$ with total number of shares was 5mil, if total number of shares were 10mil then EPS would be 7.2/2 = 3.6$
So, for the whole year, and with total shares of 10mil, total EPS will be 3.6 + 1.25 = 4.85$
No complicated calculation needed.
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Re: M03-27 [#permalink]

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New post 24 Jul 2015, 03:02
should it not be 48.5/15 ( 5 in 9 months+10 in last 3 months)??
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Re: M03-27 [#permalink]

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New post 19 Aug 2015, 10:45
harshalnamdeo88 wrote:
should it not be 48.5/15 ( 5 in 9 months+10 in last 3 months)??


If you do it (48.5/15), you will divide the annual "earnings" by 15 million of shares, but the question says that in the end of the year the total of share was 10 million.
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Re: M03-27 [#permalink]

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New post 31 Jan 2016, 01:27
Bunuel wrote:
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


I've solved it in a different way.
Since the number of shares doubled in fourth quarter, earnings per share in first 3 quarters halved. Therfore: 7.20 / 2 + 1.25 = 4.85
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Re: M03-27 [#permalink]

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New post 09 Mar 2016, 00:45
you are taking annual average ..then shouldn't 48.5 be divided by 12??
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Re: M03-27 [#permalink]

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New post 10 Jul 2016, 17:10
please explain in this way if i m nt wrng.
u first calculated total earnings-for the whole year= 48.5
next u divide it by the total share i.e. 10mn
total earnings for the whole year per share it should be- 48.5/10= 4.85 ok.
but next line, u said, the average annual earning per share= 4.85
u dont think the term "total earning" and "average annual earning" is different???
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Re: M03-27 [#permalink]

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New post 28 Aug 2016, 15:18
dp777 wrote:
you are taking annual average ..then shouldn't 48.5 be divided by 12??


It is saying average annual earnings PER SHARE based on the number of shares at the END OF THE YEAR. The share is the denominator.

Annual earnings -> the earning in ONE year which is 48.5
Share at the end of the year is 10
Thus, 48.5/10.

If you divide by 12 (months) then I believe you will be calculating the average annual earnings PER MONTH.
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New post 13 Jul 2017, 10:33
Bunuel wrote:
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


Dear Bunuel

The question ask about average. However, you categorize this problem as combination and probability. I think it should be under 'Arithmetic' or 'stats and set problems'.

What do you think?
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Re: M03-27 [#permalink]

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New post 28 Nov 2017, 06:50
I think question stem should read "annual earnings per share".

Writing average annual confuses reader. It implies two meanings average over month and average over per share
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Re: M03-27 [#permalink]

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New post 08 May 2018, 01:55
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Dear Bunuel,

The question tag is written as combinatorics and probability.
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Re: M03-27   [#permalink] 08 May 2018, 01:55

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