M03-27

Question

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?

A. 1.75
B. 2.40
C. 3.15
D. 3.60
E. 4.85

Show Answer

Official Answer

E

A. 1.75
B. 2.40
C. 3.15
D. 3.60
E. 4.85

Bunuel · Accepted Answer

Official Solution:

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?

A. 1.75
B. 2.40
C. 3.15
D. 3.60
E. 4.85

Show Answer

Official Answer

E

A. 1.75
B. 2.40
C. 3.15
D. 3.60
E. 4.85

To find the average annual earnings per share based on the number of shares  at the end of the year , we first need to determine the total earnings for the whole year and then divide it by the number of shares  at the end of the year .
 
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 for the 4th quarter, the number of publicly listed shares  increased to  10,000,000);
 
The total earnings for the whole year in millions of dollars  =36 + 12.5 = 48.5 ;
 
Finally, the average annual earnings per share can be calculated by dividing the total earnings by the number of shares at the end of the year:  \frac{48.5}{10} = 4.85 .

Answer: E

rclerkin · Answer

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.

Rory

ENGRTOMBA2018 · Answer

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

Bunuel · Answer

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.

kelvind13 · Answer

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 · Answer

Because earnings of $7.20 per share is not per month, it's for 9 months.

RAJINI123 · Answer

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.

kimnguyen · Answer

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.

Ojknows94 · Answer

I think this is a  high-quality  question and I agree with explanation. This question was sneaky, the "Increased to 10" part caught me off guard.

RenanBragion · Answer

I think this is a  high-quality  question and I agree with explanation.

Bunuel · Answer

I have edited the question and the solution by adding more details to enhance its clarity. I hope it is now easier to understand.

BottomJee · Answer

I think this is a  high-quality  question and I agree with explanation.

nikkimah · Answer

5,000,000 + 10,000,000 = Shouldn't the denominator be equal to this no.?
For the first 9 months = 5,000,000 shares and for the last quarter = 10,000,000 shares. 
Why are we dividing by 10?

What do we mean by no. of shares at the end of the year? It is the total no. of shares at the end of year right? =15000000

Bunuel

Bunuel · Answer

Notice that the question says that the number of shares was increased  TO  10,000,000 shares, not BY 10,000,000 shares. Initially, there were 5,000,000 shares, and after the increase, there were 10,000,000 shares.

Ankit__7182 · Answer

one thing to note here is that all calculations should be based on the number of shares at the end of the year: 10,000,000 shares.
Also the question maker has somewhat tried to confued in language by using average annual earnings which is basically totall earnings of all 12 months.

Vikramaditya00 · Answer

I think this is a  high-quality  question and I agree with explanation. Nice trap divided it by 5+10=15 instead of 5+5=10 thats why got it wrong nice trick question

phmahi1997 · Answer

I like the solution - it’s helpful.

kanwar08 · Answer

KarishmaB 
Why can't this be solved using the weighted average concept?
Is it because it's not analogous to a mixture?
When I approached it, I thought weights would be the number of shares in those two periods (bcz avg share price = total rev/share).

Please clarify

KarishmaB · Answer

Because the number of shares in the first group is included in the second group as well so you need to modify what you do. This earning over different time periods, not over different shares - though there were 'additional' shares later.

Avg earning/share = Total earning/Total shares =  \frac{(7.2*5 + 1.25*10)}{10} = 4.85  (Total number of shares at the end is 10 million, not 5 + 10 = 15 million

Answer (E)

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