# Effect of adding two per share quantities

by musicgold
P: 180
Hi,

In a simple calculation, I am trying to add the cash flow per share of two companies. I think I am doing something wrong as I am not able to reconcile the results of this calculation to the actual results. Can you please take a look?

Thanks,

MG.
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 Math Emeritus Sci Advisor Thanks PF Gold P: 39,568 "Per shares" is an average, the total cash flow divided by the number of shares. In general adding two averages is only sensible if they are averaged over the same thing. Without knowing the total number of shares in each case, addin "per share" information does not give you any useful quantity.
P: 180
HallsofIvy,

Thanks a lot. That is a great catch. So my mechanics was right but the logic was wrong.

1. I think I can get rid of that problem by adding gross amounts first and then calculating the per share amount. Is that correct?

2.
 In general adding two averages is only sensible if they are averaged over the same thing
I understand what you mean here. The same problem occurs when we try to calculate the average of speed by simply averaging two speeds.
However I don't really understand what you mean by "over the same thing". Do you mean to say that both average calculations should have the same denominator? Can you give an example?

 Math Emeritus Sci Advisor Thanks PF Gold P: 39,568 Effect of adding two per share quantities By "averaged over the same thing", I mean with the same denominator. Suppose company A "per share cash flow" is $5 per share and company B's is$7 per share. IF they are both based on, say, n shares, that is saying that company A's total cash flow was 5n dollars and B's is 7n dollars. They have a total of 5n+ 7n= 12n cash flow based on 2n dollars- the average is 12n/2n= 6 which is the average of 5 and 7. But suppose A's is based on 1000 shares while B's is based on 2000 shares. Then A's total cash flow is $5000 and B's is$14000 for a total of \$19000 based on 3000 shares- the average cash flow of both together is 19000/3000= 6.333, closer to B since B has the larger number of shares and carries more "weight" in the calculation. (That is, in fact, a "weighted" average.)
 P: 180 HallsofIvy, Thanks a lot.

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