If there is 48000 in earnings available to common stockholders and the firm's stock has a PE of 20 times earnings per share what is the current price of the stock?
There are two ways to answer this: Short and Long.
First, short:
PE = PPS/EPS ; PE = 20(EPS) as well.
Substituting 20(EPS) for PE gives:
20(EPS) = PPS/EPS ; Multiply EPS on both sides to eliminate the
fraction on the right side:
20(EPS)2= PPS
So, Price per share = 20 times Earnings per share2
Long way:
EPS = EAC/#shares ; Since we know EAC, it becomes EPS =
48,000/#shares
Since PE = 20(EPS) using what we got from the short way, we can
subsitute the EPS fraction into the left side:
20(48,000/#shares) = PPS/(48,000/#shares) ; Of course we would
simplify it a little bit, multiplying 20 and 48,000 and multiplying
the inverse of the denominator:
960,000/#shares = PPS * #shares/48,000 ; Multiply 48,000 on both
sides and get:
46,080mil/#shares = PPS * #shares ; Multiply #shares on both
sides and get:
46,080mil = PPS * #shares2 ; Finally, divide by #shares2 to
isolate PPS and you get:
PPS = 46,080mil/#shares2
So, you have PPS = 20(EPS)2 or PPS = 46,080mil/#shares2
Either way, you can't get a number answer because of the lack of
data on the number of shares. If we had the number of shares
outstanding, it would be pretty easy.
I know it's an old question, but still, if anyone has a better
way or a correction to make on what I did, feel free to do so.