Price-to-Earnings Ratio (Trailing and Leading)
This video discusses the concepts of
Price-to-Earnings Ratio. Please refer to infinite
period Dividend Discount Model for the background. The following is a part
of the transcript. This video requires Flash 8 or above. If it does not start, click the
play button to start. *** Please note that the DDM equation in the video should be P0=D1/(k-g) instead of (g-k). Thanks to Somashekhar for pointing out the error. And please see the comments for more details.
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In an infinite period DDM, it is
assumed that the company is growing at a constant rate (g) and paying dividends
accordingly. If the required rate of return is k, then the price of the stock
is
P0 = D0*(1+g)/(k-g)
= D1/(k-g)
where P0 and D0 are today’s price
and dividend just paid. Also, D0, D1 are expressed in per share. If we expect
the earning per share in the coming year is E1, then,
P0/E1 = D0/E1*(1+g)/(k-g)
P0/E1 = D1/E1/(k-g)
P0/E1 = PayoutRatio/(k-g)
This is called the leading P/E ratio
and can be derived directly from the DDM.
Another one is the trailing P/E
ratio. By definition, it is
P0/E0 (instead of E1)
For this one, we can also perform
similar derivation as the leading P/E ratio from the DDM model. However, this
is not necessary because both P0 and E0 are known already. This ratio is the
one we usually see in the financial reports.
Finally, it is very important to pay
attention to the questions and make sure you know which dividends and earnings
to use when calculate the P/E ratios.
Please refer to the video for more
details.
In DDM vedio you mention about
P0 = D0*(1+g)/(k-g) = D1/(k-g)
where as this Price to earning Ratio you mention
P0 = D0*(1+g)/(g-k) = D1/(g-k)
its bit confusing whether its (g-k) or (k-g)
Hi Somashekhar and all visitors,
Sorry for confusing! It should be (k-g). In the DDM, there is ***an implicit assumption that k is larger than g ***. (Otherwise, we cannot have a finite sum from the infinite terms).
So, yes, thanks for pointing out the errors. It should be (k-g) and that’s the only way to get +ve stock price. We will correct the typos.
Hi,
I can’t understand the logic behind the formula you used to explain the forward P/E ratio. i.e.
P0/E1 = D0/E1*(1+g)/(k-g)
P0/E1 = D1/E1/(k-g)
P0/E1 = PayoutRatio/(k-g)
How can it be payout ratio divided by k-g? I cant get the logic. Please explain me in detail. Another thing is that you have given forward PE explanation without giving the growth rate estimation. Please explain this process also in detail.
Regards Hari
Hi Hari,
Since D1 = D0 *(1+g), so we have
P0/E1 = D0/E1*(1+g)/(k-g) => P0/E1 = D1/E1/(k-g)
And by definition, payout ratio is D1/E1 (dividend per share / earning per share), so we have
P0/E1 = PayoutRatio/(k-g)
I am not sure if I understand your 2nd question correctly. But for growth rate, it is given as constant g in this example. And this usually how it is given in the exam. Thanks!