## Tuesday, December 18, 2012

### Computing for the "Fundamental" P/E Ratio

PERSONAL FINANCE 101

In a previous post, we discussed the reasoning behind the leading P/E ratio, how it actually reflects future cash flows, and why it is referred to as "justified" or "fundamental." In this post, I will give an example of how to compute for this multiple using commonly available data.

(This example is adapted from a question from CFA Institute's free CFA Level 1 Mock Exam.)

An investor gathers the following data for a stock. (In "real life," the following can be derived from financial statements found on the PSE website.)

 Year Earnings per share, EPS (PhP) Dividends per share, DPS(PhP) Return on equity, ROE 2011 3.20 1.92 12% 2010 3.60 1.80 17% 2009 2.44 1.71 13% 2008 2.50 1.60 15%

Given that the investor uses a required rate of return of 11.5% (for now, let's just take this as given), estimate the stock's fundamental P/E.

I have already shown that the fundamental P/E is given by

fundamental P/E = P0 / E1 = (D1/E1) / (k - g)

Where D1/E1 is the dividend payout ratio one year from now, k is the required rate of return, and g is the (constant) annual growth rate.

Let's start with the most straightforward input to estimate, D1/E1. Computing for the dividend payout ratio = DPS/EPS in the past four years, we get:

 2011 60% 2010 50% 2009 70% 2008 64% Average 61%

Seeing that the stock's dividend payout ratio does not seem to vary substantially (admittedly, a matter of subjective judgement) from year to year, the most intuitive estimate for next year's dividend payout is the (arithmetic) average, or 6.1%.

Next, we compute for the stock's growth rate. Technically, this growth rate should be the annual growth rate of dividends, which we can estimate using the annual compounded growth rate of dividends from 2008 to 2011 (i.e., geometric mean)

annual compounded growth rate of dividends = (1.92/1.60)^(1/3) = 6.27%

Another way of estimating growth is by using the sustainable growth rate formula

sustainable growth rate = (1 - dividend payout ratio)*ROE

To simplify things, let's just use the average dividend payout ratio and the average ROE, 14.25%, to estimate g

Sustainable growth rate = (1 - 0.61)*14% = 5.55%

Using the formula for P0/E1 above and our input estimates, we get the following values for the fundamental P/E ratio of the stock.

 g P0/E1 5.55% 10.26 6.27% 11.66

We can now use these estimates to judge whether the stock is overvalued or undervalued, or to value other stocks in the same industry or with the same risk.

A word of caution, though. We must be aware that estimates resulting from the procedure I illustrated here suffer from significant limitations. First, the estimates are as only as good as the inputs, so make sure that any assumption you make is realistic and reasonable. Second, all out inputs are based on historical data, so any patterns or trends that are derived from the data may not repeat in future periods. Finally, make sure that you are aware of and understand the assumptions used in the model (i.e., the fundamental P/E formula), and that these are reasonably applicable to the stock or asset of interest.

More about the "required rate of return" in a future post.