## Thursday, November 29, 2012

### Why the Leading P/E Ratio Makes Sense

PERSONAL FINANCE 101 Wrong PE?
In a post at the beginning of the year, we discussed the price-earnings or P/E ratio in detail, particularly how we can use it to distinguish between undervalued stocks (which we would want to buy) and overvalued stocks (which we would want to sell or not buy). In that post, we also took a brief look at the leading P/E ratio, which is based on the forecast earnings for the following year.

leading P/E ratio = P0 / E1

Where P0 is today's stock price, and E1 is the earnings per share next period.

While using E1 seems to make sense since it accounts for future earnings, using just one earnings forecast may not be able to completely capture the future profitability of the firm/stock.

But as it turns out, it can.

There are different ways of estimating the intrinsic value or "true worth" of a share of stock. I'll get into the basics of stock valuation in a future post, but for now just remember this:

The intrinsic value of a share of stock (or any asset) is the present value of all cash flows it can generate in the future.

Based on this idea, we get one of the simplest models of stock valuation: the Gordon or Dividend Growth Model. This model, which was named after Highly-Regarded Economist and Distinguished Senator, Dick Gordon (Kidding! Just checking if you are still paying attention ;)), makes the following assumptions:

1. Dividends grow at a constant rate, g
2. The investor's required rate of return, k, is greater than g and is also constant (per stock)
3. The investor holds the stock forever

By the magic of math, and given the above assumptions, we can compute for the stock price with

P0 = D1 / (k - g)

If we divide both sides of the equation by E1, we get

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

D1/E1 is the portion of the firm's earnings next year that it will pay out as dividends, or the firm's dividend payout ratio for next year.

Now here's the interesting part. As it turns out, firms typically have constant dividend payout ratios, making D1/E1 easy to estimate (by using the latest payout ratio, for example). So given D1/E1, and estimates for k and g, we can compute for the leading P/E ratio. Since the leading P/E ratio is based these "fundamental" inputs, it is also referred to as the fundamental or justified P/E.

The leading P/E computed using the above approach gives us what the P/E of a stock should be, and we can compare it to other P/E estimates (using the current stock price and forecast earnings, for example). If the forecast P/E is greater than the one using the fundamental approach, then the stock may be too expensive, and cheap if it's the other way around.

But how can we estimate the inputs required by the model? This I will discuss next week. Have a great weekend everyone!