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##### Subject 5. Gordon Growth Model and the P/E Ratio
There are two types of price-to-earnings ratios. Both of them have the current market price in the numerator. A stock's trailing P/E (current P/E) is its current market price divided by the most recent four quarters' EPS. The P/E published in financial newspapers' stock listings is trailing P/E. The leading P/E (forward P/E or prospective P/E) is a stock's current price divided by next year's expected earnings. For companies with rising earnings, the leading P/E will be smaller than the trailing P/E because the denominator in the leading P/E calculation will be larger.

For example, XYZ company reported \$4 earnings per share last year. EPS over the next fiscal year is estimated to be \$6. The current market price of XYZ's stock is \$60. The trailing P/E = 60/4 = 15, and the leading P/E = 60/6 = 10.

The Gordon growth model allows analysts to estimate the fundamentals-based value of P/E ratio. To calculate the fundamentals-based ratios, we assume that markets are efficient (the price of a stock equals its value) and divide the both sides of expression P0 = D1 / (r - g) by either last year's or next year's earnings:

• Trailing ratio: P0/E0 = D0 (1 + g) / (E0 x (r - g)) = (1 - b) (1 + g) / (r - g)
• Leading ratio: P0/E1 = D1 / (E1 x (r - g)) = (1 - b) / (r - g).

where b is the earnings retention (reinvestment) ratio.

There are two uses:

• After we calculate this ratio based on a company's fundamentals, we compare it to the actual ratio (calculated as actual price divided by earnings). If the ratio based on fundamentals exceeds the actual ratio, the stock may be undervalued.
• The fundamentals-based technique can be used to determine the growth rate implied in the actual P/E ratio. If the implied growth rate exceeds the expected rate, the stock may be overvalued, all else equal.

Example

An analyst has gathered the following data to analyze a stock.

• Current stock price: \$20.
• Current period earnings: \$2.
• Expected next period's earnings: \$2.1.
• Stable earnings growth rate to infinity: 6%.
• Stable payout ratio: 55%.
• Beta: 1.2.
• Required rate of return: 12%.

Fundamentals-based Trailing P/E ratio = (1 - b)(1 + g)/(r - g) = 0.55 x (1 + 0.06) / (0.12 - 0.06) = 9.72.

Actual Trailing P/E ratio = Pcurrent year/Ecurrent year = 20/2 = 10.

Fundamentals-based Leading P/E = (1 - b) / (r - g) = 0.55 / (0.12 - 0.06) = 9.17.

Actual Leading P/E = Pcurrent year/Enext year = 20/2.1 = 9.52.

Both trailing and leading P/Es based on fundamentals are lower than the actual P/Es, respectively. This means that the stock may be overvalued.

User Comment
aditya03 in cases where g exceeds r by a huge margin, then how to determine the projected price of the share. eg r-12% & g=80%
Cesarnew Another model should be used.
swt326 Can anyone explain why leading P/E is (1-b)/(r-g) and why trailing P/E is (1-b)(1+g)/(r-g)? I would expect leading to be multiplied by (1+g) since it's the next period earnings.
Andy552 look at the formulas. Trailing uses D0*(1+g), leading uses dividend in year 1 (includes est. growth).
davidt876 swt, using P & E at time=0 is the trailing P/E. both values are the most recent ones we can find. the forward P/E is where P is valued at t=0 (now), and E is estimated one period in the future t=1.

companies that are expected to grow will have lower forward P/E's because P hasn't changed, but we estimated that earning grew by 'g' in the period [E1=E0*(1+g)]. therefore when a company is growing trailing P/E should always be higher than forward P/E (opposite when company is losing market share).

to go from trailing (P0/E0) to forward (P0/E1) - we multiply by 1/(1+g) to grow the earnings in the denominator

don't mind that it's called 'trailing' - in these examples it's technically current because t=0 for both P and E. the reason they call it trailing is that you're usually stuck using the last period's reported earnings so really t=0 for P, but t=-1/12 if you're using last month's reported earnings... and thus you're trailing 