- CFA Exams
- 2023 Level II
- Topic 5. Equity Valuation
- Learning Module 23. Discounted Dividend Valuation
- Subject 5. Gordon Growth Model and the P/E Ratio

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##### Subject 5. Gordon Growth Model and the P/E Ratio PDF Download

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 P

_{0}= D_{1}/ (r - g) by either last year's or next year's earnings:

- Trailing ratio: P
_{0}/E_{0}= D_{0}(1 + g) / (E_{0}x (r - g)) = (1 - b) (1 + g) / (r - g) - Leading ratio: P
_{0}/E_{1}= D_{1}/ (E_{1}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 = P

_{current year}/E_{current 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 = P

_{current year}/E_{next 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.

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**User Contributed Comments**
5

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 |

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