# A More Intuitive Formula for the PEG Ratio

## Abstract

**:**

## 1. Introduction

_{F}.) Lynch (1989) explicitly suggests that it is the expected (future) growth rate that matters. (Henceforth, I will refer to forward PEG ratio as PEG

_{L}). Farina’s PEG ratio connects with low P/E in the past, whereas Lynch’s PEG ratio connects with low forward P/E.

## 2. The Original PEG Formulas

The P/E ratio of any company that’s fairly priced will equal to its growth rate. I’m talking about growth rate of earnings here... If the P/E of Coco-Cola is 15, you’d expect the company to be growing at about 15 percent a year, etc. But if the P/E ratio is less than the growth rate, you may have found yourself a bargain. A company, say, with a growth rate of 12 percent a year (also known as a “12-percent grower”) and a P/E of 6 is a very attractive prospect. On the other hand, a company with growth rate of 6 percent and P/E of 12 is an unattractive prospect and headed for a comedown.(p. 199)

## 3. The New PEG Ratio Formula

_{g}is the geometric growth relative for price and 1 + E

_{g}is the geometric growth relative for earnings growth. The proposed new PEG ratio formula will give us the same implications as the existing PEG ratio formulas, namely:

- If PEG
_{C}is less than 1, the stock is undervalued because price growth has been lagging behind earnings growth, and, therefore, future price growth will outpace earnings growth. - If PEG
_{C}is higher than 1, the stock is overvalued because price growth has been outpacing earnings growth, and, therefore, future price growth should be outpaced by earnings growth. - If PEG
_{C}equals to 1, then the stock is fairly valued as the past earnings and price growth should be the same and will likely be so if the stock continues to be fairly-valued.

## 4. Applications and Analysis

#### 4.1. Synthetic Values

_{F}, PEG

_{L}and PEG

_{C}are the same.

_{F}.

_{C1}× PEG

_{C2}= 1

_{C}

_{1}is the PEG ratio over the last 5 years and PEG

_{C}

_{2}is the PEG ratio for the next 5 years. For PEG

_{C}

_{2}to be at the value of 2, the price over the next 5 years will have to increase by 300%. The usefulness of the new equation is that it allows for any combination of earning and price growth rates, so long as it satisfies the condition that the PEG ratio for the next 5 years is 2. In this example, for a PEG value of 2, the price will have to increase from $14.87 to $59.48, with EPS increasing to $4 if the growth rate assumption remains the same. This gives a P/E ratio of 14.87 and thus a PEG ratio of 1 over a 10-year period. The following table (Table 3) shows the numerical outcomes.

_{C}to the desired level.

_{m}× PEG

_{n}= PEG

_{m+n}

_{m}is the PEG ratio in period m, PEG

_{n}is the PEG ratio in period n, and PEG

_{m+n}is the PEG ratio for the combined (end) period. For example, if the ending PEG ratio is 0.9 and PEG

_{n}is 1.5, then PEG

_{m}has to be 0.6, and, so, an analyst who spotted a stock with a PEG ratio of 1 currently, looking back at the PEG ratio for the last 3- or 5-year period as having PEG ratio of 1.5, can deduce that the stock must have had a PEG ratio of 0.67 over the same time distance in the past (3 or 5 years ago). Note that using Equations (5) and (6), an analyst can feel comfort in recommending a stock with short term PEG near or even above 2, as long as the previous period PEG is near or below 0.5. Trombley (2008) and Schnabel (2009) show that firms with a low cost of equity and a high growth rate can have a PEG ratio above 1. A low cost of equity implies a higher forward growth rate potential. With the stock price growth lagging in previous years, it is only reasonable for the stock price growth to catch up in following period.

_{L}is the unbiased forecast of future growth rate, by the time we reached time n, we would have the backward PEG, which is PEG

_{F}. Thus, we have:

_{C}ratio from time 0 to time T is simply the P/E ratio at time T divided by the P/E ratio in time zero. This can be generalized into any specific time length T. Consider a stock with a P/E ratio of 30, with a stock price of $30 and an EPS of $1. Assuming that the forward EPS growth rate is 20% for the next period (5 years), it would give us a PEG ratio of 1.5. Further, we can assume that the stock price growth rate is lower than the earnings growth at 15%. The following table (Table 6) shows the numerical results:

#### 4.2. Industry Examples

#### 4.2.1. Unusually Large Value for Earnings Growth

_{F}ratio value is 0.63 during that period. The stock price in October of 2019 was $280 a share, implying a P/E ratio of 19.18. The PEG

_{C}ratio in October of 2019 was 1.07. The cumulative EPS growth during that 5-year period was 132%, while the stock price cumulative growth was 289% (LRCX started to pay a dividend in 2017, so this figure will be higher when adjusted for dividends). The stock price was increasing at a rate more than twice the stock price, yet the PEG

_{C}ratio still implies LRCX a value stock (below 1). The main question is whether investors/analyst foresaw the rapid growth rate of LRCX earning? In the fiscal year of 2010, LRCX had an EPS of $2.73. So, the geometric growth rate from the 2010–2015 period was 18%. The company’s stock price was $46 at the end of the fiscal year of 2010, which implies a price growth of 9.4%. The P/E ratio in 2010 was 16.85. With a forward growth rate of 18%, LRCX had a PEG ratio below 1 in 2010. However, by 2014, the PEG ratio dropped to 0.63 due to rapid a EPS growth relative to stock price growth (PEG

_{C}ratio between 2010 and 2014 was 0.65, and the price increased by 150% and EPS by 230%). So, the price increase between 2014 and 2019 was simply the company’s stock price catching up with the EPS growth. From the fiscal year of 2019 to 2021, EPS growth was at about 100%, which was about the same as the price growth ($560 per share), giving us a PEG value of 1. This would imply that the price of LRCX is at most fairly valued. It could go to as high as $1120 a share and still have a PEG below 2.

_{C}ratio of 1, the price has to increase at the same multiple, from $46 a share to $562.78 a share, about double the current price of $280 a share (the first draft was written in November 2019, when LRCX was trading for $280 a share). Even at $562.78 a share, the company’s stock would still be considered a value stock since the PEG

_{C}ratio would still be at 0.94, according to Equation (6). If we take the average of 1 and 2 and a PEG ratio of 1.5, the price could be as high as $844 a share, and the company’s stock would still be considered fairly valued (LRCX has an average stock price of $600 over the 2021–2022 period). This would imply a price growth of about 18 times over 15 years. According to Farina’s formula, the P/E ratio for LRCX has to be in the 100+ range. LRCX never achieved an average P/E above 50 during the last 12 years. According to Lynch’s formula, the P/E ratio has to be below 20 (since the forward growth rate is 18%) for the stock to be considered fair value. Again, LRCX never achieved an average P/E of below 20 over the last 12 years. Therefore, one would conclude that LRCX is an expensive stock according to Lynch’s formula, and that it is an ultra-cheap stock according to Farina’s formula. However, according to the proposed formula, the price of LRCX is considered a fair value between $560 and $1120. The price of LRCX reached above $800 a share by late 2021.

#### 4.2.2. Negative Earnings and Price Growth

_{C}value of 1.15 for XOM. For a company with a negative EPS growth, a PEG ratio above 1 seems expensive. The price for XOM continued to decline to as low as $33 a share by late 2020. With an estimated EPS of $3.36 for the fiscal year of 2019 (reported in the middle of 2020), the resulting PEG for XOM was 0.72, making XOM a value stock by definition. By the beginning of 2022 (before the oil price shock caused by Russia’s invasion of Ukraine), XOM stock price recovered to $80 a share.

## 5. Conclusions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## Notes

1 | This is a minor error. What Farina found was a geometric growth of 100% over a 4-year period. Annually, the growth rate required to achieve 100% over 4 years in only 18.92%. Therefore, the PEG ratio for PDQ is actually a little above 100 (105.71 to be exact). However, his insight is clear. While I derived my formula with geometric growth rates independently (I obtained an electronic copy of the paper containing the original equation from the author in March 2019), it is good to know that the author of the original equation had geometric growth in mind. I also hope that this paper can serve the purpose of properly attributing Mr. Farina (who passed away in May 2022 at the age of 98) as the original creator of the formula. |

2 | I thank Grant Glenn, CFA, CFP, at Noble Wealth Management for this important insight. |

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Period | 0 | 1 | 2 | 3 | 4 | 5 |

Price | 10 | 16.1051 | ||||

EPS | 1 | 1.1 | 1.21 | 1.331 | 1.4641 | 1.61051 |

Period | 0 | 1 | 2 | 3 | 4 | 5 |

Price | 14.87 | 14.87 | ||||

EPS | 1 | 1.1487 | 1.32 | 1.52 | 1.74 | 2.00 |

P/E | 14.87 | 7.435 | ||||

PEG | 1 | 0.5 |

Period | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |

Price | 14.87 | 14.87 | 59.48 | ||||||||

EPS | 1 | 1.15 | 1.32 | 1.52 | 1.74 | 2 | 2.3 | 2.64 | 3.03 | 3.48 | 4.00 |

P/E | 14.87 | 7.435 | 14.87 | ||||||||

EPSG% | 14.87 | 14.87 | 14.87 | ||||||||

PEG | 1 | 0 | 0 | 0 | 0 | 0.5 | 1 |

Period | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |

Price | 14.87 | 44.61 | 59.48 | ||||||||

EPS | 1 | 1.15 | 1.32 | 1.52 | 1.74 | 2 | 2.3 | 2.64 | 3.03 | 3.48 | 4.00 |

P/E | 22.305 | 0 | 0 | 0 | 0 | 22.305 | 14.87 | ||||

EPSG | 14.87 | 14.87 | 14.87 | 14.87 | 14.87 | 14.87 | |||||

PEG | 1.5 | 0 | 0 | 0 | 0 | 1.5 | 1 |

Period | 0 | 1 |

Price | 14.87 | 11.896 |

EPS | 1 | 1.6 |

P/E | 7.435 | |

PEG | 0.5 |

Period | 0 | 1 | 2 | 3 | 4 | 5 |

Price | 30 | 34.5 | 39.675 | 45.62625 | 52.47019 | 60.34072 |

EPS | 1 | 1.2 | 1.44 | 1.728 | 2.0736 | 2.48832 |

PE-0 | 30 | |||||

PE-5 | 24.24958 | |||||

PEG-PE | 0.808319 | |||||

PEG-C | 0.808319 |

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**MDPI and ACS Style**

Chan, L.H. A More Intuitive Formula for the PEG Ratio. *J. Risk Financial Manag.* **2023**, *16*, 214.
https://doi.org/10.3390/jrfm16040214

**AMA Style**

Chan LH. A More Intuitive Formula for the PEG Ratio. *Journal of Risk and Financial Management*. 2023; 16(4):214.
https://doi.org/10.3390/jrfm16040214

**Chicago/Turabian Style**

Chan, Leo H. 2023. "A More Intuitive Formula for the PEG Ratio" *Journal of Risk and Financial Management* 16, no. 4: 214.
https://doi.org/10.3390/jrfm16040214