Based on reader feedback, we are incorporating fair value estimates for our future stock reviews. This is an introductory article to help readers understand the models involved.
The popular models of estimating fair value of a stock include:
DRI valuation using PEG Based Model:
PEG (Price to Earnings to Growth) ratio is a metric introduced by Peter Lynch in his 1989 book One Up on Wall Street. A stock is stated to be fairly valued if that ratio is equal to 1. The ratio as introduced in the book has many limitations:
FV = (GR + (2*DY)) * EPS
FV – Fair Value.
EPS – Earnings per Share (Trailing Twelve Month).
CGR – Current Growth Rate.
DY –Dividend Yield (current year).
Applying the formula to DRI, we get:
FV = (8.77 + (2 * 3.52)) * 3.39 = $53.59
The stock trades at $48.84 which is ~10% below the fair value estimated and so is a Buy.
DRI valuation using Benjamin Graham Model:
This model uses a formula that was first presented in the seminal book on stock investment, “The Intelligent Investor” in 1962 and revised in 1974. It calculates the intrinsic value of a stock using market-related and company specific variables but without using an interest rate factor. As such, the formula is very simple:
FV = (EPS * (8.5 + (2*GR10)) *4.4)/CBY
FV – Fair Value.
EPS – Earnings per Share (Trailing Twelve Month).
GR10 – Projected 7-10 year earnings growth rate.
CBY – Corporate Bond Yield (current yield of AAA corporate bonds).
Applying the formula to DRI, we get:
FV = (3.39 * (8.5 + (2*7))*4.4)/3.99 = $84.11
The stock trades at $48.84 which is well below the fair value estimated and so is a Buy.
One limitation of the model is the dependency on the seven to ten year projected earnings growth rate, which can be hard to accurately predict. In our example, DRI grew earnings at an 8.77% rate in the last 5-years and so we conservatively used a slightly lower rate – as a mid-cap stock, the company has room to grow and there is scope for international expansion as well - so, our estimate is fairly conservative.
DRI valuation using Graham Number Based Model:
Graham Number Based Model is an estimate that indicates the maximum price that a value investor should pay for a particular investment. It is a good general test to identify investments that are selling for a good price. The formula is:
EPS = Earnings Per Share
BVPS = Book Value Per Share
MFV = Maximum Fair Value
MFV = SQRT(22.5 * EPS * BVPS)
Applying the formula to DRI, we get:
MFV = SQRT(22.5 * 3.39 * 13.38) = $32.53.
The stock is trading well above this number and so is a Sell. Although, the formula looks random, there is a method to the madness: the 22.5 comes from the belief that PE ratio should not be over 15 and the price to book ratio should not be over 1.5 (15 * 1.5 = 22.5). The main limitation of the model is that it gives no weightage at all for such fundamentally important characteristics of an investment such as the growth rates.
DRI valuation using Discounted Cash Flow (DCF) Based Model:
DCF model uses estimated future income projections and discounts them to arrive at a fair present value for an investment. For stocks, the income projections can be the free cash flow, earnings per share, or the dividends paid. Discounting requires using a rate that can be earned on an investment in the financial markets with similar risk – weighted average cost of capital (WACC) is a good measure for this rate. The formula is:
FV = FE*(1+GR5)^1/(1+DR)^1 + FE*(1+GR5)^2/(1+DR)^2 +…+ FE*(1+GR5)^n/(1+DR)^n
FV = Fair Value.
FE = Forward Earnings per Share (Next Twelve Months).
GR5 = Projected 5-year earnings growth rate.
DR = Discount Rate (Weighted Average Cost of Capital – WACC).
For most stocks, n is an unknown and so a terminal value is used after the first 5-years of discounting. The most common method to estimate terminal value of stocks is to use the Gordon Growth Model that uses a long-term growth rate for perpetuity. The formula is:
TV = FE*(1+GR5)^5*(1+LGR)/(DR - LGR)
PTV = TV/(1+DR)^5
TV = Terminal Value.
PTV = Present Value of Terminal Value
LGR = Long-term growth rate (perpetuity).
The altered formula is:
FV = FE*(1+GR5)^1/(1+DR)^1 +…+ FE*(1+GR5)^5/(1+DR)^5+ FE*(1+GR5)^5*(1+LGR)/(DR - LGR)*1/(1+GR5)^5
= PV1+PV2+PV3+PV4+PV5+PTV
PV1..5 = Present value of income projections from year 1 through 5.
Applying the formula to DRI, we get:
FV = PV1+PV2+PV3+PV4+PV5+PTV
= 3.88+3.88+3.89+3.89+3.90+67.80
= $87.23
The stock trades at $48.84 which is almost 50% below the fair value estimated and so is a Buy.
DRI valuation using the Dividend Discount Model:
Dividend Discount Model is a conservative variation of the DCF model that is based on the idea that a stock is worth the discounted sum of all its future dividend payments. Discounting requires using a rate that can be earned on an investment in the financial markets with similar risk – weighted average cost of capital (WACC) is a good measure for this rate. Also, the calculation requires a value for the long-term dividend growth rate. As such, the model is suitable for steady dividend paying stocks. The basic formula applicable to dividend paying stocks is:
FV = D/(DR-LGDR)
FV - Fair Value
D - Dividend
DR - Discount Rate
LGDR - Long-term Dividend Growth Rate
Applying the formula to DRI, we get:
FV = 1.72/(0.0786-0.04) = $44.56
The stock trades at $44.56 which is above the fair value estimated and so is not a Buy.
For stocks that pay no dividends, additional assumptions about when a dividend will be initiated, growth rate of such dividends, and discounting back to a present value is required to get a value. A variation of the Dividend Discount Model Formula can be used for the purpose (click for details on applying dividend discount model to growth stocks).
As one would notice, the four models can give very different figures. So, it is important to understand the assumptions made and the likelihood for the assumptions to become reality. The difference between the fair value estimate and the current stock price represents a margin of safety. When making a decision to Buy or Sell a security, these numbers do not give exact answers but can act as data points to consider.
Last Updated: 03/2012.
The popular models of estimating fair value of a stock include:
- PEG Based Model,
- Benjamin Graham Model,
- Graham Number Based Model,
- Discounted Cash Flow Based Model, and
- Dividend Discount Model.
DRI valuation using PEG Based Model:
PEG (Price to Earnings to Growth) ratio is a metric introduced by Peter Lynch in his 1989 book One Up on Wall Street. A stock is stated to be fairly valued if that ratio is equal to 1. The ratio as introduced in the book has many limitations:
- The formula does not make clear what earnings number to use – projected or trailing.
- The formula does not make clear what growth rate to use – expected 1-year, projected 5-year average, etc.
- Dividends are not accounted for.
FV = (GR + (2*DY)) * EPS
FV – Fair Value.
EPS – Earnings per Share (Trailing Twelve Month).
CGR – Current Growth Rate.
DY –Dividend Yield (current year).
Applying the formula to DRI, we get:
FV = (8.77 + (2 * 3.52)) * 3.39 = $53.59
The stock trades at $48.84 which is ~10% below the fair value estimated and so is a Buy.
DRI valuation using Benjamin Graham Model:
This model uses a formula that was first presented in the seminal book on stock investment, “The Intelligent Investor” in 1962 and revised in 1974. It calculates the intrinsic value of a stock using market-related and company specific variables but without using an interest rate factor. As such, the formula is very simple:
FV = (EPS * (8.5 + (2*GR10)) *4.4)/CBY
FV – Fair Value.
EPS – Earnings per Share (Trailing Twelve Month).
GR10 – Projected 7-10 year earnings growth rate.
CBY – Corporate Bond Yield (current yield of AAA corporate bonds).
Applying the formula to DRI, we get:
FV = (3.39 * (8.5 + (2*7))*4.4)/3.99 = $84.11
The stock trades at $48.84 which is well below the fair value estimated and so is a Buy.
One limitation of the model is the dependency on the seven to ten year projected earnings growth rate, which can be hard to accurately predict. In our example, DRI grew earnings at an 8.77% rate in the last 5-years and so we conservatively used a slightly lower rate – as a mid-cap stock, the company has room to grow and there is scope for international expansion as well - so, our estimate is fairly conservative.
DRI valuation using Graham Number Based Model:
Graham Number Based Model is an estimate that indicates the maximum price that a value investor should pay for a particular investment. It is a good general test to identify investments that are selling for a good price. The formula is:
EPS = Earnings Per Share
BVPS = Book Value Per Share
MFV = Maximum Fair Value
MFV = SQRT(22.5 * EPS * BVPS)
Applying the formula to DRI, we get:
MFV = SQRT(22.5 * 3.39 * 13.38) = $32.53.
The stock is trading well above this number and so is a Sell. Although, the formula looks random, there is a method to the madness: the 22.5 comes from the belief that PE ratio should not be over 15 and the price to book ratio should not be over 1.5 (15 * 1.5 = 22.5). The main limitation of the model is that it gives no weightage at all for such fundamentally important characteristics of an investment such as the growth rates.
DRI valuation using Discounted Cash Flow (DCF) Based Model:
DCF model uses estimated future income projections and discounts them to arrive at a fair present value for an investment. For stocks, the income projections can be the free cash flow, earnings per share, or the dividends paid. Discounting requires using a rate that can be earned on an investment in the financial markets with similar risk – weighted average cost of capital (WACC) is a good measure for this rate. The formula is:
FV = FE*(1+GR5)^1/(1+DR)^1 + FE*(1+GR5)^2/(1+DR)^2 +…+ FE*(1+GR5)^n/(1+DR)^n
FV = Fair Value.
FE = Forward Earnings per Share (Next Twelve Months).
GR5 = Projected 5-year earnings growth rate.
DR = Discount Rate (Weighted Average Cost of Capital – WACC).
For most stocks, n is an unknown and so a terminal value is used after the first 5-years of discounting. The most common method to estimate terminal value of stocks is to use the Gordon Growth Model that uses a long-term growth rate for perpetuity. The formula is:
TV = FE*(1+GR5)^5*(1+LGR)/(DR - LGR)
PTV = TV/(1+DR)^5
TV = Terminal Value.
PTV = Present Value of Terminal Value
LGR = Long-term growth rate (perpetuity).
The altered formula is:
FV = FE*(1+GR5)^1/(1+DR)^1 +…+ FE*(1+GR5)^5/(1+DR)^5+ FE*(1+GR5)^5*(1+LGR)/(DR - LGR)*1/(1+GR5)^5
= PV1+PV2+PV3+PV4+PV5+PTV
PV1..5 = Present value of income projections from year 1 through 5.
Applying the formula to DRI, we get:
FV = PV1+PV2+PV3+PV4+PV5+PTV
= 3.88+3.88+3.89+3.89+3.90+67.80
= $87.23
The stock trades at $48.84 which is almost 50% below the fair value estimated and so is a Buy.
DRI valuation using the Dividend Discount Model:
Dividend Discount Model is a conservative variation of the DCF model that is based on the idea that a stock is worth the discounted sum of all its future dividend payments. Discounting requires using a rate that can be earned on an investment in the financial markets with similar risk – weighted average cost of capital (WACC) is a good measure for this rate. Also, the calculation requires a value for the long-term dividend growth rate. As such, the model is suitable for steady dividend paying stocks. The basic formula applicable to dividend paying stocks is:
FV = D/(DR-LGDR)
FV - Fair Value
D - Dividend
DR - Discount Rate
LGDR - Long-term Dividend Growth Rate
Applying the formula to DRI, we get:
FV = 1.72/(0.0786-0.04) = $44.56
The stock trades at $44.56 which is above the fair value estimated and so is not a Buy.
For stocks that pay no dividends, additional assumptions about when a dividend will be initiated, growth rate of such dividends, and discounting back to a present value is required to get a value. A variation of the Dividend Discount Model Formula can be used for the purpose (click for details on applying dividend discount model to growth stocks).
As one would notice, the four models can give very different figures. So, it is important to understand the assumptions made and the likelihood for the assumptions to become reality. The difference between the fair value estimate and the current stock price represents a margin of safety. When making a decision to Buy or Sell a security, these numbers do not give exact answers but can act as data points to consider.
Last Updated: 03/2012.
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