ABSTRACT:
This methodology for valuing common stocks utilizes unique features that are consistent with economic theory and empirical evidence. The method is based on a model into which fundamental factors such as estimates of the income statement (such as earnings estimates) and balance sheet (tangible book value) are used as inputs, and output can be considered reliable, proportional to the accuracy of the estimated input parameters.
I.Background of the Valuator
In developing the concept behind the valuator we wanted to adhere to the basic philosophy of valuing a financial asset. The intrinsic value of a financial asset is equal to the summation of the present value of all cash flows associated with it in future. This is illustrated below:
where Intrinsic Value represents the summation from period "0" to period "n." CF (sub "t") represents the cash flows at time "t," and k represents the risk-adjusted discount rate (required return).
Another methodology for valuing stocks is the Dividend Discount Model (also known as the Gordon Model). This is illustrated below:
where IVi represents the theoretical intrinsic value for stock "i", D1 represents the current indicated dividend, ki represents the risk-adjusted discount rate (required return) and gi represents the growth rate for stock "i". (The Gordon Model is a special case of [a.] that assumes constant growth of dividends into perpetuity, which is known in mathematics as a Taylor Series.)
The first shortcoming of both the models is that it lends itself to forecasting the future into perpetuity. This can be highly speculative since even minor changes in the growth rate can have a significant effect on the estimate for intrinsic value. Another shortcoming of both models is that they do not take into consideration the balance sheet for valuation purposes. For example, a company which is not economically profitable might have a lower value assigned by the models even though the firm's assets can be liquidated at a higher value. Many times, economically unprofitable firms exist due to management missteps even though the underlying assets have a higher value or the assets can only be replicated at a higher replacement cost.
Additionally the Gordon Model cannot be used for companies that do not currently pay any dividend. In such cases the value of all of the discounted future dividends is zero even though a company might be reinvesting its earnings to grow its business. Clearly there is value in re-investing the earnings for profitable growth. However the mechanics of the Gordon model do not capture this value. Furthermore, this model cannot calculate the intrinsic value for companies where the growth rate (g sub "i") exceeds the required return (k sub "i). This happens in companies that are in the high growth phase for the next five years which eventually slows down at some point of time in the future. In such cases (and where a current dividend exists), some investors will use a rearranged formula for the Gordon Model:
where k'i is an estimated annual return, by using the current price P0 [with the estimated growth rate gi]. Although this lacks an explicit required return, it can be used to calculate a risk-adjusted excess return by subtracting an explicit required return from the estimated annual return. The risk-adjusted excess return is commonly referred to as "alpha."
An alternative valuation technique that has become popular compares a stock's current price ("P") divided by its current earnings per share ("E") (thus P/E ratio, or simply "PE"), with its expected growth rate ("G") of E over the next five years. This is sometimes called a PE to G, or "PEG ratio". The idea is that the lower the ratio the better since an investor is paying a lower valuation (numerator) for every single unit of growth (denominator). The problem with the PEG ratio is that it simply provides an indication of relative valuation (one stock compared to another), but gives no reasonable estimate of the intrinsic value for a stock. Another issue with the PEG ratio is that it does not differentiate between profitable growth and unprofitable growth. Companies sometimes may take on projects that are not positive NPV. Although a zero NPV or a negative NPV project can lead to increase in earnings it does not create shareholder value. Clearly, a company that invests in a positive NPV project creates more value than a company that invests in a zero NPV project even if both companies have the same valuation and growth rate. However the PEG ratio will not distinguish one from the other. Therefore the PEG ratio does not provide a sufficient basis upon which one can make appropriate investment decisions. Furthermore, because the PEG ratio does not explicitly consider risk (and required return), it is not useful for comparing stocks having different risk characteristics.
II. Theoretical Basis for the Valuator
The idea for the Diamond Hill Investment Model ("Valuator") resulted from understanding the limitations of the above models, combined with familiarity with both general economic theory and empirical evidence on various components of such models and concepts.
First, the Valuator utilizes the current price of a stock as a dynamic variable in the model with assumed information content. Second, the valuator incorporates an important component of valuation that is typically ignored in most valuation models, i.e. the tangible book value. The tangible book value is important because it helps determine the ability of the company to fund its growth prospects without needing any external financing. For example, the Gordon model uses earnings growth as one of the inputs without taking into consideration whether the company has the capital to generate that earnings growth. To the degree that accounting statements reflect economic reality, the tangible book value can be also thought of as an estimate of the liquidation value of the company. Hence a company that has no growth prospects or its future earnings are not expected to be economic, then the company is at least worth its book value/liquidation value. The tangible book value can also be thought of as the amount needed to replicate the current asset base that generates the cash flows (also known as replacement value).
Third, the Valuator assumes mean reversion for equity valuations (in this case the adjusted PE ratio which will be explained in detail below). Competition theory suggests that excess returns allowing for growth will be competed away over time. Various studies have shown that with the exception of a few companies, the rest possess a competitive advantage that helps them generate excess returns for a brief period of time (less than 10 years). These excess returns are competed away due to various factors such as low barriers to entry, supplementary products, technological changes, regulation, etc. Often, this is referred to as the "Competitive Advantage Period". As a result of this competition, high valuations assigned to companies generating excess returns revert to the mean eventually as those excess returns revert back to zero. Empirical evidence (Beaver and Morse, 1978) also suggests that the mean reversion process for valuations take place in as few as four years.
The Valuator is a tool that calculates an estimate of intrinsic value of a stock and the expected return. In case of a stock held for a finite time period, the value is equal to the sum of all the future cash flows discounted at a risk adjusted required return, which includes both dividends and the proceeds received when the stock is ultimately sold.
The challenge for the security analyst is estimating these future cash flows and the return investors require to compensate for the inherent risk. The Valuator assumes that the current dividend and earnings grow at a certain rate during the holding period and that the stock is ultimately sold for an estimate of tangible book value plus the adjusted multiple of earnings at the end of the holding period. A required return ki is estimated by the user.
The Valuator then, is a modified form of the dividend discount model with a pre-determined holding period. A preferred implementation due to industry convention and empirical evidence uses a period of five years, and can thus be written mathematically as follows:
where IVi represents the theoretical value for stock "i", Dt defined as dividends received at time(s) "t" over the five years, and P5 representing the price of the stock at the end of year 5.
Estimated annual return (ki) can be solved by substituting P0 for IVi in Equation c. This can be written mathematically as Equation c1.
The estimated P (sub "5") is calculated as the sum of two components as seen above. The two components are the tangible book value and the excess value. The tangible book value at the end of year 5 is calculated by adding the tangible book value at year 0 to the sum of all earnings from year 1 thru 5 and deducting the sum of all dividends from year 1 thru 5. Thus tangible book value for year 5 is calculated by adding all retained earnings for the holding period to the current tangible book value. This can be written mathematically as Equation d.
The second component is called the "excess earnings value". To understand this concept it is essential to understand that the excess earnings value of any company depends on the extent to which the earnings are economic. So for example, if the company earned a return on equity equal to the required rate of return, no excess value is created and the value of the business/ stock would be the tangible book value. However if the company does earn excess returns the excess value would be positive. Another way of thinking about this excess value is that, the higher the tangible book value and the higher the future profitable growth prospects of the company, the higher the excess value will be since the company can profitably grow its business without much need for any external financing either in the form of debt (which increases interest expense) or equity (which leads to dilution in share count) both ultimately lead to lower earnings per share growth.
This excess value is calculated by multiplying the earnings per share at year 5 and the adjusted PE. The earnings per share in year 5 is calculated by growing current earnings E at an annualized rate for five years, resulting in EPS (sub "5") (For cyclical companies, a normalization of earnings is preferred). Next, EPS (sub "5") is multiplied by a terminal adjusted PE ratio (adjusted PE at year 5). This can be written mathematically as equation e.
The adjusted PE5 can be calculated by equation f and g. The adjusted current PE (sub "0" at year 0) is calculated by deducting the tangible book value from the current market price and then dividing the result by current normalized earnings per share. Conceptually the adjusted PE ratio just like the PE ratio is a measure of equity valuation with the main difference being that the adjusted PE ratio measures the excess earnings power of the company. A high adjusted PE equates to high earnings power. The calculation of adjusted current PE(sub "0") can be written mathematically as equation f.
The Valuator is unique in that it incorporates one of the key basic rules of economics. It is that excess returns earned by companies will be competed away over a period of time. In case of the mechanics of the model, this key point is captured in the adjusted PE, which we earlier described as a measure of earnings power. The adjusted PE reverts half way to its long term average of 10 over five years. Hence the terminal adjusted PE is equal to the average of the adjusted current PE and 10 as equation g. The calculation of P(sub "5") can be written mathematically as equation h.
Thus based on the above, the estimate of intrinsic value as per the model takes into consideration important balance sheet aspects of valuation such as the Tangible Book Value, earnings and dividend forecasts for explicit forecast period (the time horizon), required rate of return (considering the risk characteristics of the stock) and a terminal adjusted PE multiple.
III. Application of the Valuator using current examples:
The Valuator provides a framework in which to analyze the valuation of a stock, and allows the analyst flexibility to input earnings and the expected growth rate of those earnings, as well as the necessary risk-adjusted discount rate. In addition, the user estimates the adjusted terminal market P/E, and thus different users with different macro-economic outlooks are accommodated.
The flexibility to overlay individual judgment regarding such issues as translating accounting earnings into economic earnings, incorporating recent developments, and factoring in qualitative information, leads each user to a conclusion based upon one's own scenarios. Given the possibility for imprecision in these estimates, being able to conduct scenario analysis to investigate the sensitivity of the calculated value to the various estimates is also useful.
IV. Examples
Table A summarizes various exemplary data used to compare the intrinsic value of a stock, determined by an embodiment of the present invention, to other methods.
Table A
| Companies | |||
| Parameter | A | B | C |
| Current Price (P0) | $45.94 | $27.77 | $84.04 |
| Tangible Book Value (TBV0) | $11.03 | $10.44 | $0.81 |
| Current EPS (EPS0) | $3.09 | $1.99 | $0.98 |
| Current PE ratio (PE0) | 14.9 | 14.0 | 85.8 |
| Return on Equity | 27.9% | 19.1% | 121% |
| Adjusted PE Ratio (Adjusted PE0 = (P0-TBV0)/ EPS0) | 11.3 | 8.7 | 84.9 |
| Current Dividend | $0.88 | $0.32 | $0 |
| Required Return | 8.0% | 9.0% | 9.0% |
| Estimated Growth | 13.0% | 15.0% | 24.0% |
| Where, in the adjusted PE Ratio, the adjusted terminal market PE assumption is 10 | |||
Example A: Comparison of this valuator with the Gordon Model
Gordon Model (Using equation [b (sub "1") ] results is shown is Table B.
Table B
| Companies | |||
| Parameter | A | B | C |
| For each company, | 14.9% | 16.2% | 24.0% |
| Required return | 8.0% | 9.0% | 9.0% |
| yields alpha | 6.9% | 7.2% | 15.0% |
As can be seen from the results of the Gordon Model, C comes up as the most attractive stock since it has the highest alpha, followed by B and A in that order. This is because the assumptions of constant growth till perpetuity results in a wide variance in estimated returns between C and the other two stocks.
Valuator (Using equations [c1] and [g]) results is shown is Table C.
Table C
| Companies | |||
| Parameter | A | B | C |
| TBV5 | $27.21 | $23.39 | $10.59 |
| EPS5 | $5.69 | $4.00 | $2.87 |
| Adjusted P/E5 | 11.6 | 10.4 | 48.5 |
| P5 | $93.5 | $64.8 | $149.8 |
| Annualized Price Appreciation | 15.3% | 18.5% | 12.3% |
| Annualized Dividend Return | 1.9% | 1.2% | 0.0% |
| Annual Return | 17.2% | 19.6% | 12.3% |
| Required return | 8.0% | 9.0% | 9.0% |
| Alpha | 9.2% | 10.6% | 3.3% |
As per the results above, B seems to be the most attractive stock followed by A and C comes up as least attractive. This is in contrast with the results of the Gordon Model but more reasonable since the Valuator does not extrapolate the growth rate into perpetuity and also because it assumes that excess returns get competed away in the long run.
Table D presents an analysis obtained using Equation [c] of the Valuator.
Table D
| Companies | |||
| Parameter | A | B | C |
| Intrinsic Value ("IV") | $68.71 | $44.02 | $97.38 |
| Current Price / IV | 0.67 | 0.63 | 0.86 |
With the lower ratio of Current Price divided by Intrinsic Value preferable, B is considered more attractive, which is consistent with the alpha calculation.
Example B: Comparison of the Valuator with the PEG ratio
Table E presents an analysis obtained using the PEG model.
Table E
| Companies | |||
| Parameter | A | B | C |
| PE / G (i.e. Price/EPS0/Growth rate) | 1.1 | 0.9 | 3.6 |
The PEG ratio model also suggests similar results as the valuator i.e. B being the most attractive stock followed by A and C being the least attractive. However, the relative attractiveness of A and C compared to B is significantly magnified by the PEG ratio model. This model does not give C enough credit for its unique business model that generates significantly high returns on equity as compared to B or A. Another shortcoming of the PEG model is that it does not explicitly consider a required rate of return/ hurdle rate. Hence of two companies have the same valuation and growth rate but different required return, the PEG ratio model will not differentiate between the two.
V. Holding Period
It will be appreciated, of course, that the DHIM is not limited to a holding period of five years. Equations [c], [c1], and [d] can thus be represented as Equations [c'], [c1'], and [d'] for a generalized holding period of "n" years: Preferably "n" would be chosen in correspondence with the period required for PE mean reversion in a particular industry of interest.
